Поиски закономерностей в физическом мире - Шварц К., Гольдфарб Т.

Автор: Шварц К. Гольдфарб Т.
Теги: физика общая физика
Год: 1977
Похожие
Физическая лаборатория
Физический фейерверк. Вопросы и ответы по физике
Физика и физический мир
Избранные труды. Термодинамика. Теория излучения и квантовая теория. Теория относительности. Статьи и речи
Текст
                    A search for order
in the physical universe
Clifford E. Swartz Theodore D. Goldfarb
State University of New York at Stony Brook
W. H. Freeman and Company,
San Francisco

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OCTaBaﬂCb HeBpeILHMblM, oraecm 3TH sapanu B 3eMmo. Heﬁonbmaa oonaCTb BO-
r crepmm 6y11eT TeM caMbIM aaummeHa OT momma.
TpH CToneTHH Hasan Hmero He 613130 HBBeCTHO RH 06 OmIOM H3 yHOMHHyTbIX
311 n o ue
co n .
II H o na
O JIH H a p
mn ao
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b HBe O T
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[‘11 I. ﬂocruqb Bceneuuyro
—
HeraTuBax He 00Bna1111. H.119 113Mepe111111 1*a1111x CMemeHHﬁ 11, TaK11M 06pa30M, 111m
onpeaenenna paccroamm 110 3Be311B1 11e06x01111M0 HCHOJIb3OBaTb MHKpocxon!
l.6. E01111 B OCHOBy Knaccncpnxaunn BbI 1101101111110 uBeT, T0 rpammbl 6y11yr
BaBepHHKa paSMblTbIMH. Bonee Toro, M110111e 05’beKTbl, xax mIe, Tax 11 11e-
)KHBbIe, c TeHeM BpemeH11 HBMBHHIOT CBo1”1 uBeT. Momere 1111 8131, He B11a11a11
B npornnopeqne, eqHTaTB Bce, I110 paCTeT B 3eM11e 111111 113 KyCTax, (bpyKTaMn
111111 0B0111aM11? LI'ro Taxoe 110M11110p? A 6ax11a1xaH?
1.7. E01111 BbI cxameTe, I11‘0 puma—910 HHCMeHT, ncnonbsyeMBIﬂ 111111
1111111111, TO Bame onpeneneHHe He 6y11e1 yIIOBJIeTBopHTEJIIM. E01111 >1<e Bbl cxa-
mere, L1'10 111‘11a—3'ro 1011111111, aaoc'rpeHHBm Kycot1e11 c*ra1111, T0 31:] ynycw're ee
CBOﬁCTBa. Onpeneneune 11011111110 BK1110B KaK Bnemnm‘a BHIL, Tax 11 11p11me11e1111e.
H0110, L110 ec1111 Bbl onpenenme Koxreﬁnb <<Mapr111111>>, yKaaaB TOJIbKO ero co-
(THE, 11 He onmueTe ero HCHOJIbBOBaHHH 11 110c11e11c13111'1, Bame onpeneneHHe 6y11e1‘
HelIOCTaTOQHbIM, a BO3MO)KHO, 11 6830TB€TCTB€HHbIM.
1.8. I‘paBHTauHa—a'ro naoneﬁCTBymmaa c1111a. Ee Be1111q1111a 3aB11c111 or
Macc paCCMHBaeMbIX 06Be111~03 11 OT 06pa11101‘1 Be1111q11HB1 KBanpaTa pacema-
111111 mexmy 3THMPI 06’beKTaMH. Korna ¢yH11aMeHTa11B11b1e qaCTHIIbI neﬁc'rBHTeJIbHo
«KonTaKTmT» (T. e. Haxonmca 11a paCCTOﬂHHH B npenenax 0110110 10'15 M),
ﬁlleIe 01111111 l'IpeBbIHIaIOT I‘paBHTaIIHOHHbIe B 1039 pas! Oanaxo yme 11a pac-
CTOHHHHX, HeMHOI‘O 6011B 1 01 Ma
e
l e1111 1
1
y eb HaO
TH
11 0 H 111
. I
paH T a H
HH a011
11 a Me n M e
a ﬁ e
ﬁ 1 a 11 e

FA. 1. ﬂocruub Bceaermyro
$333
L .
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ﬁpaxruttecxue pa6om ’ 33
__K_ .56. _ __A_ ____ - - +€oJIHezmue
yam Memﬁy Hanpawieﬂamu _. .033 .95 E .5311 ‘5.”5 _ .. — -<- “71/”
Ha Acyaﬂ u m: Axle/manip _________ _ _ . .
4 .
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34 1‘11. 1. ﬂocrpuub BceAeHHyto
MGZKJITY BaHIHM- MBCTOHaXOKneHHeM H TO‘IKOFI, rue COJIHIIe CTOHT HpHMO H811 FOJIO-
BOH. orna
namepemmﬁ BaMH yron 360°
= I
nyra zuuma 3eMHoﬁ oxpymnocm
3A11ALII/I
l. BanTe oOMepu Bamero TeJIa B Me'rpnqecxnx enmmuax:
Pocr CM
Bec (Macca) Kl‘
Tamm CM
. Ileluy sxnnnanemna a Knnomerpax a qac (T. e. B Me'rpnqecxofa cnc'reme)
cxopoc'rb, paBHan 60 MHJIb B qac?
3. Bbl nsMepaeTe cxopocxb B caHTnmeTpax B ceKyHny, CKOJIbKnM (py'raM B
ceKyHny paBHa cxopocna 30 caHTHMeTPOB B ceKyHny?
4. Bona nmee'r nnomocn: 0mm rpaMM Ha Kyénqecxnﬁ caHTHMeTp. LIeMy
paBHa IIJIOTHOCTb 30
B pH
r a H a
y é
qecxn
ﬁ p
5 O e He
a o o
' eM
B
x y

I‘naBa BTopaa
Hpocrble npaBmIa
111m npocmx 113111211111?
BceJIeHHaa CJIPIUJKOM BeJIHKa H CJIHIHKOM CJIO)KHa 11.1151 Toro,
qT06B1 MO}KHO 61.1110 OXBaTHTb ee B ueJIOM. ECJIH MbI XOTHM HOHHTb,
IITO 0Ha c0601'51 HpeIICTaBJIHeT 11 Inc B Heﬁ nponcxonm, npnnerca
HaB c KaKoﬁ-Hnéynb maneHBKoﬁ 11 npocmﬁ ee qacm. ECTe-
CTBeHHO, qTo, ecnn 6151 Mb] CTaJIH HOCTHI‘aTb BceJIeHHy1o maneHB-
KHMH qacmMn, MbI BaTHJIH 651 Ha 3T0 CJIHIHKOM MHOI‘O BpeMeHn.
K eqaCTBIO 11.1111 Hac, Bo BceJIeHHoﬁ Bce HOCTpoeHo 113 Heéonbmoro
qHCJIa KOMHOHEHTOB, KOTOe BsanMonefmTBymT mexmy coéoi’l
Bcero JIHHIb HeMHorBMn cnocoéaMH .11 nonBIOTca Bcero 11111111:
HCCKOJIbKHM 061mm BaKOHaM. OILHaKO BeT HnKaKoﬁ rapaHTun
B TOM, qTo, 113yt111B 3m (pyHnameH'PaJIBHbIe BsauMoneﬁnH, MbI
cpasy CMomeM HpelICTaBHTb KaHy Bo Bceﬁ ee MHOI‘OCTOpOI-I-
HOCTPI H IIOJIHOTe. Ho Bce x1e TaKHe B03MO}KHOCTb 11 Hanemna cyme-
CTByIOT. Bo BCHKOM cnyqae, pasyMHo npennonoB, L1T0 ecnn MbI
He nocmrneM npOCTeﬁmne HBJIeHHﬂ, T0 y Hac He 6y11eT HHKaKoﬁ
Hanexmm nocmqb 11 6011ee caoxmme.
LITOébI 110115115, KaK Mb] ynpomaeM CJIO}KHbIe npoéJIeMBI, pac-
CMOTpHM, KaK MO)KHO oaTB HyTb mapHKa, 6p0111eHHoro B BOS-
11yx. KaK HpaBHJIO, B nepBOM npnéJImKeHBH npennonaram“, qTo
Bosnyx He 0Ka3B1BaeT 3111111111151 Ha mapHK, I110 cnna TmKeHHH
DOCTOHHHal’H I110 BJIHHHHeM BpameHHH 3eMJm MO)KHO upeHeép.
11.1151 MHo B n
a q
T
BHO I H
ee JI
e Be p nJI
K e H H
B e -
3JI
T a T no
n yqe

1‘22. 2. ﬂpocme npaeu/za am npocmx nenenua’
Bb160p upOCTBIx MOBeJIeﬁ mm aHaJmBa He Bcerna HpOCT. B 6H0-
JIOI‘HH HOHbITKH TaKOI‘O pona HaSbIBamTCH HHOI‘IIa «penyKunonnB-
MOM». HeKOToe énonorn yHOTpeémuor 3T0 CJIOBO B upeHeépe-
)KHTBJIbHOM CMbICJle, yTBepmnaH, qTo 3HaHHe neTaJIeﬁ Monexynﬂp-
HbIX npoueCCOB eme He oéecneqHBaeT HOHHMaHHH 6n0JIoeCKoﬁ
CBCTeMBI B ueJIOM. B caMOM Heme, eCJIH uenoe eCTB Heq'ro éonbmee,
c
y Ma
e o
q B T
e
ﬁ m e
c n
anon b u
m ﬁ
BT e
pc H
p e
l T
a B -
I H eTJI
b O
C KI ‘
pa
c em
a , T HT C
M
b I
JIH a HH aT B
m a -
H e m
/
1

2.]. Hoseaeuue oauuouuoeo Te/za
expaH, MbI He CMO)K€M yCTpaHHTb ﬂeﬁCTBHe cmm Tamecm. Cpmy
TmKeCTH HeJlbssI 3a3KpaHHp0BaTB; He cymeCTByeT Taxme cn0c060B
nuotmTB THI‘OTeHHe mm nsMeHmB HanpaBJIeHne ero HEﬁCTBHH.
ECJIH MbI ynaJmMca OT 3eMJm Ha nocraTotmo 60J1Bu10e paCCTOHHHe,
T0 npaBHTauHOHHoe none qTaHeT He3HaeJIBHBIM. OnHaKO, Haxo-
JUICE) B Conneﬁ CHCTeme, MbI Bce paBHo GyneM PICIIbITbIBaTb BJIHB-
Hue Comma, K0T0p0e B CBOIO oqepenb Haxonmca non BosneﬁCTBHeM
CHJIbI THI‘OTBHHH I‘aJIaKTHKH. OlIHaKO Bce >Ke cymBCTByIOT B03M0>K-
HOCTH JIH6O KOMHeHCHpOBaTb THI‘OTeHHe, Jméo npeneépeqb ero nefa-
CTBHeM. 0mm H3 nyTeﬁ KOMHeHca
ﬂ e
CBI ITH
I ‘OT
HH C
O
COT y
T
a HO B K
e
6b e T
a a
110
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0
6 b
K n
o npm -
H e y
y eH
ﬁ T O BaT
H CTH H a H a
npBI e Ha
B pT H a

38 132. 2. Upocrbze npaeu/za 61m npocrbtx neneuud
(DI/11‘. 2.1a. C'rpo6orpaMma Tenemm, xa'rnmeﬁca BnpaBo PI nocreneHHo samennmo-
meﬁ cnoi’i x011. Tenemxa HpelICTaBJIHET coéoﬁ Kycox nepeBa, enJIeHHbIﬁ Ha
qe'rupex Konecnkax OT pOJIHKOB KO H
K B .
a e nm xe e n
JI eH
a e m
anb H a
l e n
a CT e
I a
y a
hI Ba o m
a em nm
e u ne .

2.1. ﬂoaedeuue oduuovmoeo Tent! 39
a
.q. 1,.V.,.,.v.w-.“. .2 . ﬂaky, . Mu.“ . . m-x I,-
{
,xc.ma~mm~4an.mau.-w..~,¢y,.>.....W,M gm... -- . . a
w.-Mm,mm..w.-.cu._ :-.wi‘?_u--r.~vozany-Ava». », -...w.v...-, w “w... v. y‘ {f
,. .NMMMHN ..,. . ~.~.,,-.....v..-:;~.wmv) k Np.
Mew-w .rmwv -.-,.-:-mm..M~w....—.«gymmmm . ...~,....,:~-.- .w. .. .,......V..
‘. 4
(DI/IF. 2.2. CTpo6orpaMma nByx TBebIX mapHKOB, OIIHOBpeMEHHO nanaroumx
co CTOJIa. Oman mapux Haxonnnca Ha T-oépasnoﬁ noncraBKe Ha Kparo CTOJIa,
npyroi‘i Kamncn cnpaBa PI ynapml neﬁ mapnx «B n06». 06a mapnxa none-
TeJIH co CTOJIa BJIeBO, Kammﬁ co CBoeFI ropnsoHTaoﬁ cxopocnﬁo. 3TH cxo-
poem ocraBaJ H O
CTH H
b I H
B T
Opm a a
K ep
mx anbn u exo ocm
pa BHo m po
B
0
p a
T JI H n p
n
OI
H K
OB Ooo
nm p x o a. u a
Hao , a
pnxn p n
o na

r12. 2. ﬂpocme npaeu/ta 5M1 npocrbzx'ne/zeuud
mapHKOB, KOToe 6mm C6p0UIeHbI co CTOJIa B ropnsoHTaJIbHOM
HanpaBJIeHnn. Hpu nanennn maOB CKOpOCTb nx nBHmeHmI BHHB
yBeuBaeTca, HO nx FOPHBOHTaJIbHoe nanmenne nponcxonm c30-
6011HO, n OHPI DBPDKyTCH Kamnbli’i co CBoeﬁ HOCTOHHHoﬁ CKOpOCTbIO,
He PICUbITbIBaH HHKaKHX BOBﬂeﬁCTBI/lﬁ, sa ucxnmHeM He3Havm-
TeJIbHOI‘O TpeHHH o Boanyx.
B o noc
.
.
I
I
M e e I
OHO H a I
Iee eM e
m e H
m Ba x b
lﬁ n 3 a HbI
n
pm e y T
O B p
e m e H
H .
I O
po c
xn m c
I OH O T a
I
b
H o
C o O
T I o ?
Oa b
aeT ca
,
qTo Me
H

C’mpodoc/mnwecm;
.na
%:~ Henodeummlé
cwr
% Wamo/ramepa, amalgam/7M c ym’opeﬂueM
V
V
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1‘11. 2. Hpocme npaau/za 6/111 npocrbtx ﬂexzeuud
Bonpoc 2.4. ECJIK Haxonﬂumﬁca pSmOM c HaMH Benocnnen C‘TOHT
HenomamKHo, MbI l‘OTOBbI HOBepHTb, IITO 0H He HOIIBepl‘aETCH HHKa-
KI/I'M BO3HeﬁCTBHHM, no KpaﬁHeﬁ Mepe B FOpHBOHTaJIbHOM HanpaBJIe-
HKK. HpennonomnM, IITO KTO-TO, CHJIbHO HaaH Ha nenaJm, npo-
e3>KaeT MHMO Hac c HOCTOHHHOI‘Z CKOpOCTbIO 20 KM/q. 03HaqaeT JIH
9T0, qTo Benocunen He nonBepraeTca Bgsneﬁcmmo?
CyIILeCTByeT eme onHa npoénema, CBHSaHHaH c HOBeIIEHHeM H30-
JmpOBaHHoro Tena. ﬂonycmM, qTo MbI CHaIa HaémonaeM OG'bEKT,
Haxommnﬁm B COCTOHHI/II/I n0KosI, Korna ero CKOpOCTb paBHa HyJIIO.
Mbl yTBeaeM, qTo BHeIHHHe Bosneﬁcmnﬂ OTcyTCTByIOT. 3aTeM,
He HpHKacaﬂCb K 06’b€KTy, nona6J1IonaeM 3a HKM, mam M
KO Hr o
HOCT O H H O
’ IK OO
CTbIO
10 KM/q
.
H
o
r K a
b ﬁ K e J
I B
o -
O
HO CT
I
C
O p Tb K
O
Ka a
Hb
I mn o e
na , K o
na H K H a

2.2. Baauuoacdcréue aayx TBA 43
(DI/11‘. 2.4. Ha IlaHHOM CHHMKe, CILBJIHHHOM c nomomblo JIaMHbI-BcnblmKH B Mo-
MeHT ynapa KJIIOIIIKH Ma ronmba no Mﬂlly, xopomo ammo cma'me M. Cnycm
-MI‘HOBeHHe C)KaTbIﬁ Mm; OTCKO‘IHT 0T KJIIOIHKH. IleTaJm Baaumoneﬁcmna B momem
CTOJIKHOBeHHH Ob cnoxmu. Onnako, enenaB Ob npoc'rble OéOéHlBHHH, momuo
oaTb pesyJIbTaTu TaKOI‘O Baanmoneﬁcmna nByx Ten. (Cuumox mo6e3uo npeao-
eras/zen npo¢. Papa/2126014 Sauceprouou us Maccaqycerctcoeo Texuoxzoeuueclcoeo
uncruryra.)
HesnaqHTeJIbHo H MO)K€T paCCMHBaTbCiI KaK H€KOT0paﬂ nonpaBKa
K pemeHmo OCHOBHoﬁ npoéneMbI.
TaKaa np06J1eMa «mayx TBJI» He Bcema HBJIHETCH x0poumM
npnéeHHeM K neﬁ’ICTBHTeocm. xonomqecxoe n-3yHe
TOI‘O, KaKHM 06pa30M 0mm HHﬂHBHﬂyyM BmmeT Ha npyroro, He.B
COCTOHHHH Oé’bﬂCHI/ITB, qTo nponcxonm‘ B Tome, me Kaxmblﬁ HHJIH-
BunyyM oxasbIBaeT BJIHHHHe Ha Bcex OCTaJIIX. ﬂsnmeaue aneKo
jrpOHa B Tenennsnonnoﬁ éxe MO}KHO B n

1‘ ll. 2. Hpocrbte npaeu/za 61m npocrbtx neaenud
A
HeﬁCTBHH JIaoopaTopHBIX yCTpofICTB, HpHMeHHMbI K COJIHuy n ma-
HeTe, K BsanMonefICTBmo CBeTa c a’I‘OMaMH n K 3HaKOMbIM H3 no-
BcenHeBHoﬁ mnsnn upenmeTaM (qmr. 2.4).
BagnMoneﬁcmm 11Byx Ten MOI‘yT xapaKTe'pnsoBaTBca caMOi’i pas-
Hon npononmmenbnocmro, Hatmnaﬂ, HanpnMep, OT Immenb-
HOCTH n060Boro CTOJIKHOBeHHH nByx aBTOMoonJIeﬁ H Konqaﬂ nepno-
IlaMH LLBmKeHHH HJIaHeT no opomaM BOI‘ Comma. B nepBOM
cnyqae Ia BsanMoneﬁCTBnB paBHa HyJIIO no Tex nop, noxa aBTO-
Moomm He COHpHKOCHyTbCH, Bo BTopOM cnyqae cma BsanMoneﬁ-
CTBHH MeHHeTCH B BaBHCHMOCTH 0T paCCTOHHHH Mexmy TeJIaMH, npn-
M H H
T CH o
n p
cM y
a
K H I
JIB H OH e n eBB H
o
Mo me
B a n M
n e CT Bn
ﬂ H a n
p ne, a m e
K a
K C O JIHO
eH ea TM o
me
’I O
I H

2.2. Baauuoaedcmue 63y): Tea
(MAP. 2.5. CTpoéorpaMMa CTOJIKHOBeHHﬂ éonbmnx maOB (K3 nonHKon)
Ha nony. mapHK-MHHIeHb no CTOJIKHOBeHPIﬁ 6bIJI HenonaumeH-K 61m c¢0Torpa-
(impOBaH B pBoeﬁ onHoﬁ noammu npn HECKOJIbKHX BcmKax; B peaynb'ra're
ero Hsoépamenne Ha CHHMKe HMeeT Bun éonbmoro 6enoro HHTHa. llpyroﬁ mapKK,
CTonKHKﬁca c nepBbIM, Kamnca eneBa. I'Iocne CTOJIKHOBeHHH mapHK-MHmeI-Ib
noxamnca Bnepen, a mapHK-cnapsm OTKJIOHKJIca OT cnoero nym BJIeBO.
HapaMH TaKnx 06'beKTOB MO}KHO COSILaTb 1113a mma I‘IpOCT 3
a
m
-
o e ﬁ m
n ,
HC
O I
b y
HH
-
H bI ma
H T
bI
p a
n J
0 Ke
H
I H a o

1‘4. 2. ﬂpocme npaeu/za 61m npocmx neaenud
4
(DI/11‘. 2.6. IIBe napu 6eryHKon 11a Bosnymuoﬁ nonymxe. Hapa 6ery11x013, Haxo-
mmmxca cnena,‘133anM011eﬁCTByeT memny c0601’1, HOCKOJI 1 a e
rn a x e n
n n no
'ro a nnu
ea
IH
HH p
a nonm
e m e
ax, 1
11
0 11
JIHHM e HH n o oa
11 11
0
p au 111 b
n pr n
pr . a
a ey 1
oc
n pa a
Ba n oneﬁCTB e
T
qe ea np y H
e a m o
pa
a
'
r p
u
, y
T H

1
(DI/IF. 2.7a. IIBa aneHuux 6era,- nepnonaqanbuo c'romamnx Henonnnxmo Ha
cepemme Tpexa, pacranxnaaro'rca cma'roﬁ nemny HHMK npyxmnoﬁ.

(DI/ll. 2.7r. Ilsa memnuuux Gerynxa. Berynox c npocmﬁ c'rpeJIKoﬁ (cnpaBa)
BHaqane c'roan Henomanxmo Ha cepemme 'rpexa. Ilpyroﬁ 6eryHox (CTpeJIKa c TO‘i-
Koﬁ) ILBHFaJICﬂ cneBa, H enJIeHHuﬁ Ha HeM marnu'r OTTaJIKHBaJI 1'0
T ao
m e ann
r a e r
y H e M H eH
n B
e yH
K
-
n meb

(DI/II”. 2.7m. BeryHOK c ynBoeHHoﬁ maccoﬁ (oéoanaqen npoc'roﬁ crpenxoﬁ) CTOHJI
HenomHo nocepennne TpeKa. BeryHox c ennnnqnoﬁ maccoﬁ,'n3nraamnﬁca
cneBa, TOJIKHyJI nepauﬁ 6eryH0K BnpaBo n OTCKO‘IHJI c meHbmeﬁ cxopoc'rblo
Hasan. Oépam're BHHMaHHe Ha nKaTop HanpaBJIEI-lﬂﬂ, yCTaHOBJIeHHbIﬁ Ha CTpeJIKe
BToporo 6eryHKa. Hoxa 6eryHOK JIBHI‘aJICH BnpaBo, HHILHKaTOp 6131.71 OTKHHyT Hasan,
KaK pyMbe 3a nneuaMH IOBeKa. Hpn CTOJIKHOBeHHH nxaTop OTKnouaeTca
BnpaBo n npn meHnn BJIeBo 0mm: oxasuBaeTca «3a HJaMH» CTpeJIKH.

50 1‘21. 2. Hpocme npaau/za 61m npocmx na/zeuud
(DI/IF. 2.7K. Berynox c y'rpoennoﬁ maccoﬁ (npoc'raa CTpeJIKa) c'roaJI HenonBo
nocepennue TpeKa. Berynox c ennnnunoﬁ maccoﬁ, nBHraﬁca oneBa, TOJIKByJI
Gerynox c yrpoeBHoﬁ Maccoﬁ BnpaBo u OTCKOQHJI Hasan c menbmeﬁ CKOPOCTbIO.
Kax u npexme, uKaTop BanpaBJIeBmL «3a nnen» c'rpemm 6eryBKa c enn-
Huquoﬁ maccoﬁ yKaauBaeT Basan.
( I I
.
. .
11
. C
' ro
m nonen eB
y xonna o
nx
‘ 6
eryHK B m x yo

2.3. [Ipocme rmaau/za 61m uacmux cayuaee 51
f
TOJIKHyJI e1‘0 qepea npyy. Ilsa onenymumx c1111 11y1
11 p 11
CH Ta HH a
a yx e 1 51x H
H K a
c 01
2
pa nn u e
ﬁ I
11 0 H
a 11110
.
111
.
1
B a
n onﬁ
T B Heon
e T a
a c1
eT
T a JIKBHH M
r nn
o
, e 111 H
51 Ha e
r y
H a
x B oce 311
1 51 e 01
y 111
x e
y H 11 O K
H e qa T
I e
H n
b ,
a

m. 2. Hpocme npaeuna 61m npocmx ﬂaﬂeuud
crutcu dOJLOICHbL ocraearbcn HeuSMBHHbLMLt. Ecnn MbI CMO)K€M pac-
mmBaTb 3TH BaKOHbI, T0 CMO)K€M 3HaeJIbHo ynpoc
on
-
a H H
n o n
n a HC
JI O
K H bI
c
o b
T n
.
‘ ho OCT a e
CHe
n
Me H
I Bo
T a c
H e H
HbI
n 6
e rH K
a
n ?
a 3
M
6
T H
, a
H 6eryHK H e
M e H OT
b Op y p
a s
e mm
B e T
KO H e, e
C

2.3. ﬂpocme npaeu/ta 61m ‘tCICTI-lbtx c/tyttaea
ﬂa paapblea Em Mmym:
M = ?‘ M = I
ﬂame paapuea ED
<——— —>
_ U + U
—Mv + 10 = 0
Tam/4 odpaaaM, M =1
(DI/IF. 2.8. CxeMa, mmocrpnpyromaa me'ron HamepeHna nHepTHoﬁ maccm Hens-
Bec'moro Tena.
meHH

[‘11. 2. ﬂpocme npaeu/za 6m: npocrbtx neAeHud
CKOpOCTH TeJIa Ha HeK
Be
I H ,
a
paT e p
n y om y
o p a MeT eJI a
I M
a T p a
I H
KO
o p O
I OH
0 c e ao
.
T a a pa
en m a K
TO y
I M
bIH a b
I a en H e
pH o M c
c o
, o onp e
e e H m o a
K
Oa , -
I TO K o
na B
a e I
a M acc a
n M

2.3. ﬂpocme npaeu/za 0M uacmbzx cayeaea
surf
Bonpoc 2.9. HpHBellHTe npnmep, Korna capHBIi’i 06BeM llByX
TeJI omnqae'rca 0T cyMMbI HX HHlIHBHllyaJIIX 06’beMOB. HpHBe-
mare aHaJIorntIHbIﬁ Mep mm cnomemm CKopOCTeﬁ.
v.7
J
mee OI
‘ O aK
pam npa
e
r cn
r H JI HB
ﬁ
, 1
.
1 1
OT
O
X y
cne O HH
e H T H TBe
p
m eH B
e o CO
pHH H
IHH
y Ib a ,
T 0T
e p
me HHe B
e Béo n me
ﬁ
' TI
IHH T a HB HTH
«a O
HO

FA. 2. 17 pocrbze npaeu/za 01m npocmx neneuud
JIH60 CBHBPI Mexuly HHepTHoﬁ Maccoﬁ p1 CBOﬁCTBOM ma'repml, Haabll
BaeMbIM rpaBmaImOHHoﬁ Maccoﬁ, KOTOpaH nponopunonaa Becyg
Tena. I'IepBasI BenHa KaKHM-TO 06pa30M CBHBaHa c «Hemenaég
HHeM» TeJIa nsmenmb c3010 CKOpOCTb, BTOpaH—C BOBHCﬁCTBHEM
,npyrnx Ten, ynaneHH O TIaH
H I
Oe a II
ep a
H en nan
Me -
pH T a
n T eH émo en
1
30
p e e u
a
LB K H eMe
I aB
I
S -

2.4. Kuueruuecrcan auepaua
'———
HbIMPI, nonyHbIMH c HOMombIo (bur. 2.7. HepBbIe

1‘11. 2. 17 pocrbte npaeu/za (3/111 ﬂpocrbtx neneuuﬁ
*-
Te111:110, Haqaoe 3Hat1eH11e (M02) 61:11111 paBH1:1 Hy111o. Tax KaK
saTeM 111111 o6o11x 6ery11KOB 3Hat1e111111 (M02) 61:11111 HOJIOXH/ITeJIb-
HbIMId, 01111 He Mo
Ba
M o H
HT o
aTb a
c 11111 3
a e 11
H o 11
a -
I
H H e 11111 H
a M
0
2
He
01 11 c o
x p a
1111 : 11 M
om e
r
nm e 11
0
Ka a Tb H q
o TO T n y
a

2.5. ﬂpuueueuue sarcoma coxpaneuun
'.———
CoxpaHeHHe BeHHbI Ema, paBHoﬁ (1/2Mv2):
1 2.. 1 2 1 2
3 M100 _ ‘2' M101+ 'é' M2v2° (2'2)
HOCKOJI M ,
.
= 2
3
H y paBHeHn aM
I
0 K
e y
I I p
OCT H
T
b
, o
K pT H
m a cya K
0
6 m m
H om e
b a
Ta
xe a
ne m B
ypaBHeH

60 FA. 2. ﬂpocme npaeu/ta 61m npocrbzx neneuua
BoaseneM B KBanpaT ypaBHeHHe (2.8)
vg=vf+4v§+ 40102 (2.10)
n BTeM ypaBHeHHe (2.9)- ns ypaBHEHHH (2.10)'
0 = 203 + 40102.
PasnennM Ha 202:
0 = 02 + 201’
OTCIOIIa nonyqaeM KOHeLIHYIO CKOpOCTb 01:
l
01 = — U2.
KOHeqHaH CKOpOCTh aTaKyromero 6eryHKa paBHa IIOJIOBHHe cxo-
poem 6eryHKa-Mnmenn n HaHpaBJIeHa B upomBononomn
CT -
o y
H O I T
aBH n n yH
BeH H
y0
1 By p aH
HH
e

Oreem Ha eonpocm 61
Chang K BsanMoneﬁCTBmo mayx Ten, nponssozm COOTBeTCTBmee
eILHEHHe mm nonycxaa HeKOTOe npnéJImKeHnH. B naHHoﬁ ma-
Be Mb! paCCMHBaJIH TOJIbKO OIIHOMeIe sanatm o BsanMoneﬁ-
CTBHH nByx TeJI. LIToébl KaK MON/{HO qme Bocnponsnecm yCJIOBpm,
npn KOToX CHCTeMa H3 mayx Ten 611% 6b1 CBoéonHa OT BHeIHHHX
BosneﬁCTBnﬁ, HCHOJIbBOBaJIHCb 6eryHKn Ha Bosnymuoﬁ nonymKe.
Hama uenb cocmana B TOM, ‘IT06bI Haﬁm BenHbI, COXpaHHIOIlIHe
nocne BsanMonefiCTBnH Te me qHCJIOBbIe 3HanH, KOTOe 01m
uMeJm no Hero.
Hpn HﬂeHTHIX 6eryHKax CKOpOCTH coxpaHHnHCb, ecnn yumm-
BaJICH HX 3HaK (nonomnTeJIIﬁ mm 0TpHuaTeJIIﬁ). L{1‘06131 no-
JIb coxpaHmomca BeJmy B cnyqae BsanMoneﬁCTBnH He-
rmen

1'11. 2. Hpocme npaeu/ta 6M npocrbzx naaeuud
B aanpaaneunu caoero KeHHa, onnaxo B momem‘ CTOJIKHOBeHHﬂ 9T0 HanpéBJIe-
Hue HameHaeTca. I'Ioa'romy mm TOI‘O, q‘roébl map Hanan nBHraTbca B HOBOM Ha-
mpaanennn, on nonmen cnerKa aaropmosn'rbca n, wenonaTeo, manner: a
nonepxnocn: crona. OHnHo Taxme, tno nponcxonm HeKOTopoe samenneane
nBHmeHna mapon.
2.6. Mu 1103mm HpHIIHC8Tb cxopocw annexe, omeqatoumﬁ ee HaHpaBJIeHHe.
C maTemaTHﬁecxoﬁ Totnm 3peHHH T
ao m
I H
M e
H
OM n B m eH H
K op OCT
b , a
na n e
H o
p pa no m
o m a B
a bn onom nﬁ
o
ﬁa cx o om
,
a n p
a
ne a H y O
J e o ,
0
T p n
a Te
I H o
.
'
o

ﬂpaxruttecrcue paéom 63
YpaBHeHHe coxpaHeHHa Eu“:
1 l 1
(3) <2) 03 = (3) (2)0? + (3—) (1103- (2.12)
HepennmeM 3TH ypaBHeHHa B BHIIe
200 = 201 + 02,
203 = 20? + 03 (2.14)
H peumM ypaBHeHHe (2.13) omocmenbuo vz:
02=200— 201»
BosaeneM nocnennee ypaBHeHne B Knanparz
a; = 403 + 40? — 80001 (2.16)
n HOJICTaBHM a; B ypannenne (2.14):
203 = 20? + 403 + 40? — 8000]. (2.17)
PaanennM Ha 2 14 06361114111411! coorne'rc'rnyxomne menu:
2 2 _
3311— 40001 + 00 —- 0. (2.18)
PemnM 3T0 KnanpaHoe ypaBHeHHe 0THOCHTeJIbHO vi:
400 i 4/1603 — 1203 400 :1: 200
6 6
l
01= 00 HJIH '5' 00.
I'Ionc'raBJma 3TH Benaqnnbx B ypaBHeHne (2.13), HaxonuM 02:
02 =2vo— 20, mm 02 =2vo - 2 00) =% 00.
mm 02=2vo-—2(vo)=0.
~I'IPAKTI/I‘IECKI/IE PABOTbI
OCHOBHHC nanume, HCHOJIbSOBaHHbIe B 37011 I‘JIaBe, Momno nonyqn'rb, 06pa‘
mailer: K (pororpacpnam (par. 2.7, BbIIIOJIHeHHbIM c Bucoxofi TOQHOCTBIO. Cnenyn
yxaaaHHaM, HpHBeneHHHM Ha CTp. 62, BB! momeTe nponaaecm Bce namepenna
HenocpencmeHHo no 9mm (po'rorpacpmm. OnHaKo 6131110 651 HaMHOI‘O nerqe HOHHTI)
annenna, earn 651 momro 6mm yanneTb, KaK onn B neﬁcrnmenbnocm nponcxo-
Mr. Benn BbI pacnonaraeTe BoanyIM Tpexom PI Gerynxamu, T0 paccuorpenume
anneuna nerxo Bocnponsaecm, no Kpaﬁneﬁ Mepe KaTBeHHo. HonHTaﬁT
n
o B T
pT b
a m b
lﬁ H a
xne p H e
HT O
, pe

64 1‘11. 2. 17,006
n ae u
/
a
6
m n o rb x
6
1 m
m? T o T pe x
I Op H 30
HaIe Hn
B e n
n n e H
qo
l a
JI
e HHe Boan xa
O Ta TO
m T
I
O , To
b
I ne p a
r
b e
r y
H KH na m
e ca o
n a p
m nb
m a
Ta M
n Ha o
e
, n
cr n e

Baaaqu
HaXOJIHLHHMCﬂ B COCTOﬂHHH noxoa. Macca Tena paBHa macce Tena B. Home
CTOJIKHOBeHPIH CKOpOCTb Tena A paBHa cxopoc'm mm B, HOCKOJI
O H
H
CJIHI H b
.
.
T o A
,
u an
y
m
eao CK
p O T b
lO
0

I‘JIaBa Tpe'rba
BBaHMOBBP’ICTBHB
B ﬂByMepHOM HpOCTpaHCTBe
33K0H0Mepnocm CTOJIKHOBeHl/Iﬁ, KOTOe MbI yCTaHOBHJm B npe-
nbmymeﬁ I‘JIaBe, MeHnMBI numb B OI‘paHHHOﬁ 06JIaCTH. He-
COMHeHHO, BsanMOBBBCTBBH nByx TeJI HBJIHIOTCH HpOCTbIMPI B3aHMO-
nefICTBnHMB H COCTaBJImOT OCHOBy Hamero nonnmamm (pHBHIIeCKoro
MHpa. OﬂHaKO naJIeKO He Bcema BéanMoneﬁue npoucxonm TOJIb-
KO BlIOJIb npaMOﬁ JIPIHHPI. B HaCToameﬁ maBe MbI np0BepnM, Ha-
CKOJIbKO nonesnbl Baum onpeneJIeHHH HMHyJIbca H KHHeTCKOfI
SHepFHH B CJIyx Bsanmoneﬁcmnﬁ B llByMepHOM np00TpaHCTBe.
BmeCTo aHaJIHBa CTOJIKHOBeHHﬁ, BHBaHHbIX K onnoﬁ JIPIHHH, Mb]
HpeIIOCTaBHM BO3MO>KHOCTb CTaJIKHBaIOHLHMCH TeJIaM 0306011110 11814-
I‘a’I‘bCH B IIJIOCKOCTH.
HaM BHOBb HOTpe6yIOTCH SKCHepHMeHTaJIIe yCTpOﬁCTBa, K0-
Toe l'IOBBOJIHIOT yCTpaHHTb mm KOMHeHCHpOBaTb CPI

1'4. 3. Bsaumoaedcreun 3 aeymepuou npocrpancree 67
(DI/ll. 3.1.
He OKasbIBaﬂ BJIHHHHH Ha Bsanmoneﬁcmne mapuxoa, THI‘OTeHHe B
Ila-HHOM cnyqae HpeLIOCTaBJISIeT B Hame pacnoeHe yno6H31
cnocoé OTCI-IeTa Bpemenn.
B np o
c .
.
CT JI KH e
KaK e
J m
o e JI
O o
T
OIH n n
l n e

FA. 3. Baauuoaedcmuﬂ a asymepnou npocrpancrae
HpOXOIIHMbIe TeJIOM I‘OpH3OHTaJIIe OTpe3KH. rOpI/I3OHTaJIbHaﬂ CKO-
pOCTb vrop Kaxmoro n3 maOB paBHa omomenmo lnpoﬁneHHoro
paCCTOBHHB no ropnsomanu Ax K BpeMeHH At, KOTopOe sao
Ha ero npoxoxmenne n Koropoe BCTB He qTo BHoe, KaK BpEMﬂ nanenna:
vmp = Ax/At. BpeMa nanelmm At OIIHHaKOBO 1mm oéonx mapn-
KOB. ECJm BaKOHbI COXpaHeHHB, nonyHBIe HaMH mm onHomep-
HOI‘O HpOCTpaHCTBa, OCTaIOTCSI CHpaBellJIHBbIMH n sneer), TO MbI,otIe-
Bmmo, IIOJI}KHbI nonb
M00: M01 + M02
1 l 1
'3 MU? + 7MU2.
CKOpOCTb vo aTaKyromero mapHKa nepen CTOJIKHOBeHHeM onpene-
JIBeTCB npn CBoéonHOM (6e3 CTOJIKHOBeHHB) CKaTbIBaHHH mapHKa
c TpeKa. IIJIB yLLOGCTBa 0603Ha C K p
O CTb aa
K
me
r
oma H an c e
T OJI K HOeH B
0
1
aC KOpOCT m pH
a
M ne n
0
.
B n o c
3 .
H O Be p
B e am
Ia H I e

FA. 3. Bsauuoaedcreuﬂ e aeyuepuom npocrpancree
(DI/IF. 3.2. CTOJIKHOBeHHe mapuxon Ha KpOMKe c'rona. MeCTa HX naneHHa OTMe-
qaro'rca Ha nemameﬁ Ha nony 6ymare, nol'roﬁ JIHCTOM Konnponanbnoﬁ 6yMarH.
HanpaBneHHe JIHHHH, HBJImomeﬁca npononmeHHeM TpeKa, H camaa Kpaﬁmm Toa
Ha sroﬁ JIHHHH onpenenmoTca, KOI‘JIa aTaKymmnﬁ mapnx CKaTbIBaeTCﬂ 6e3 CTOJIK-
HoneHHa.
CymeCTByeT onHa, oneHb cneumpnqecxaa, oc06eHHocrb CTOJIKHO-
BeHHH Ime

1‘11. 3. Bsauuoaedcreun 6 deymepuou npocrpaucree
fopuaoymanmuﬁ cwdaiﬂué ﬂpadee
amaxyloweao Luapulra. ﬂﬂuﬂa eao
fopwanmubmn‘z' npadea amalry/aweaa / Pompmwmmm Uo
mapuzra. Eco imam nponapuuaymwa u, cacmawmowu 8 MW
Haﬂpllaﬂé’ﬂwl, npanopquayuwax v;
Cocmamxwmx a ﬂpﬂMOM v
mammalian, ﬂp0ﬂ0pllUOHM6/‘ﬂzﬂ a, fopuJa/Imaﬂwuu npoo’ea tad/num-
Mmaemz. 12mm: e20 npanopauoHaJ/wa vz
Cocmamxromax a ﬂqpneﬂé’ulry/mpﬂam Cocmaa/mouzaa 3 nepnexlﬁwrylmpﬁam
Hanpaar/eﬂuu, nponapuuomﬂmaﬂ U, Han/703179111111, nponopuuoﬂaﬂwax Dz
(IMF. 3.3. I‘eomeTpnn CTOJIKHOBBHHH nByx maOB. (Dax'mqecxaa mmua npoéera
Kaxmoro mapHKa mome'r Gbl'l‘b pasnomena Ha coc'raBnmomHe B HpﬂMOM u nep-
nennnxynapnom HaHpaBJIeI-IHHX.
nByx TeJI HMeeT MeCTO HeKOTOpaﬂ ManosameTHaH ne¢opMauHm B pe-
3yJIBTaTe qero TepHeTCH qaCTB KHHeeCKoﬁ 3Hepmn. MbI HsM
STOT npouecc B m. 6.
cymeCTByIOT npyrne ynpyrne CTOJIKHOBBHHH, CBoéoIe OT Tpe-
HPIH n TBrOTeHHB,—3To Bsanmoneﬁcmna cy6aT0MH
qa cuH
e
-
ob m ea
c
a n
Ta xe a m
bl H p JIT a
O
s a T
O Ib K
O O K e p e
M , T
one c m
e H I
O T HHH
e
yne aeT K
a a b
C
. o H
o

FA. 3. Baaumoaedcreun 6 deyuepnom npocrpaucme 71
.0
O
I
90. 4399.’ ‘3021‘!’
‘v
(DIKII‘. 3.4. Tpn cnyqaa cxonbsamnx CTonKHoBeHHﬁ KneHHHx mapuKOB. Heaa-
BHCHMO 01' mm, Ha KaKoﬁ yron 0T nepBonaqaoro HanpaBJIenna OTKJIOHﬂeTCH
a'raKyloumﬁ mapux, yron mexmy JIHHMHMH, coennnmomnmn meC'ra OCTaHOBOK
maa-MHmeHH PI aTaKyromero mapnxa c Tollxoﬁ nx CTOJIKHOBeHPIiI, Bcerna
paBeH 90°. 3T0 caMbIﬁ Tblﬁ nKaTop Toro, 651.110 Jm CTonKHOBeHne ynpyrHM
H [napalm HneHTHqHuMB.
“—
—’—‘.‘
.--————~-
I
I
————-———-.Q
gr
Ha (1)0Torpacppm, nonyHoﬁ B KOHneHcauHOHHoﬁ KaMepe
(char. 3.5a), aJleKTpOH, nBumyumiiCH oneBa, CTOJIKHyJICH c 3JIeKTpO-
HOM OllI-IOI‘O us aTOMOB rasa. SneKTpOH-Mnmenb OTOpBaJICH H yJIe-
TeJI, OCTaBJIHH CBoﬁ COGCTBeHHBIﬁ cnen, a aTaKumﬁ 3JIeKTp0H 0T-
CKoImJI B npM HaUpaBJIeHHH. HpOC'I‘OI‘O cnocooa namepenna HM-
nyJIbca Kamnoro n3 aneOHOB no sToﬁ (pororpacpnn He cymeCTByeT
(xom B npyrnx 3KcnepHMeHTaJIBHBIx yCJIOB
30 Bo
M on o
). 0
6 p 'T
eBH a H e OIHa
KO
q T o
yro Me
xm y
B y
M
ﬂ
KO e H
BI H p a e
To p H
H a e H

(DI/IF. 3.58. Penxnﬁ CHHMOK CTOJIKHOBeHHH anex'rpona 'c snex'rponom. Bénuan
Konnencannonnoﬁ Kamepu c ansxnm llaBJIeI-IHEM 651.11 yCTaHOBJIeH nc'rotmnx ramma-
.nyqeﬁ. CaMH ramma-nyqn He OCTaBJIHIOT cnenon, H0 onu BuénBalo'r H3 CTeHOK
xamepu n rasa MHOI‘O anex'rponoa. B IlaHHOM cnyqae 0mm n3 snex'rponon, npo-
.ne'reB qac'rb cBoero ny’rn B Kamepe CBO6OJIHO, npe'repneJI 3aTeM cxonbsamee
CTOJIKHOBeHHe c anex'rponom omioﬁ H3 MOJIeKyJI rasa. Hocxonbxy CTOJIKHYBHJHeCﬂ
qac'rnnu HMEJIH onnnaxonme maccu, yron memny nx nocnenyromnmn TpaeK'ro-
pHHMH COCTaBJmeT 90°. TpaeK'ropmi aneKTponon HCKpHBJIeHbI, Tax xaK anex-
'rponu oénanaio'r MaJIbIM nMnyJIbcom n JICI‘KO paccenBaloTca monexynaMH, OKOJIO
Ko'ropux om: npoxona'r.
7’ {ammo}; w
$3}
'64 ﬂpamm
-
(DI/IF. 3.56. Hpo'ron, npone'ralomnﬁ qepea Konnencaunonnyro Kamepy, aaHOJIHeHH
B O I
OO IO ,
TJ

<bI/Il. 3.513. l'Ipo'rou-npo'ronuoe pacceanne n‘cnyqae Ob Bucoxoﬁ auepmn.
Ha STOM CHHMKe, cneJIaHHOM B nyaupbxonofi Kamepe, sacpnxcnpoaaHo CTOJIKHOBe‘
Hue npOTona, Hmeromero sneprmo B Tpn MHJIJIHaa 3JIeKTpOHBOJIbT, c HILpOM
a'roma nonopona, HaXOILHUIHMCﬁ B cocmanun noxoa. 3a cueT peJmTHBHCTCKoro
adacpex'ra macca 60M63pnnpylomero nporona CTaJIa.B qe'rbtpe pa3a Gonbme maccm
HenonBHmHoro nporona. B pesyaTe yron CTOJIKHOBeHHﬂ oxasanca menbme 90°
(p—npOTon). (C mo6e3uoeo paspezuenun tcxeﬁaeuctcoa' Haquona/tbuod na-
6opaTopuu, Anron, Halo-Home.)
JIEHPIeM TaKOI‘O peJmTHBHCTCKoro yBeJIHHH maccm M0>KeT CJIy)KI/1Tb
CHPIMOK, onenaHHbIﬁ c HOMombIo nysblpbKOBoﬁ KaMe. Mon mexmy
TpaeK’I‘OpHHMH HpOTOHOB He paBeH 90° H COOTBeTCTByET cronxnoge-
HHIO Gonee Tamenoﬁ qaCTHubl c 60JIee .nerKoﬁ.
Tenepb MbI 110131 HpOBepHTb CHpaBelIJIHBOCTb saxonoa coxpa-
Henna HMIIyJIbca Pl KnHeTCKoﬁ aneprnn B 603% oémnx cnyqanx
CTonKHOBeHHﬁ HenneHTHx Ten B nByMepHOM HpOCTpaHCTBe. ﬂan
CJIy H

1‘ A. 3. Baauuoaedcreun 3 aayuepnou npocrpaucrae
3038“: 60.11% nerxnﬁ ma. B STOM cnyqae 063 maa 6yny'r
IlBHl‘aTbCﬂ BI'IBPBII. ECJIH aTaKumﬁ mapnx Heme mapuKa-MHmeHn,
OH momeT O'I‘CKOII'HTb Hasan n 3aKaTHTbrCH 06paTHo Ha TpeK. KaKHM-
JIH60 nyTeM Haﬁnme coomomenne Macc mayx mapHKOB. 3T0 MO}K-
HO cnena'rb, H3MepHB OTHOCHTeJIIe cxopocm nocne npﬂmoro
CTOJIKHOBeHHH Mexmy TmKeM n nerKnM mapHKaMH. AHaJms Ta-
Koﬁ cmyaunn HpPIBOlI-HTCH B Konue HaCTomn'ei’I I‘JIaBbI (CM. CTp. 92).
TaM noxasaHo, qTo omomenne CKopOCTeﬁ nocne HpHMOI‘O ynpyroro
CTOJIKHOBCHHH TeJIa Maccoﬁ M1 c TeJIOM Maccoﬁ M2 onpenenaeTca
daopmynoﬁ
&__1_(1_&)____M1—M2
02 — 2 M1 _ 2M1 '
Ha (par. 3.6a cxemamqecxn HpeﬂCTaBJIEHO CTOJIKHOBeHPIe nByx
TeJI. Cpa3y ammo, qTo yron Mexmy TpaeKTopHHMH nocne ynapa He
paBeH 90°. Hocxonbxy CTOJIKHCb TBepe mapmm, CTOJIKHOBeHne
1190 6bITb ynpyrnM. Toma nonyHbm pesyaT 03HaqaeT,
q'ro Maccm mapnxoa HeonnHaKOBbI. IleﬁCTBmeJIbHo, B llaHHOM
KOHT'HOM cnyqae Macca aTaKyromero mapnxa 6b1JIa same 6031:-
me Maccm mapuKa-MnmeHH. OépaTme BHHMaHHe Ha T0, qTo Ha-
IbHaH CKOpOCTb mamxemm B HpHMOM HanpaBneHnn He paBHa
apn'cpmemqecxoﬁ cyMMe mayx KoHelx cxopocreﬁ B TOM me Ha-
npaBneHnH; nepneHnnKymIe cxopocm uocne CTOJIKHOBeI-IHH Tax-
me He paBHbI Memny coéoﬁ. CoxpaHH-eTca He cxopocrb, a umnynbc.
Mbl 110.71% H
3
6 a
x a
be
K
O O
CTH
a H MI
JI IB H pH O
n n
e ne nn

FA. 3. Baauuoaeﬁ’creug e aeyuepuou npocrpaucrae 75
(DI/IF. 3.6a. HpencraBneHHue B macmTaée nannue.
nonyHue npn CTOJIKHOBBHHH a'raxylomero mapnxa
c maccoﬁ, paBHoﬁ IIBYM enuaM, n maa-Mnmeuu
c maccoﬁ, paBnoﬁ elmmme. 06pa'm're Buumauue Ha
'ro, qTo yron 01002 He paBeH 90° H nepnennnxynap-
Hue cxopocm He Komnep
n p
yr p
r a
.
C o -
OT
b ma a -
MHmeH H
0
2
p a
x
m e
c n o b ea
a -
o c oo
c m
0 aT a
y mm e ro
a p na

1‘11. 3. Baaumoaedcmua 6 aeyuepuou npo

8.]. Hexoropbte npuuenenuﬂ sarcoma coxpanenun - 7'9
‘
H0812)! mpaelrmopux
name Bapuea
Ir
/ I
’
/ ' x
X
I
l/ V
I / ‘4
Mumemoe npoﬁomrceyue Haqaﬂaﬁoii
mpae/rmapzzu 60 (3

1‘11. 3. Baauuodedereun a daymepuom npocrpaucme
(DI/IF. 3.11. CHHMOK, nonyqenuuﬁ B nysupbxonoﬁ Kamepe. 31x
o 'r p u
ae
JIH
sa a
e n ﬁ
n m
e
son p a nn

870 M35 7:” + 30* W4» A9 7+ 60
l 6!}
L* 17” + Y?
in” 10 +
(DI/IF. 3.12. CHnMOK, nonyqennuﬁ B nyaupbxonoﬁ xamepe. OTpHIIaTeJIbHO sapa-
meHHuﬁ ﬂ-Meaon CTOJIKHYJICH c anpom aroma nonopona. (KaMepa 6mm sanon-
HeHa )KHILKHM nonoponom.) B pesyJIbTa're CTOJIKHOBeHHﬂ odpasonanncs nae Hei-
Tpanbnue qac'rnnu. Hocxonbxy nmnynbc coxparme'rcn, 01m nnmxy'rca B odmeM
B TOM )Ke HanpaBJIeHnn, two a onHuﬁ meson. Hpoﬁna Hedonbmoe paccroaHne,
onHa H3 HeﬁTpaJIbHux qacmu (A0) pacnanacr: Ha nonoxcm'enbno sapameunuﬁ
nporon H OTpHnaTeo sapamennuﬁ meson. ra HeﬁTpaJIbHaa qacmua (6°)
c'ronKHyJIaCb c HILpOM nonopona n TOJIKHyJIa ero Bnepen. Caua B°-qacmna 0T-
cxotmma Haaan, no'repsm éonbmyxo qac'rb caoeﬁ Knnemqecxoﬁ aneprnn, nocne
qero pacnaJIaCb Ha 113a MesoHa. (C mo6e3uoeo paapemenun tcxedeeucxod
uaquonaawoﬁ aa6oparopuu, Anrou, Hora-Home.)

3.1. HeKOTOpble npuuenenuﬂ sarcouoa coxpaueuun
ﬂpyroﬁ T1111 B3anM011e1’10TBm1 qacmu HpellCTaBJIeH Ha (pm: 3.12.
OTpHuaTeJIIe HH-Me3OHbI HpOCTpeJIHBaJIHCb qepe3 rly3b1pbKOByIO
KaMepy, BarlOJIHeHHyIO B0110p0110M. OILHH 113 MeSOHOB 0011311 B ﬁnpo
011H0r0 113 aTOMOB B0110p011a, B UpOTOH, 11, IIO-BHILHMOMy, 11p00T0
OCTaHOBHJICH. H0 Hac yme He 11p0Be11e1ub! onnblﬁ HMrIyJIbC 1111-
Me3011a nonmen rue-To HpOHBHTbCﬂ. LIyT_B nanbme Bnepenn B TOM
)Ke HanpaBneHBB éepyT Halo KaK 6B1 113 HHOTKa liBe Ila
c enB
B
e
1
0 M O KH
O
é b
H HH
Tb
u pe non omn
B 1
T O
p H a T eJIb
H
s p
am nn m
ﬁ n
-meso
C O JI
H J IH
nno n
r
e n n o a
eHH B MH
p OTO H O
11
0 p 30 B
a I 1 11 1
m He
KO IB
O e

84 1‘ A. 3. Baaumoaez‘icreun e aaymepuom npocrpaucme
(DI/IF. 3.13. I'Ionyqenne napu enexrponon c IIOMOLLIbIO raMma-nyqeﬁ Bucoxoﬁ aHep-
mm. (C mo6e3uoeo paspewenun xxeﬁeeucrcod Haquoua/zbuoﬁ .aa60pa2‘0puu,
Anron, Halo-Home.)
OllHOM HanpaBJIeHnn (no qacosoﬁ c'rpeJIKe, c Hameﬁ Totnm speHna),
a nonommenbno sapameHHbIﬁ nosmpon mamxe'rca no cnnpann B
I'IpOTHBOl'IOJIOMHOM HanpaBJIeHHH (upomB qaCOBoﬁ CTpeJIKH). B NI. 7
MbI paCCMOTpHM HeKOToe npoGJIeMbl npeBpameHna aneprnn B
M'accy. B ,ZlaHHOM cnyqae paCCMOTpHM cmyaumo TOJIbKO c Totum
spenna coxpaHeHHH HMHyJIbca. PeHTreHOBCKue JI—sro 131m
SJIBKTpOMaI‘HHTHOPO HsnyHH, aHaJIororo CBeTOBOMy, H0
uMeIomero 3HaqHTeJIbHo 60J1ee BbICOKyIO aneprmo. ECTeCTBeHHO, qTo
peHTreHOBCKHﬁ KBaHT oénanae'r nMnyOM, qaCTb KOTOpOI‘O 0H ne-
penaeT sneKTpOHHoﬁ nape.
Hama (popmyna ILJIH nmnynbca Mv ﬂBJIHeTCﬂ TOJIbKO npnénnme-
HHeM, KOTopoe cnpaBenJmBo JIHIIIb npn He6onbmnx cxopocmx.
B 60JIbIHHHCTBe CJIytIaeB HaM He Hymno 6€CHOKOHTBCH o TotIHoﬁ
(popmyne, ecnn TOJIbKO cxopocn, He 0b 6JIH3Ka K cxopocm CBe-
Ta. HeKOTOe cy6aT0MHb1e qacmum MOI‘yT IlBPII‘aTbCH TOJIbKO co
CKOpOCTbIO CBeTa. I/Ix HMI’IbC paBeH E/c, me E—sneprna 3THX
qacmu, a c—cxopocrb CBeTa. 3T0 Bblpamenne nosaomeT yc-
nemHo upencxasbIBaTb HMI‘IyJIbC peH-Tl‘eHOBCKHX KBaHTOB n Hefn-
o.

3.2. Eduuuubt uamepenud u ae/mtmubt 85
IIJIH MHomx cnyqaeB HMHyJIbC HBJIHeTCH éonee (pyHnaMeHTaJIb-
Hoﬁ Bennqunoﬁ, M
ac a.
I
a c
‘ o u o e
eo c pH
CBe HH H
3 e pm H
MI I
y I bC
a c m
u l
,
eeM
a c . H
n p M p
, a nny
c m
:

86 1‘22. 3. Baaumoaedcreun a aeymepuom npocrpancrae
(DI/IF. 3.14. OCHOBHHB meTpnqecxne ellPIHHIIbI COUOCTaBHMbI c paaMepaMn IIeJIo-
BeKa. OllHaKO B Kamoﬁ odnacm BuénpamTca Taxne elIHHHIIbI, KOTopBIe ynoéuu
mm BHHOJIHBHHSI nmenno amx pa60T. Hanpnmep, B nonnrpadmn ocaonnaa elm-
Hnua lIJIHHhI HaaBIBae'rca nyHKTOM. 0mm nyHKT COCTaBJIﬂeT 1/72 moﬁMa, T. e.
oxono 0.35 MM. B anepnoﬁ (pnsnxe pacnpOCTpaHeBHoﬁ enmmueﬁ JIJIHHbI BBJmeTcn
- 5
(pepMH; ona paBHa 1-10 M. B oéonx cnyqaax nonnemamne HaMepeHmo Be-
Jmtmnu HBJIHIOTCH Heéonbmumu KpaTHbIMH smx ennann.
HomepmHBaTB Haéopbl 3TaJ'IOHOB. B Konue 1800-x I‘OllOB 6BIJI nony-
c n e
u
an n u
ﬁ CH JI a B
l l I aT
IHbI n p
n mn KT
pIO6 m HI
O TB I e bl
HO BI
e Ta
IH I ma cI n
I JI
H I
OH
b
6 b
I JI
I T ae

8.2. Eauuuqm uauepenud u emu-mum
Bonpoc 3.11. ECJIH 6m cyTKn ILCJIHJIHCb no necamqnoﬁ cncreme,
TO 6b1JIa 61:1 KaKaa-Hnéym: n3 nonyH-blx qaCTeﬁ GJIusmeJo
paBHa ceKyHne? a 6m coma qaCTb cyTox (caHTncyTKH) ynoé-
Hoﬁ enHHnueﬁ mm namepenml upononmmeglbnocm nexunn? Ho-
qemy ceKyHna HBJIﬂeTCﬂ «eCTeCTBeHHbIM» BpeMeHHb'IM HHTepBaJIOM
mm IOBeKa?
C K p
CTH
a epm m
cn M eT
p a
x
Bce K
y H
n
.
C mm B é
pam e HH nu
bH na
:
B
e eH n T 0
m e
mn
c x p
o
cm H e
O CTa eT H
B b

1‘12. 3. ‘Bsaumoaeacraun e aeymepnom npocrpancrae
maccaMH oénanaroT Taxme OIIHHaKOBbIMH I‘paBHTaHHOHHbIMH Mac-
caMH. He 3a6BIBaﬁTe, qTo STOT Bonpoc HaM eule npencmm usb.
A rIOKa MbI M0)K€M HOJIbBOBaTbCH KHJIOI‘paMMOM KaK aTaJIOHHoﬁ
Maccoﬁ. Baxmoﬁ nponsBonnoﬁ BeJIHqHHoﬁ HBJIHeTCﬂ emmnua, paB-
Bag 10*3 (0,001) KnnorpaMMa n HaBBIBaemaH I‘paMMOM (r). 0mm
I‘paMM norm! TOI-IHO paBeH Macce OIIHOI‘O Kyénqecxoro caHTnMeTpa
BOIIbI npn 4°C—3’I‘0 onHa H3 npwmn TOI‘O, n0y nMeHHo K-HJIO-
rpaMM 6w] BB16paH B KaTBe eIIHHHubI maccm. Tblcsma KHJIOI‘paM-
MOB COCTaBJIHeT MeTeCK TO
H K
(
e y
1
0
H o
) —

Oreerbt Ha eonpocbt
qecxoﬁ aHepmn oxasaJ n pm
H M bI M
H
n Kn B
m pH om
y u p
o-
T a H CT
ye
C J m nomxnbl
m
0
p a
3M b B
Tb p n c
ym
e M I '
JI b -
cyHa p B JIH He
.
/
3 o é
m p or o
na ca
B a no ne
ﬁ T H
,
O T o e O
KHO b
I I O 6
1

90 1‘ A. 3. Baaumodedcmun 6 aaymepnom npocrpaucrae
v7—
60113111e 11M11y1130 ra303, 3316paC313aeM31x 11a3a11, TeM 601131111111 11M3y11300M 0611a-
naer 001a3111a11011 macca paxem. H0 01110111e111110 K 11a6111011a1e1110, 11ax01111111e-
myca 11a 3eM11e, paKeTa 1131111101011 6310'rpee. LIepes HeKOTopoe 3peM11 ncrexa10u1113
man no 01110111e111110 K aromy me 11a6111011a1'e1110 6y11y1 113111313011 enepea. 31a
c11'rya111111 a11a1101‘111111a 1011, 3 K010p01'1 oxaaanca 631 ma113t11111, Haxonamnﬁca 3
11011113 110e311a, 11311111yu1erocs1 co cx0p001310 100 KM/q. E01111 M3113311K 6poc111
11a3a11 Kamenb, 0006111113 emy cx0p0013 50 KM/q, 10 Ha611101131'e1110, crosuuemy 1111
same, noxame'rca, l1'10 Kamenb 11311111e1‘ca aneped co cxop001310 50 1111/3.
3.6. Haqa11311311'1 11MI1y1130 CHapana 3 cepennne Tpaexropnu 63111 pa3e11
2M0 = 2. B rop113031a113110M 11a11pa311e111111 3101 11M11y1130 1101111151 coxpamrrbca
KaK 30 apema 33p311aa, Tax 11 nocne Hero, E01111 rop1130111a11311a11 cocra3111110111a11
11MI1y113ca 01111011 1101103111131 cnapana yme1131111111a03 110 11y1111 113-3a 1010, 1110 011a
63111a 016pome11a 11a3a11, 10 HMHyJIbC 310p01‘1 1101103111131 c11ap11113 1101111<e11 63113
pa3e11 ero nep3011at1a11311mdy 311at1e111110. HOCKOJI 11 3
p111a 1a c a 30 110111 3111
p 111a pa311a poc
'ro1
, a e
1
M1y
130 e ne
b 10111
e1 3 111131 1
M
, O e c
x
o p
c 'r 1111111 1
a a1 111 ca
— y 1 3
e 11111 11113
111 c
x p
c 11 a e
pe 11111 e
' p e
K Top1111
. a q
ab na K
H e T

1‘11. 3. Baawuoaedcreuﬂ a aeymepnom npocrpaucree
noncraBKoﬁ, 'r. e. non TotIKoﬁ CTOJIKHOBeHHH. Cnena'rb 3T0 Bblcmomere,ecnn 0cm-
pomHo yponme mapnx, upenBapHTeJIbHo HOMeCTuB ero non IIOJICTaBKy, mm ony-
cmre H3 3T0?! TOLIKPI orBec. Hocne CTOJIKHOBeHHH Bbl 6y11e're HMeTB Ha éymare
Tpn omeTKH: ome'rxy non “rouxoﬁ CTOJIKHOBeHHH, ome'rxy, Kyna ynaJI aTaKylo-
mnﬁ mapHK, H omemy, Kyna yuan mapHK-Mnmeab. UpOBenHTe .HPIﬂHlO OT OT-
MeTKH, coorBeTCTByromeﬁ TO
COJIK H
O B eH H
n or o x n a
n e HI aT
a K y
oe oa
n a n nn ao
n y
H ro p e x
n pn
pn o nn
n a c p
s o u a
n b n o
c x p -
c ma a
K y o e
o m apH a n
cn e T O JIH OeH
H
. II o ea
’ r
e
T
0
)
e c a
M
om m a
pH a M

17 parcmttecrcue pa6om 93
BosseneM 06e qacm ypaBHeHna (3.4) B KBanpaT:
2_ M2 M2 __
00— (I + 74—192)(01+ $4702) —
M M M 2
_ 2 ._2_ _2 __2_
_”I+(M, v?)vl+(M1 “Dad—(M1) 03'
Hocne ynpomeHHH 3T0 BbrpameHne HnmaeT Bun
M M 2
03: of + 2 0201 + 03. (3.6)
BbItITeM (3.5) H3 (3.6):
M q M M
0:71202- 7'f—1)+2m:—vlvg. (3.7)
OCTHM (3.7):
o — —M—2 — 1) + 20 3 8)
__ M1 02 1. ( .
Pemaa omocmenbno 01/02, nonyqaeM
a. _1 _ﬂ _M.—M2
E_§(l M1)— 2M: ' (3'9)
CneJIaeM caenyloume HOIICTaHOBKHI
Hp M1 =
’v_] 0, 01: 0:
U2
npn M1 =‘ 2M2
v_l__M_'-; L.
02 — 4M2 _ 4 ’
rIpH M1 = ‘/2M2
01 __ I/2112 ___1_
02 — M2 — f.) .
npn M1'_>T> M2,
£1— M1_ _ I
02 N 2M; _-2-
,ZIorcasaTe/zbcreo T080, 270 npu ynpyeom crommoeeuuu
menu; 0 paenbmu maccamu yea/z meo/cay ux Tpaexropuﬂmu
nocxze era/muoeeuuﬂ cocraexmer 90° (qbue. 3.16)
CoxpaHeHne HMHynbca B l'IpHMOM HanpaBJIeHHH:
M100: (M101 cos 91) -l- (M202 cos 92). (3.10)
COXpaHeHHe HMrIyJIbca B nepnennnxympHOM HanpaBneHnn:
0=(M,vl sin 91) —- (M202 sin 92). (3.11)

FA. 3. Baaumodez‘icmun a aeymepnou npocrpaucrae
1
I
' vzcosaz
- ——— V2
°<
1
(DI/IF. 3.16. BeKTopHaa nnarpamma c'ronxuoaenna qacmu, odnanaiomnx onnnaxo-
BbIMH maccaMH. A'raxyiomaa qacmna Hmena Haqanbnyio CKOPOCTb vo. lJac'nma-
Mnmenb HaXOlIHJIaCb B coc'rommn noxoa. I'Iocne CTOJIKHOBBHHH CKOpOC’l‘b a'ra-
Kyiomeﬁ qacmnm CTaJIa paBHoﬁ v], a CKOPOCTb qaCTHubI-Mnmenn paBHoﬁ 02.
Coc'rannmomne cxopoc'reﬁ OTMeqenm Ha qepTeJKe.
CoxpaHeHHe KnHeeCKoﬁ aneprnn:
1M1v3=[(-‘2-)M1v%]+[(-;-) Maria]. (312)
ocmM ypaBHeHnn (3.10), (3.11) PI (3.12), HOJICTaBHB M1=M2.
I'Ipn STOM yCJIOBHu nenenne ypaBHeHHn (3.10) Ha M1 naeT
00 = (01 cos 9,) + (02 cos 92). (3.13)
IleneHHe ypaBHeHna (3.11) Ha M4 mm
0 = (01 sin 01)_(02 sin 02); (3.14)
B pesyJIbTaTe neJIeHnn ypaBHeHnn (3.12) Ha l/2M1 nonyqaeM
03 = v? + 02. (3.15)
BosseneM B KBallpaT 06e qacm ypaBHeHHH (3.13):
03 = (0% cos2 0]) + (03 cos2 92) + (20102 cos 91 cos 02). “(3.16)
BosseneM B Ksanpa'r ypaBHeHne (3.14):
0 = (of sin2 01) + (0% sin2 92) — (20102 sin 91 sin 92). (3.17)

17 paxruttecrcue paéorbz 95
(DI/11. 3.17. BexTopHaa nuarpamma nmnynbcos
C
TOI
KHOBeH
I
H a
cu .
K
OT o

['12, 3. Bsauuoaedcreun 3 deymepnom npocrpancree
3AﬂAqI/I
I. TBepnbm mapnx, nanaloumﬁ c naéopaTopHoro crona Bblcoroi’i B 1 M, 110-
CTHI‘aeT nona qepes 0,45 0. OH Kacae'rca nona Ha paccroaanu 80 CM OT OCHOBa-
HHH CTOJIa. KaKOBa 6bma ero I‘OpHBOHTaJIbHaH cxopocrb B meTpax B ceKyHny?
2. TBepﬁ [Ila c p a
c m a e ca
o
T O
JI a
npn
T
OMO HHI TI a
T J
1
0 0 B o
e
TO J
I K O
e H c I
p I HM ap
no m
H axo m n
m a BH e a
p enn no m
c o cm -
m Ha T
o p a
ﬂ
o n o
n c a
KH a pa
r o r
oa
. H oe r n
H Be Hu
a 0 a a

I‘JIaBa BepTaH
HOTeHuuaaH aHeH
Haémonaa HOBeneHue HpOCTbIX 06’bexTOB B CTporo CHeHHaJIIX
yCJIOBPIiIX, MbI yCTaHOBBJIu cymeCTBOBaHBe ﬂByX Bennqnn, KOTopBle
OCTaIOTCH HensMeHBBI'aTo KHHeTCKaB sneprnﬂ B HMHyJIbCD
Ham KamnonHeBHBIi’i OI'IbIT He naeT HaM HOBOIIa npennonaraTB cy-
meCTBOBaHHe TaKHX 3aKOHOB coxpaHeHHH. B caMOM negle, mom! H He
HOlIOBpeBaJIH 06 amx 3aK0Hax no CpaBHHTeJIbHO HenaBHero Bpe-
MeHH. I-IaM KameTCH, lITO Tena, Kamumeca no BeMJIe mm nemume
no Bosnyxy, HenpepBIBHo Tepmor CBoﬁ HMHyJIbC. I/Ix KBHeeCKaH
aneprml ynenBaeTca n HOCTeneHHO OHH npnxonm B cocmmme
HOJIHOI‘O ‘rIOKOH. ynpomeHnH, KOTOe 6mm HeoéxonnMBI mm TOI‘O,
tn‘oébl yCTaHOBnTB 061mm 3aKOHOMepHOCTH, CTosmme 3a BceMB
3TBMH, BOCTaTOIIHo CJIO?KHbIMH, (paKTaMH, 6mm HaﬁneHBI B peByJIB-
TaTe BeCBMa cepBeBH
y n
n n
. ameB n o m
e H y
C IO H
H, Te
B T
y
T CBeT
e H H I
B
3
H M O
l e

98 m. 4. ﬂorua/zbuan suepeun
__
Mb] l'IOCTapaeMCﬂ Haﬁm 3TH npyrne (pol anepmu B caM
pa
s- I
H I
.
m a
u
m
i
x K
o n n
eC TyIO r a
B a nan pm Hu
aIH T I
Bo
Be a x
C I
y
x
y
11 nn n b
o a b
H e
n
I m e
rn o ne
e JI e H H on
u

4.]. ﬂorenqua/zbnan aHepeun apasuraquu
ﬂameﬂuuamﬁan ﬂomeuuuaﬂu/ax
aHepeun maKcuMaJIwa JHPpé‘lM maxcuma/Iwa
U = 0 O 0 U = (.7
v = max
[IO/TIFHuUdJIbHdﬂ 3/18/7810! mummy/ma
(DHF. 4.1. Upn Kaqamm MaaTHnKa ero KHHeTcxaa aneprna npeoépaayerca
B HOTEHuHaJIbHYIO aHeprmo rpanmauun n Haoéopor.
DI/IF. 4.}. Mann namepenna cxopocm mapHKa Kax (bynxunn BbICOTbI, c KOTopoﬁ
0H CKaTbIBaeTCH. FopnaoHTaaa -CKOpOCTb onpenenae'rca (popmynoﬁ VropH3=
=R/At. HOCKOJI Be
nnu
a
t
o nna
on a
m
Be xm
an o a ,
cx a T

(DI/IF. 4.3. Cepna CTpodorpaMM, cua'rux npn c6pacu3aunu CTaJIbHOl‘O mapnxa
o'r nonmnmmxa c pa‘aJmtmux BHCOT: l, 0,8, 0,6, 0,4 a 0,2 M, KOTOe o'rctm'ru-
Banner, 0T HyJIeBoﬁ OTMeTKn Ha me'rponoﬁ Jmneﬁxe. LIac'ro'ra crpoénpoaamm
paBHa 30 Bcnumex B cexynny, macm'raé omeqamon —'rotmo 1:10. llpyrHMH
CJIOBaMH, BpeMﬂ memny BCHHIUKaMH coc'raBJmeT 1/30 c n paccmanne B 1 CM Ha
¢o1~o COOTBETCTByeT 10 CM B HaType. Cxopocn: mapnxa npn ero npoxoxmennu
qepea HYJIeBYIO o'me'rxy memo npnénnmemio onpenemd'rb, namepnn paccmarme,
Ko'ropoe mapnx Ha STOM yqacrxe npone'ran mexmy Bcnumxamn, n pasnenua 9T0
paccroanne Ha 1/30 cexynnu. (B Hexo'ropux cnyqaax caenye'r (Span cpeAHee
aHa'ne n3 cxopocreﬁ Hap. HyJIeBoﬁ omeTKoﬁ a non. Heﬁ.)

4.1. ﬂorenquaxzbnan anepaun apaeuraquu 101
r— ‘r —t f ..
Haﬁm BeJmy HOTeHuHaJIBHoﬁ aneprnn, KOTop
m a
p n
H e JIH
aI e . K
O H
u a T
oI
JI
a Bb HH
B e
IeH I
o np
o n
b e
yaa
n
ﬂ
0 T OC T
JO oo
, a BbI
lI
JIH T
C
3
1 0 1

102 FA. 4. ﬂoreuquanbuan aHepeun
20,0
18,0 — /
16,0 — [1/
14,0 — /
12,0 — I’
(memp/cexf
Z
U
4.0— 2
2,0 '/
V I L I -l l
0 0,30 0,40 0,00 0,30 [.00
Mem

(DI/ll. 4.5. t-Ie'mpe paan penMe'ra Ham nana'rb onnonpemenno. Y me): 113
max npn nanennn cxopoc'rb Boapac'rae'r oxmnaxoao. Cnenyronme npyr 3a npyrom
(c HHTepBOM 0,1c) 'CTp060cxonnqecKHe Bcnumxu cneTa (pnxcnpoaann nx Ha
onunaxoaux ome'rxax. Onuaxo y qe'rBep'roro 'reJIa— mapnxa n3 nannpocnoﬂ
6ymarn— ycxopeHne 651.110 npyrnM. COHpOTHBJIeHHe Boanyxa OKaSHBaJIO Ha ero
Anameane cepbeauoe Humane name npn He60nbmnx cxopocmx. B peayaxb'ra're
on OTCTaJI o'r donee nnomux TeJI.

104‘ , FA. 4. ﬂorenquanbuaa suepeun
O
BpeMeHHO c6pacmBaJ ne
o n
C a
I H a
H a x a
. e o
n y
c
x e r a H
B a a m e nn
o ee
H e e
,
r
a xa
.
O
lH a KH
a o c e H
e
MH H
M ene p
o ua ﬁ
a aa o
'r o n Hao
m n KO O T
M
H
BTO cn
y a e

4.1. ﬂoreuquanbuan auepeun epaeuraquu ( 105
Koa¢¢nuHeHT npoqopunonanbnocm g MO}KHO Haﬁfm, namepaa
CKOPOCTb, KOTOpYIO TBJIO npno6peTaeT, JIOCTHI‘HYB npn cnoeM na-
nennn onpeneJIeHHoﬁ BblCOTbI:
,.
g=—;’F. (4.4)
06paTnTe Bnnmanne, Inc B 3T0 Bmpamenne HHepTHaH Macca M
He nm. HOCKOJI
B eT
e
Ia nnen
H c o
n H
a o a
o BI -
C T
I, e O H
H a o
mm
m
) H e O
l HH
OMO
CT
H H H H,
n e O
T un -
H a OBb I
e co omn o
pa H eﬁ me pe
B a K ye
m

iOé h. 4._ ﬂoreuqua/zbnan aHepeun
L E -
_ Lg -
“ 5 ° “ * /|J'
3— LS-I- 0 ‘1’
Z— —Z— -1-
I— —3- _Z-
0 x
a d 6
(DI/IF. 4.7. TpH pasnblx cxemamqecxnx H306pamemm onHoﬁ 1410171 )Ke (1)143-
cxoﬁ yauHH. CxeMBI omnqarorcn npyr OT npyra TOJIbKO monomeBHeM HyJIe-
BOI‘O ypOBHﬂ BOTeHuBanBHoﬁ sneprnn, KOTopoe MBI‘ BuénpaeM nponaBoo.
Honomenne ByneBoro YPOBHH ax He BJIHﬂeT Ha pacueTu, IIOCKOJI
M b n a e
pe M T O I
bO n a e e
n e B O e
H uaoﬁ aep m
u
CBem eHo O
IH H K
OB O, e
s
BCH M O
T T IO
, K aK ne B
e HH b I O
T
-
JI
a
l
I
BaI T
C n OH
.
O Ha o K
B
o e M
y ne H

4.1. ﬂorenuua/zbuan suepeua epaeuTalmu _107
hrh! v EHMH=M9hI
[7:172 ' EHMH=M9172+%MUZZ
[7:173 v Enolm=v§
M9h1= Mghz+ %
=

108 [‘11. 4. Horenqua/zbnaa suepaun
H BCH onuaa anepmm Haxonmca Tenepb B (popme KnHeecxoﬁ
snepruu. ope, onHaKo, KHHeTcxaa aneprna nepexonm‘ CHOBa
B HOTeHunaJIBH an pm o p
aH a
.
T
n o n c
x o m no e
e a e
JIeH H K e
H r y
a Ha O He
u , B a
oﬁ B ep
ne T
O
K , KOTop
lI
O THIH e
T aT
H, e o o e
n n
a n b a
a nepnn
T
H O-
B IT
CI a
K n a JI H
oﬁ
.
B
n p
c

4.2. ﬂoreuuuaxzbuaﬂ anepeun npywcunbz 109
J»
(DI/IF. 4.9. HOTeHnnaJIbnaa sneprna npyxmnbl mome'r npeBpamaTbca B KHHeTH'
qecxyro aneprmo H 3aTeM 0mm: B norennnayxo.
o6ecnet1HTb‘coxpaHeHHe aHeprnH B STOM cnyqae, MbI npn onpenene-
HHH noreﬂnnanbnoﬁ aneprnn netbopmaunn'npymnnbl ILOJIHG-Ibl cun-
TaTb, Lrro HOTepﬂI-IHaﬂ KnHeeCKaH aneprua Tena HpeBpaTHJIaCb
B no1‘eHuna

110 [‘21. 4. ﬂorenqua/zbuaa auepeuﬂ
(DI/IF. 4.10. Cepaa c'rpoéorpaMM GeryHKa Ha Bosnymnoﬁ nonymxe, KOTopuﬁ Ha-
qnnaeT llBPﬁ‘aTbCﬁ non neﬁc'rBueM cma'roﬁ }KHHbI. CKopoc'rb B HHTEPBaJIe
memy BCHbImKaMPI nponopuuonanbna pacc'roanmo mexmy BepTHKaJIIMH mer-
KaMH, enJIeHHuMH Ha 6eryHKax. Ha Bepxaeﬁ c'rpoéorpamme npya 6mm
cma'ra Ha 1 CM; Ha Kaxmoﬁ nocnenyxomeﬁ CTpoéorpaMMe cmame npyxmuu yBe-
JIHqHBaJIOCb Ha 1 CM.
B KOHue aToﬁ I‘JIaBbI B n. 3 pasnena «Hpamnqecxne pa60TbI»
onncaH npyroﬁ npocmﬁ nyTb, BonHmnﬁ K TaKHM )Ke pesyJIb-
TaTaM.
TaKiHM 06pa30M, OKaBBIBaeTCﬂ, qTo npouecc HaKOl'IJIeHHﬂ aneprnn
npymunoﬁ nunnHao omnqae'rm 0T HaKOIIJIeHHH aHep-
run B rp_aBma_uH0HH0M none. B cnyqae rpasmauuonnoro nona

4.2. ﬂorenuuanbuan. auepeun npyaicunbz 111
[6 P
V I
[47
‘
12L- I
A’Jéﬂpam empo oe z
y
ﬁ
m
, npom o
m m
e e
u
m
q
u

112 FA. 4. ﬂorenquanbuan anepeun
(DI/ll. 4.12. CTpodorpaMMH nnyx 6eryHKoB, Ko'ropue Haqami nnnpa'rbca non
neﬁcmnem onnoﬁ n Toﬁ me npymmu npn onnou n TOM me HaIbHOM cmamu.
CKOpOCTb Kaxmoro 6eryHKa nponopunonanbna nepeMemeHmo yxpenaennoﬁ Ha
HeM ‘Bepmxanbnoﬁ meTxn B HHTepBanax mexmy nocnenonarenbnum CTpoéocxov
unnecxnmn apnumxauu cBeTa. M2 =2M1.
aannceTb OT maccu He caasaHHoro c Heﬁ Tena, c KOTOM, eﬁ'npenv
CTOPIT BaanMoneﬁCTBOBaTb. Mu M0)KeM, CCbIJIaHCb Ha OIIbIT, yTBep-
mna'rb, qTo HaKonJIeHHaa aneprna npym HHKaK He csasana
c nHepTHoﬁ maccoﬁ camoﬁ npyorcunbt. PasyMeeTca, éonbmaa 6p0H-
soBaa npyxnna cnocoéna HaKonmb éonbme aneprun,
ma n H
b -
a n p
0H 0
a a
npy a
C npy
r o
ﬁ
CTO p
H

4.3. Maeuuman norenqua/tbnan suepeun 113
a. 6
(DI/II. 4.13. a-naOopaTopHue Tenexcxn, Ha KQTOpHX yc'raHon'JIenu unnuaﬁffn-
qecxne marnmu, OTTaJIKHBaIOInHe Tenemxu npyr 0T npyra; 6 -- 6erynxn 53 1303-
nymHoﬁ nonymxe, Ha KOTophIX yxpennenu unnnnnpnqecxue marnn'ru, OTTaJIKK'
' Balomne Gerynxu npyr 01' npyra.
Bonpoc 4:11. Macmraé CHﬁMKOB 1:12; CTpoénpume
Bcnbunxn nponcxommn 113a pasa B cexynny, HHepTHaH macca
6eryHKa 0,1 Kr. KaKOBa B STOM' cnyqae neHHaa Bennqnna
HOCToaHHoﬁ npybI?
4

(DI/IF. 4.14. Cepna c'rpoéorpaMM Gerynxon Ha Boanymnoﬁ nonymxe, xo'ropue o'r-
Tanxnnalo'rca npyr OT npyra 3a eqe'r yxpennenaux Ha HHX marnn'ron. Cxopoc'rb
6erynxa Ha Kamnoﬁ c'rpoéorpamme nponopunonanbna cmemenmo onnoro as KOHIIOB
6erym<a 3a Bpema memy Iuayma HOCJIellOBaTEJIbHHMH Bcnumxamn. Ha nepxneﬁ
c'rpodorpamme pacc'rosmne mexmy 'xonnamn marnmon com-ammo 5 CM. Ha
Kamnoﬁ nocalenylomeﬁ C'rp060rpamme 9T0 paccmanne ymenbmaJIOCb Hal cm.

4.3. Maeuuman norenqua/zbnan auepeug 1'15
15-:- +
14 -
. _
GDI/II‘. 4.15. 3aBHCHMOCTb KBanpa'ra
cxopocm v2 6eryHKOB 0T paccma-
mm x memny KonuaMH Mal‘I-IHTOB. [0 h
SKCIIepHMeHTaJIIe «Totum» H30-
Gpamenu xpeCTaMH, qTo 0Tpax<aeT llv
norpemHocrb pesyaTon HaMepe- 8 —
mm. B Kamnom cnyqae
H
M
e
-
p HH
x n
orp m
HOCTb COCT a
B m JI a
0
3
.
p H ope
eJIe H
H 0 n o
pe m
-

116 FA. 4. ﬂoreuuuanbnan anepeun
l .
eeomerpuu npnmepHo nponopunorianbna oépaTHoﬁ Benntmne pac-
CTOHHHH memny MaI‘HHTaMH. MaTemaTCKn 3T0 3arIHCbIBaeTCH ene-
nyloumM 06p330M:
l
Euarn. nor 5:” ‘1? -
‘.
onpoc 4.13. ECJIH 3T0 Tax, TO BaBHCHMOCTb 02 OT l/x nonxma
npenc'raBJ H H MIOJI H
HI .
H p
H o y
I
O
JII
K o
H a Ta
.
H OJI
B HC
I
:
l a HH I
H
n n
y H I
n p un n
u e
p a
.
.
1

013cm Ha BonpOCbl 117
0mm, nonb B Bnne sneKTpnKoﬁ 3HepFHH. I/ICTOqHHKOM KHHe-
ecxoﬁ aneprnn gBHraTeJIH cnymm‘ nKaH aneprna 6e11-
3HHa. Bana'COM aneprnn oénanaeT cmaTbIﬁ Bosnyx mm nap. Hnmy
MO)KHO paCCMHBaTb KaK onHy n3 (popM sanaceHHoﬁ aneprnn,
KOTOpaH B OpI‘aHH3Me )KHBOTHbIX M0)K€T HpeBpaﬂlaTbCH B KHHeTH-
K
se
p m oH
e
cmm n
n c
m
an M
O
K H O u
eH Tb o
n e -
T O
M
o e pan
w H e

118 FA. 4. ﬂorenqua/zbnan aHepeun
4.2. HOTeHuHaJIbHaH aneprna rpaBméuHH mapnxa, Koropoﬁ OH o6nanae'r, Ha-
xonacr, Ha TpeKe B HaqaOM I'IOJIO}K6HHPI, HOJIHOCTbIO nepexonm B aneprmo 113n-
menna. ECJIPI aneprna nanmenna cxnanbmae'rca P13 aneprnn Bpamenna a aneprnn
nocryna'renbnoro mamxenpm B l‘OpH3OHTaJIbHOM HanpanneHHH, T0 ropuaoHTaaa
CKOpOCTb 6y11eT Menbme, oa
M oa 6
1
6
5
1 1
. O Ha e
b e ,
6 ba
6 1
1 , a
M
e p e
C I H
611
m anc o cxa b a
b m a no pe K
y
e T eH a H 6
e
3 pa m
e
H a . na
o Ha
e a x cn
ep HM eH e
M I e e

17 paxruuecxue pa6om 119
nmenuuanbuoﬁ sneprnn, Ko'ropoﬁ oénanana npya B ucxonnom cocmannu;
0Ha paBHa lMarx”. Peum're ypaBHeHue omocmenbuo nocrommoﬁ npymnnu k.
(ILna comaconanna enmmu x H3Mepm'4're oéasaTeJIbHo B MeTpax. HOMHHTe 0 mac
ul'ra6e CTpo6orpaMM.)
4.12. HaﬁnHTe oruocmenbnue cxopocrn 6eryHKa, Hamepaa CTpOGOI‘paMMbI Ha
(par. 4.14. HOCTpoﬁTe sanncmuocn 0 OT x. Hponopunonanbna Jm cxopocn: 0 Be-
Jme x?
4.13. ECJIH 02 ~ (l/x), T0 Ha rpae sanncnmocm 02 or x MaJIbIM x coo'r-
BeTCTByIOT éonbmne anaqenna 02, a 60JIbIIIPIM x—manble 3HaHa 02. Kpnnaa,
ouncmnaeMaa Taxoﬁ BaBHCHMOCTbIO, npelICTaBJIﬁeT coéoﬁ omiy P13 BeTBeﬁ runep-
60am. Ecgm )Ke Mb] HOCTPOHM rpacpnx 02 0T 1/x, TO nonyrmM npsmylo JIHHHIO,
upoxozmmyro qepes HaIo KOOPIIHHaT.
I'IPAKTI/ILIECKI/IE PABOTbI
I. H3mepenue norenqua/zbuoa’ anepeuu cxarbtaatotquxcn
wapurcoe
[Ina 'raKnx namepennﬁ npnmeuaerca Ta me nycxosaa nopomxa (Tpex), KOTO~
pan oaHa B m. 3. B IlaHHOM cnyqae CTonKHOBeHim He HYMHbI, H0 Bhl nonm
a a r
H n a
y
IBI
C O T, K
O o o ﬁ r a
m
-
ye rm an
x
I
lo n
n

120 FA. 4. ﬂoreuqua/zbuaa suepeun
ﬁ
06pa'm're BHHMaHHe Ha OéCTOHTEJIbCTBO, yKasaHHoe B Bonpoce 4.2. LIacm
noreHunaoﬁ aneprnn rpaamaunu mapnxa npeapamaerca a Knnemqecxyxo
sneprmo Bpamemm, OllHaKO ropnaomanbnmﬁ npoéer HBJIHETCH mepoﬁ Too KH-
He'mqecxoﬁ aHeprnH nocrynaTeoro nBHmeHHa. Floxa “Mb: pacemHBaeM
TOJIbKO CKaTbIBalOLLIHeCﬂ mapmm, coxpauaerca nocmmmoe coomomeune memny
KHHeeCKHMH sneprmmn apamaTeoro H nocryna'renbnoro llBHHieHHﬁ. Ho-
a'romy Iwnaenennue Bume coomomeuna OCTarorca CﬂpaBelIJIHBblMH.
2. Hamapenue nepuoda nauauuﬂ maﬂmuica
B Bonpoce 4.7 BaM npennarauocx: H3MepHTb nepnonbl Kone6aHHﬁ MaHTimKon
c rpyaaMH, ImeloumMH pasmmnyro HHepTHyIO maccy. Mam cn
e na rb
en o
m o e oo x mo n
o e c m n p
axm e c n
B o
O Mme e
OIa K
H o é
o n H o y
t ec r c
a en y one c
n e 'r u . II
J ma
HH o o onb
a B O b H e
o o n o
e p a T o
no m
é o
c 'r pn m
n
p o m r o
H
HT. e n o na
y ﬁ rca
m Hp KM m e pe
K o

I7 paxruuecrcue pa6orbt I21
(Medina: npyarcuﬂa
.2'
/ (-—————-—>
MO —_~—~.~
‘
R
A ‘
QI/Il‘. 4.16. YCTpoﬁCTBo 11m; namepenna nomaunaoﬁ aneprnu npyxmnu. Benn-
a x npencraBmeT coGoﬁ cmame npyxmnu, R — paccmanne, nponopnnonanbnoe
cxopocm, cooémeHHoﬁ mapnxy.
To me yCTpoﬁCTBo c HeéonbmHMH H3MeHeHHﬂMH ((1)111: 4.16) moxmo HCIIOJIb-
SOBaTb mm Hamepenna aaBMocm no'renunamanoﬁ aneprpm upyxum 0T nx ne-
pmaunn. B STOM cnyqae Tpex nonmen 613m: I‘OpPl30HTaJIbI-IbIM. YeraHonme ema-
Ty10 npyxmny Tax, qToém, paamHMaHCb, ona Tonxana mapnx Ha Tpexe B I‘OpH30H-
TaJIbl-IOM HanpaBJIeHPIH. I-I'r06bI He ocnomnmb sanaqy, Macca npymnnm nomKHa
65m: suaqmenbno meHbmg maccu mapHKa. BMeCTO MpaMolx mapaxon KC-
nonbsyfne mmenblve CTaJIIe mapHKH OT mapnxononmnnunxon rum mapu mm
KpoxeTa. xmna nonxma 65m: ManeHbKoi’i u nerxoﬁ. I/IaMepb're I‘OpH30HTaJIb-
nbu'i npoéer (on nponopunouanen cxopocm) no xpaﬁneﬁ mepe 1mm 1mm paanbtx
creneneﬁ cmama npyxmnm. I'Iocq‘poﬁ're rpadmx n onpeneJmTe coomomenne
meyxny ’
Bnpymrmu nor H xo
ECJIH y we ecu: Tpex Ha Bosnyumoi’i nonyume, namepenne 0 [MR (bynxunn x
momno BbIIIOJIHPITb men}: 10 H
e 3 Tp
OO l
p
a
M
I I p
oc o a me p
b e e yH n
o -e p

I22 FA. 4. ﬂoreuqua/zbuan suepeun
s N ‘ ~
.
lluﬂuﬁﬁpwlemue
menu/ml
i
I? ~ 0
(DI/I I‘. 4.17.
Te )Ke H3MepeHHH M0}KH0 nponecm, ecnn BH110H3MeHHTb yc'raHonKy Tax, Irra-
6u ona C6paCbIBaJIa mapHKH co CTOJIa ((1)1412 4.17). IIJapKK yCTaHaBJIHBaeTca Ha
Heéonbmyro Tenemxy, KOTopaa PIMeeT BoaMomHoc'rb KaTHTbca‘K Kpalo CTOJIa. Ha
Tene>KKe KpEIIHTCH maT. IHapHK nonmen nemarb Tax, tnoébl 0H nerKo MOP
CKaTHTbCH, Korna Tenemxa ynapaerca 06 ynop Ha Kpalo CTOJIa. Ilpyroﬁ mamm‘
nomKeH 65m), >KeCTKo HpHnJIeH K crony Ha Toﬁ )Ke BbICOTe, Ha KaKoi’i pacno-
nomeH marnm T€JI€)KKH. MarHHTu oépamenm npyr K npyry OILHOHMBHHBIMH no-
mocaMn. Ynepmnnaa Tenemxy, namee paccromme x memny MaI‘HHTaMH. OTny-
cnrre Tenemxy; ona n0KaTmca K KpOMKe crona. Korna TenemKa, IIBHI‘aﬂCb co
cxopoc'ruo v, ynapmca 06 ynop, mapKK enem'r c Hee K ynane'r Ha non, npone-
Ten no ropnaomanu paccwosume R. 311

Saaattu 123
4. CqHTaHTe, qTo HOTCHuHaJIbI-laﬂ 3HeH rpaBHrauHH paBHa Hymo Ha no-
BHOCTH 3eMJIH. B STOM cnyqae moreHuHaaa aneH KaKoro-JIHoo TeJIa B
Kononue GyneT orpHuaTeoH. I'IonomHM, qTo KaMeHb BeCOM B 1 Hr, HaxonHB-
mHHCH B Kononue Ha rJIy6HHe 5 M, nanaeT Ha 11:10, HaxozmmeeCH Ha paccmHHHH
30 M or IIOBHOCTH 3eMJIH. LIeMy paBHa KOHeqHaH HOTenuHaaa sneH
KaMHH, Korna 0H IIOCTHI‘HCT nHa Kononua? LIeMy 6bma paBHa HaqaaH IIOTeH-
uHaJIbHaH anea KaMHH, Korna 0H neman Ha rJIy6HHe 5 M? LIeMy paBHO H3-
MeHeHHe moreHuHaoH aneH H KaKoH 3HaK 0H0 HMeeT—nonomHTeJIbHuH
HJIH 0TpHuaTeuﬁ? LIeMy paBHa KoneqHaH CKOpOCTb KaMHH nepen ynapOM
o IIHO?
5. JIerKaH HpYiKHHa HaXOIIHTCH Mexmy nByMH 6eryHKaMH Ha BosnymHoﬁ no-
nymKe; Macca OILHOI‘O H3 HHx 200 r, macca npyroro 400 r. ECJIH HOCTOHHHaH npy-
)KHHbI paBHa 100 HbIOTOHOB Ha MeTp (H/M) H npymHHa B HCXOILHOM COCTOHHHH
cma'ra Ha 2 CM, T0 y paBHbI cxopocm 6eryHKOB B MOMeHT, Korna OHH Harm-
HaIOT pa36eraTbca? (HOMHHTe, Ino HMnyJIbc ILOJI}K6H OCTaBaTbCH HeH3MeHHbIM:
3T0 TpebonaHHe onpeneJIHeT omomeuue cKopOCTeﬁ 6eryHKOB.)
6. SHBKTPOCTaTCKaH noreuuHaaa auea E B a
H Oe
H CTH H a
y
: o e
I x
H IH c p e
e K H
x
s
a a n o a n
pn
o pH
n a a
l
r
r e r pC T
HH mm ny eH
Ta

I‘JIaBa 11511351
C14
B
1
11. M bI
aJ m n e
a n n e
p e x 111
1 0 13 me
u nn b n
o a e
p n
n
HTe H
na p
an e
prn
n o
y none
no r ama
n e,
H JI

5. I . Onpeae/teuue cum»: 125
'4
l
E, dmaymz
N
1 l
l
l
i
I
AE
—b
I
I
I
I
I
1 1
I Ax
l .
1 2 3 4 5 6 7
0 I .
.r; mem
¢ .
I
I
I
.
.
.a rmon
nom n n m
11
‘
B O
JI b

126 ['22. 5. Cantu
onpenenmb cnny KaK BenHy, paBHYIO OTpHuaTeJIbl-IOMy Harmony
Kpueoﬁ BaBHCHMOCTH n0TeHuHaJIbHoﬁ aHeH or nepememennﬂ:
F=-—(AE/Ax). OTpnua'renbﬁ 3HaK BBeIIeH 11.1151 TOI‘O, qT06bI
3T0 BameHne HpaBHJIbHO onpenemmo HanpaBneHne ‘cmlbl. TaK,
Hanpnmep, HaKJIOH B TotIKe A Ha (par. 5.2 I'IOJIO}K_HTeJIeH. B COOT-
BBTCTBHH c HaumM onpeneneHneM cma 311
6
ne
T T pH a
T JI b
Hoﬁ
.
T
0
0
H a a T ,
r o
0aa p BI
e H a B T
pH
yan

128 [‘11. 5. Cum»:
5.2. Cuua, paBBnBaemaa npyxmuoﬁ
B NI. 4 MbI npnéemn K onepauHOHaJIbHOMy CUPBJICJIEHHIO
HOTeHunanBHoﬁ snepmn npyBI, npeoépaBOBaB ee B KnHeTuqe-
CK
se p mo e
K O To po
o ea I
I M pH
BH eT
C K I a
ne p mo
M I y
T aH
OH
JI I qo
HTe H H a
I
H aH
ae p
n n y B
n on pu
H Oa JIHa B
a
np a y
e n e
b
op a
nn E
n p y
n HIH

5.2. Cu/za, paaeuaaeuaﬂ npyolcunod 129
30—-
I
I
E) 20 — y
° —r
§ --------- I
Z 10 r yup/011m
L— _A___’ _
(DI/IF. 5.4. BBepxy BeneHa 3aBncn- 0 I 2122;1'7 '2 ;
MOCTb no'reHuHaJIbHoﬁ SHEPI‘HH npy-
)KHHbI o'r BeJIHqHHbI neQJopmauHH. Kpn- I, My”?
B
y 1
0 a
n 0
m
H J
b I
p a
B a M o n p
y m n
o ﬁ ,
T e ap
a HH e o
n o

130 1‘ A. 5. Cu/lbl
(DI/11‘. 5.5. a—naéoparopnble npyHme BI, Kanuépoaannue B HblOTOHax;
6—npnmenaeMb1e Ha (pepMax npyHbIe BI, KaJIH6p0BaHHbIe B aumnﬁcxnx
QJyHTax.
1/2 12262. B Bblpamemm 11.1151 CHJIbI, KOTOO pasauBaeT npymnna, MHO-
)Kmenb 1/2 HsaeT p1 ocrae'rca HpOCTaH (popMyJIa F = —kx.
Emmy HpaBHJIy, KOTopoe HOCHT HassaHHe saxona FyKa, non-
qHHHeTCH 60JIbIIIHHCTBO 06Hb1x npy, ecnn nx TOJIbKO He
paCTHFHBaTb qpesMepHo. To oécmmenbcmo, qTo BOCCTaHaBJIHBaIO-
maa Ia npymI nponopunonaa Mane, Ha KOTOpyIO ona
napopOBaHa, HpeﬂOCTaBJlﬂeT HaM otIeHb ynoénblﬁ cnocoé Hame-
peHHH can. CymeCTByIOT CTaHﬂapTHbIe npymuHHbIe BeebI, Hanpu-
mep, Tame, KOTOMH Bbl nonbsyeT

132 FA. 5. Canal
05*
Jr =
5-; I: 0,005
5, (hwy/III
4 L a
0 0,01 002 0,03 0,04 0,05
.zg,Mem
0
0
—
-
5
-
4

5.4. Coomozuenue newcay pa6orozz ‘u anepeuezz 133
I'IOTeHunaJIbHaH anepma CHCTeMbl nByx MaI‘HHTOB no Mepe c0Kpa-
memm paCCTOHHHH Memny MaI‘HHTaMH 6bICTpO HapaCTaeT, HO
Ia, CTpEMHmaHCH pa3IIBHHyTb 3TH MaI‘HHTbI, HapaCTaeT eme
6b1CTpee. BbI M0)K€Te Ha l'lpaKTHKe yéenmbCH B STOM, BbII‘IOJIHHB
H3MepeHHﬂ, onncaHHbIe B n. 2 pasnena <<HpaKeCKHe pa60Tb1>>
B KOHue HaCTomueﬁ I‘JIaBbI.
B p
o
c
.
.
CI H a
I
HH Tb I y
C a H
BH T T a
, To
b
O H u pm
a -H B aI
H ny n p
y
a
T K a
K 61
yTB II
‘JIH IT b
pa
H HO TH
‘ n a
JIH ﬁ n e
p n n
I H

134 ['11. 5. Cum):
20 — 1
§ .
E ’0 7/ 9.8
£ //
k: A I 1 Ma
0 I 2 3 4
.2', Mem
(

5.4. Coomomeuue mewcay pa6orod u anepeuea’ 135
30—
% 20 —--———
E
2
§ 10 — /
K:
//L . 1
0 I 2 3 4
.r,mempu
(DI/IF. 5.8. Ha HeKOTopOM yuaCTKe nyTu neﬁCTByeT HBHOCTOHHHaﬂ no Benwmne
cmra. B lIaHHOM cnyqae cnna nponopunouanbna cmemenmo: F=kx. l'Ipousae-
neHHas paéoTa paBHa 3amTpnxonaHHoi’1 nnomanu.
Ha Benny x, B TO‘IHOCTI/I paBHa BospaCTaHmo HOTeHunaJIbHoﬁ
sneprnn npybI. Ha rpadmxe 9Ta pa6OTa n306pa>KaeTca uno-
IllaIIbIO TpeyI‘OJIbHHKa non JIHHHeﬁ, npeILCTaBJmIomeﬁ H3MeHeHne
cmlbl c paCCTOHHHeM. HOCKOJI ll
JIOI a
lT e
ro n a p
a H no n
a ee n
o
l
lO I B
IH ICH
BHH H a
B IO T
, r a p
qcxo epm e H
ean a n HO
I OT
IO K
B I Ba
I e HT

5.5. ﬂorenuuanbuaz auepeun epaaumquu 137
CpeﬂHHﬂ Bennqnua CHJIbI, KOTOpyIO c0311aeT TeJIO npn nsmeHe-
HHH csoero HMnyJIbca, caMbIM cymeCTBeHHbIM 06pa30M BaBHCHT
OT TOI‘O, CKOJIbKO Ha 3T0 3aaeTca BpeMeHH. ECJIH, HanpnMep,
BbI eneTe B aBTOM06HJIe co CKOpOCTbIO HpHMepHO 100 KM/q, T0 H3Me-
HeHHe Bamero HMI‘IyJIbca 6yneT cosepmeHHo OIIPIHaKOBO, OCTaHOBIvI-
TECb Jm BbI 3a 10 c mm sa 0,01 c. OIIHaKO BO BTOpOM cnyqae 0mm,
KOTOpaH 6y11eT neﬁCTBOBaTb Ha peMHH 6e30nacnocm mm Ha BET-
pOBoe CTeKJIO, GyneT B Tblcmly pa3 60JIbuIe.
5.5. Eme 0mm BSPJISUI Ha l'lOTCHllﬂaJ

138 FA. 5. Cum»:
A 1
931/11. 5.9. CHJIy rpaBB'rauHOBHoro npnmmenua moxmo H3MepHTb B CTaecxnx
YCJIOBHHX c nomommo KopOMbICJIOBHX mm npymmnux Bec0B. B nepBOM cnyqae
HeHBBec'rHuﬁ rpys ypaBHOBemnBaeTcn CTaHIlapTHhIM rpyaom. Bo BTOPOM cnyqae
HeHBBeCTHBIﬁ rpya ypaBHOBemnBaeTca CTaHnapmoﬁ mm rpanOBaHHoﬁ npy-
)KnHoﬁ.
B—L A
@141. 5.10. Honame maccu nmeeT nBoaKHﬁ cmucn. C onHoﬁ CTopOHbI, 3T0 mepa
COHpOTHBJIeHHﬂ, KOTopoe TeJIo oxasblBaeT HBMCHeHHIO cxopocm (cueBa); c npy.
roﬁ — nepa cnocoénocm Tena OKa3bIBaTb rpaBHTauHOHHoe Bosnei’mTBHe Ha npy-
roe TeJIO (cnpaBa).
~
H H y
e
c M
Tena no om n
n o o a n y
y o a x
B
e c
B . oB T
O
p
O M npnme
e H a
p .

5.5. ﬂorenqua/zbuan anepeuﬂ apaaumquu 139
llpeiemﬂoe JHalIPHUE
EZPUB. nam
l7
(DHI‘. 5.11. Hpennonaraemaa saBHCHMOCTb rpaBHTaunonnoﬁ aHeprnn 0'1 BHCOTH.
HpHBJIeKaeT orpOMHoe BHHMaHHe. B 1966 r. PoéepT 1131111 113 HCToncxoro
yHnBepeTa HpOlIeMOHCTpHpOBaJI paBeHCTBo amx Macc c Totmocrbto no enHHHu
B OJIHHHalllIaTOM anaxe.
B nanbneﬁmeM Mb] 6y11eM CqHTaTb rpaBnTau1101111y1o 11 HHepTHy1O maccy HILCH'
1111111511111 11 0603Hab 11x 011111111 11 TeM x1e CHMBOJIOM m. TaKHM 06pa30M, no-
TeHunaaa sneprna rpaBHTaunn paBHa mgh, a KnHemqecxaa 911epr1151 paBHa
l/2mvz.
2. B BOIIpOCe 4.8 Mb] CTOJIKHP cme
011111 p
J I H
CTI , Ka c
a
m e c
a n 1
e 1 11
1a n 1 1 0
ﬁ
11 p r m
1 rp a H
T
a
u HH
. aa B o
m oH , l
1
0 111 a nepr a
11 11 no nou no n a n
b nB b
I
OTe

140 1‘ A. 5. Cajun
ﬁ’ 2/? 3K 41?
if I I l I l l l
—_——r
2. _z_ : :Rm Ix’
' /
g -3- I | //
LL] -4 :__ Ill
—5 L_—.————-— 0’
(DI/ll. 5.12. BanncuMocm norennnanpnoﬁ anepmu rpaam'aupm o'r paccmanna r,
OTCqHTbIBaeMOI‘O 0T neH'rpa Bewm; na'ro, qTo norenunanbnaa aneprna paBHa
Hymo npn 6eCK0He
6
OI M a n a
H H r .
Ha o ﬁ IH a
e p na ny
r n
T
O q a
x T p
u ae
IbH a
.
—an
c 3
e rm B e
m,
M bCI
L
I
B e
o p
o JI O

5.5. ﬂoreuquanbuan anepeua epaeurauuu 141
Anreépanqecxn H3MeHeHHe HOTeHuHaJIbHoﬁ 3Heprnn rpaBHTa-
111m onHCbIBaeTca BameHHeM
AErpan. now = Exon — Enaq = — o
YMHomaH nepBbIﬁ lmen Ha R/R (3T0 HpOCTO CJIHHHIIa), a BTO-
poﬁ qJIeH Ha (R+h)/(R+h) (Tome emmnua), nonyqaeM 06mm?
3HaMeHaTeJIb (R + h)R B BblpameHHu
—KR _—K(R+h)
(R+h)R (R+h)R ‘
YpaBHeHHe, 3aaHHoe B TaKOM Bane, nae? BO3MO}KHOCTB
nponsnecm cnenylomee ynpomeHne:
R — (R + h) ] _ h
K[ (R+h)R ‘K R2+Rh°
IlJm 3HaHi’1 h, KOToe MaJIbI no CpaBHeHHIO c R, Mo>KHo
BOCIIOJIbBOBaTbCH npn6nnmeHHbIM BupameHHeM
h K
K R2+R'h§?h°
B STOM 6JImKeHH0M Bblpamennn MbI npeneépemm npons-
BBIIBHHCM Rh B 3HaMeHaTeJ1e, nocxoy 0H0 MaJIo no CpaBHeHHIO
c R2. LIToém ynocmBepmbcsl B KoppeKTHOCTH TaKoro 6J1mKe-
mm, BCIIOMHPIM, IITO pannyc 3eMJIH COCTaBJIHeT 6400 KM. ﬂame
B TOM cnyqae, Korna MbI paCCMHBaeM nanenne c BbICOTbI 1 KM,
npousseneH-ne Rh COCTaBHT Bcero 3141111: 6400, B T0 BpBMH KaK
R2=41 000 000 KM2. I'Ipn nepeMemeHHHx, HOCTaTOI-IHO Man
'
110
pB HHHI
c a H

142 FA. 5. Cum):
moéoro npyroro Tena. H03TOMy 15pm13 ~ mM/r. K03¢¢HuneHT npo-
nopunonanbnocm 110mm}! 613m) KaKHM-TO 06pa30M cnﬂsan c rpa-
BHTauneﬁ. OH 0603Haqae’rca CHMBOJIOM G. KOHee Bblpamenue
npnoépeTaeT 13pm
mM
Erpan. now = _ G r -
STOM
B a eH
nn a c a H e
I T a Tn epn
a M HK
aK
s p m
m
ma HT
OHH K p a

5.5. ﬂoreHuua/zbuan anepeua apaauraquu 143
(popmyna, IlpeﬂCTaBJIHIOT coéoﬁ ccpepbl. 3T0 OGBHCHﬂeTCH TeM, qTo
Mb] paCCMHBaeM 06Ho rpaBnTaLmOHHBIe BsauMoneﬁna
Mexmy unaHeTaMn mm 3Be3naMn.
OnHaKo (popMyJIa CHpaBeIIJIHBa 11.7191 cnyqaa nByx Ten c0Bep-
meHHo np0H3BonBHoﬁ (pOpMBI, ecnn TOJIbKO paCCTOHHHe Memny ux
ueHTpaMn r B0 MHOI‘O pas upeBBIInaeT pasMepBI Kaxmoro H3 amx
Ten.
B p
c .
1
. a c
me T eM
J mo JIH B
IO T a B me
n p -
e H O
3
8
0
0 M .
a nn
ce J
m paB e
HH pH e p H O

144 1‘4. 5. Cum»
llhramz
(DI/IF. 5.13. CxeMa yc'rpoi’icrna, c nomombxo KOTOPOI‘O Kasennnm «BSBeCHJI
sewuo», 113a mapa enJIeHhI Ha KOHuax CTepxma, IIOlIBeIIleHHOI‘O Ha Tonxoﬁ
HHTPI. Ob Heéonbmoe npn'rmxenne Mexmy HOJIBeIIIeHHbIMH mapaMH PI Gonee
MaCCHBI-IHMH HenonBHmHmMn mapaMH C03113€T mmnﬁ Memenr, Koropmﬁ c'rpe-
MHTCH noaepHy'rb crepmenb. LI'roém MOJKHO 6mm oénapymrrb H Hamepmb Manoe
OTKJIOHEHHe, B neHTpe c'repmm, Ha ocn ero Bpamenna, yxpenneno SepKaJIO.
B Taxoﬁ CHCTeMe nonopo'r CTepxma *Ha Heéonbmoﬁ yron BblablBaeT anaqmemv
Hoe nepeMemeHHe caeTonoro JIyqa no HIKaJIe.
qTo, ecnn HaM usaecma BenHa G, T0 MbI MO}KeM QupeneJIHrb
maccy 3eMJIn H3 ypaBHeHnH rpaBmaunn. nepHMeHTaJIbHoe
onpeneneHHe G paBHoueHHo BBBeUIHBaHHIO 3eMJIH! I/IMeHHo 3T0
nponenan B 1798 r. anmnﬁcxnﬁ XHMHK n (pnsnx FH KSBeHJIHIII.
BMeCTO TOI‘O qToébI H3MepHTb npmameHne Mexmy TeJIOM H KOJIOC-
caoﬁ Maccoﬁ 3eMJm, 0H namepnn Ob MaJIEHIO cnny
BsanMoneﬁCTBnH mayx Ten B naéopaTopnn. axcnepnmeHTaaa
yCTaHOBKa, KOTopoi’I 0H HOJIbBOBaJICH, cxemamqecxn u306pa>KeHa
Ha (pm. 5.13. KSBeHﬂHIH HMen BosmomHOCTb H3MeHHTb PI H3MepHTb
Maccm npnmmsatomnxca Memny c0601?! TeJI, a Taxme H3MepHTb
paccmsmne memny HHMH. HOMHMO Bcero npouero, OH HMeJI Bos-
MO}KHOCTI: namepmb ncxmoqmenbno maneHIo Iy, KOTOpaH
Heoéxozmma mm TOI‘O, qToébI COBllaBaTb TaKoe )Ke YI‘JIOBoe OT-
KJIOHeHHe nonBeca. 3aTeM y>Ke aHanneCKHM nyTeM 0H HameJI
Hensaecmylo BenHy G. 3Ha51 Benny G H CHJIy, paBH

5.6. Saercrpocraruqecrcoe aaaumoaedcraue 145
OHBHb mana:
G=6,67-10—11H°M2/KF2-
Bonpoc 5.14. LlonycmM, qTo ypaBHeHne rpaBma m
me I c e
pne co
ﬁ
po
I moe 6Ib
n om
r
o m
ﬁ
Te H
e b I
O o
-
H OCT H
npne eH
o K
B a
nm nﬁ mo
e no e
K n T e
n
.
a
c m -
ri’ n e
p
ne
c oe TH

146 r ll. 5 Cum):
momao cv-ma'rb, qTo Kaxmbm n3 sapsmos cocpeuomuen B 'Ke,
a He pacnpeneneH no KaKoﬁ-Jméo noaepxnocm.
B STOM cnyqae ypaBHeHne, OHH'CbIBaIOHLBC sneKTpOCTaTCKoe
BsanMoneﬁCTBue, OIIEHb noxome Ha ypaBHeHHe rpaB‘nTauHOHHoro
Bsanmoneﬁcmnn. OILHaKO ecnn npn I‘paBHTaHHOHHOM BsanMoneﬁ-
CTBHH Bsalmnoe BJIHHHHe OHPBIIeJIHJIOCb maccoﬁ m Tena, TO B cny-
Iaae anempocmmuecxoro BaaHMonei’xC'rBHH 0H0 onpenenae'rca aneK-
TeCKHM 3apﬂn0M q. HeKOTopoe ILOHOJIHHTeJoe ocnomnenne
CBHBaHO c TeM, tn‘o snempmecxnﬁ sapyw. MO}KBT 65m) nonommenb-
HbIM n OTpHHaTeJIIMZ +4 H —q. (ATOMHbIe SJICKTPOHbI HecyT
OTpHIlaTEJIIe BapHLLbI, B aTOMHOM nape cocpenomqen nonoxm-
TebIﬁ sapsm.) Snempocmmuecxaﬂ HOTeHunaaH anepmn
,uByx sapsulos OHHCbIBaeT-CH _Bb1pa>KeHneM
E33. 1101' = K 'qz.
me f—paC-CTOSIHHe Memny sapmaMn, a K—K03(p(pnuueHT npo-
nopunonanbnocm. ConocTe 3T0 BblpameHHe c (popmynoﬁ mm
HOTeHunaoﬁ anepmn rpasmamm, BeneHHoﬁ Ha CTp. 142:
mM
r .
Ep
a n
no
r

Pearone I47
menus: [um H'OTeHuHaJIbHOﬁ anepmn. Ecnu HOTeHLlHaJIbHaH aHep-
rpm HSMEHHB’I‘CH odpamo nponopunonanbno paccmsmmo, T. e. KaK
l/r, T0 Ia 6yner H3MeHHTbCH 06paTHo nponopunonanbuo KBaIl-
paTy paccroamm, T. e. KaK 1/r2. HoaTOMy BameHne mm CHJlbI
anempocramuecxoro Bsanmoneﬁcmna BaHHCbIBaET‘Cﬂ B Bnne
F3n=+K-qr_lzq—2'-
3T0 ypaBHeHHe H3BeCTHO KaK BaKOH KyJIOHa. 0H0 HaBBaHO Tax no
HMCHH OTKBIHeI‘O EI‘O (ppaHuyscxom (pnsnxa Illa
K y
J OH a
( 1
3

148 FA. 5. Guam
HOTCHuHaJaH aneprna cmamﬁ npyxmubl uponopunouanbna
KBanpaTy cmaTnH: Enpymm, n0T=1/2kx2. B STOM cnyqae cuna, c
KOTopoﬁ neﬁCTByeT npyxmna, nponopunonanbna BeJIHqHHe cmama
n HanpaBJIeHa B CTopOHy, npomaononomnyro cmaTmo, T. e. CTpe-
MHTCH BOCC’I‘aHOBHTb CBoéonHoe COCTOHHHB npymnnm: F = —kx.
B cnyqae OTTaJIKHBaHHﬂ nByx unnHnqecxux MaI‘l-IHTOB 110-.
TeHuHaaH aneprna npnMepHo nponopnnonanbua o6paTHoﬁ Be-
Jme paccromma Mexmy nomocalvm MaI‘HHTOB: Emu.ELIIOT ~ l/t.
CHJIa OTTaJlKHBaHHH 06paTHO nponopunonanbna KBanpaTy pacema-
HHH, T. e. ~1/x2.
Mm BBeJIH Texnnqecxoe onpenenenne paéoTbI KaK nponsaenennﬁ
cum Ha paccmmme, Ha npommennn KOT0p01‘0 neﬁCTByeT Ia
FAx. I'Io caMOﬁ cyTn STOI‘O onpenenenna pa60Ta paBHa Han/[ene-
Hmo nmenunanbnoﬁ 3Hepmn Toﬁ CHCTeMbI, Ha KOTop
B o
ne ﬁ
CTBy e TI
aM
3 p a
c m pm a
M H T
O-I OH e
I JI e H
H no a
- a,
-
I OH B a
Bo

Omerbz Ha eonpocbz 149-
,f —
rpaBnTaunonnoﬁ nocmHHHofl, MO}KHO Bblqncnm‘b Maccy 3eMJm He-
nocpeneHHo no (popMyJIe mm (:11 r
a B
T a n
n , K
y a
cn e ny e
ro na
Be
T
e JI amc
o 1

1‘11. 5. Cu/zbt
osnaqaeT, q'ro OHa HanpaBJIeHa B CTOpOHy MeHbUJHX 3HaHﬁ h. ﬂocxonbxy 3T0
HanpaBJIeHue no CBoeMy CMbICJIy eCTb HanpaBJIeHHe «BHHB», cnna rpaBHTauHOH-
Horo TameHHa HaHpaBJIeHa HMeHHO Tax, Kax 3T0 H nonxmo 6bITb.
5.2. HaKJIOH KpHBoﬁ E(x) HeBeJmK npn man
sae ux e po
ma u m n o
pa 're
r np n o ne
b C
O
K I s
n ae p m
x .
Ka T B e H
OTB e p H o
B o
craHa n n a
o a a n na aa mn x
n e
p pa
na a sa r np
n
o n b u
m n
e c o
maun an p m
b. O
K
OI Han n
pa
o nn m n
r
n n, B O CT aHa B
JIH Ba r
m aH T a p
y b no
x a
6 m, o
r n u T e
o
.
T
0 o aa a e

Oreerm Ha eonpocw 151'
+ 1 KP-M/C. Hananbnmﬁ Mnnynbc, (nMnynBc)aaq, paBeH —1 Kr-M/c. CHJIa paBHa
(“MHYﬂbc)xou — (HMnyJIbc)Haq + 1 — (— 1)
F = — — 20 H.
At 0,1
ﬂocxonbxy Ia uMeeT 0TpnuaTebm snax, oua HanpaBJleHa BHHB. I/ImeHHo
TaKoe HanpaBneHHe CHJIbI Mb] 11 npennonaranu.
~
1 0
. O l HH
co c oon
o a
a'r b
,
I T
O
E
1 r
, coc mT O,
q T o b n
o H OIH

152 FA. 5. Cu/lbt
I'IPAKTI/ILIECKI/IE PABOTbI
I. Hpoaeprca sarcona Fyrca Ha npywcuue
B COOTBETCTBHH c onpenenenneM CHJIbI, Ko'ropoe npnnnro B nacmnmeﬁ rJIaBe,
Bocc'ranaBnHBaroman cnna, paBaeman necpopMBpOBanHoﬁ npyxmnoﬁ, paBHa
-—kx. Oqenb HpOCTO npOBepmb, yLLOBJIe'rBopneT Jm Bron/1y ycnoamo Barman npy-
)Knna. (Hexompue npymnnbl He yJIOBJIETBOpHIOT; B 3TOM cnynae Haxonnennaa
B
3 e pnn
ea B a
/
2
x
. H one
CBe
O
JI H
o e n
y nb H
a H
O
Ta T
O
I Hn p o
m
l ﬁ
pon r
en nx pen e p
I I
MH
em a c
n r a o n

3a6at¢u 153
M
JI HI O no
o a
m yo epe
H a a no O
OI
HaT . H cx
n
b
x BaH H
o
c n
y a e
a
0H a e H e
H HH JI
b l Bl H
O
JIHeTCH TO JI
b
On n
n ne
n n
o , IH O
mH
n aT
b ,
T T OH H
IH
r y T
or o a
M JIH H I
O
1. B

6.1 . O epaeurauuu 155
Rifemﬂu
E1701
-———-—————1
Ompuuammwaﬂ .mepaux, Ira/na
y e
a c
a e m a
eH ane p
ﬂ o m,
e m u

156 FA. 6. Hercoropbte npwueneuun necrcoxzbrcux xouqenqud
¢I/II‘. 6.2. CHJIH, neﬁc'rByxomHe Ha TeJIO BHYTpPI 3eMJIH. Bum Teno pacnono-
)KEHO Ha paccmamm r 0T ueHTpa, T0 Hanpaanenuaa Hapyxcy cana, o6ycnoanen-
Han npummeHHeM ceKTopa, pacnonoxceHHoro Han TEJIOM, 1'0
y pa BHo aem u
-
B a
T C
c n
o
n p m e
nn a a
c C
KO apa
n
ono en oo
o T eJ O M
3a ne

6.1. 0 epaauraquu 157
4
Bonpoc 6.1. HpennonomnM, I1'10 3BMJI$I He BpamaeTca, 1110 0113
HMee’I‘ OIIHOPOIIHyIO IIJIOTHOCTI: 11 two COUPOTHBJIeHHe Bosnyxa 0T-
cyTCTByeT. KaK 11pm TaKHX ycnosmx CTaJI 61:1 llBHFaTbCH M5111, 6pc-
meHHbIﬁ B OTBepCTne, npocsepneHHoe 110 nnaMe
3 e J m
H a 1
1 0 H H
,
r
ocm a
, e
C T B
m m aH
M 111 op
e
e m
e

158 Dz. 6. HeKOTopble npumeneuun Hectco/zbrcux Konqenqud
rapdumu Jenna
I ran wanna
£110”!
ﬂanoﬂﬂumeﬂwax nomeﬂuuaﬂmaﬁ
ma, (Joya/703179311113 3€MHbIM IIIIYZUIIIEHUPM
(DI/IF. 6.3. COHOCTaBJIeHHe norenunanbnux $1M, 06yCJIOBJIeHH n
n T am
HH M e M
Jm H Co
m a .
o n oc
.
. T
OH OC bI
O
10
ne pB
n y
x Ha
a m n
x u m
p p O HT HT
I M I T ae
ny r
om yo
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6.2. Bpazqare/zbnaﬂ anepeuﬂ 159
BeJmLIHHbl Ha 3eMJ1e. CpaBHHM sneprnn saxsa'ra, 133513 111x 0THO-
IHBHHBZ
_ G ( mM3eMJIH)
EHOT. Bewm _ R3eMJIH
Enor.JIyHb1 — __ G ( mMJIyHb! )
rJIyl-ibl
_ M3eMJ1H rJIyHbI _ (6' 1024) (0’27R3emm)
_ MJIyHuRBemmz _ (7 1022) (R3eMJIH) N .
'Bonpoc 6.4. IJeMy paBHo omomenne cxopocm, HeoéxonnMoi’t
mm O’I‘Ba OT 3eMJm, K cxopocm, HeoéxonuMoﬁ mm OIBa OT
.HyHbI?
6
2 . p a
ﬂ a
Te IH a ae
p m T
a mH a e,
M
b B ea Ky
o T o a
T b
B e
e H O Be
me mm e
nne o o
p m noc . a x
m y
L m
K H o
C O T
BeT C

162 FA. 6. Hexoropbze npuueuenuu uecrconbrcux rcouqenqud
Korna BbI pacxpBaeTe. KaMeHb, BHBaHHbIﬁ x BepeBKe,
npnpona ueHTpocmeMHTeoﬁ CHJIbI OHnHa. Bama pyKa Ham-
I‘HBaeT BepeBKy, KOTOpaH THHET KaMeHb K ueH. Ecnh BepeBKa
pBeTCH mm 8131 BbInyCKaeTe ee H3 pyK, HEHTpOCTpeMHTeJIbHaH CPIJIa
HsaeT n KaMEHb JIeTm no KacaTeJIbHoﬁ. Hponcxomnenne ueHTpo-
CTpeMHTeJIbHoﬁ cum, onpenenmomeﬁ I‘OBoe KeHHe HJIaHeT
BOI‘ Comma, He TaK ouéBHnHo. HbIOTOI-I HepBbIM noxasaJI, qTo
HeooxonnM HH p
O T p
M I T e JIb
Hy I
cn y
o
aa e r pa
H Tu HII
p na H H
B a
a Tnae HI I
, ‘ o n
n n
b ax o e
co 0H
o
u e He e
m
' neH I
O o
pameHI I
IHeT
I m c

6 2. Bpamarenbuaﬂ auepeuﬂ 163
means; Kennepa, nonoB Taénnuy BepTBIM CTon6u0M co 3Haqe-
111mm: r3, HHTbIM CTon6u0M co 3H‘aHHMH T2 H, HaKOHeu, meCTBIM
CTOJ16110M co 3‘HaHBMn r3/T2. ECJIPI r3~T2, T0 r3/T2—IIOCTOSIH-
Haﬁ BeJIHa.)
[Inauera 'op6HTH T
Mepxypnﬁ 039 ram 0'24 TBemm
BeHepa 0.72 f3eMM 0'61 T3eMJIH
3eMJm 1,00 rsemﬂ 1:00 Tsewm
Mapc 1,53 gem“ 1’88 T3eMJIH
[OHHTeP 5'22 r3eMJIH “’85 T3eM-HH
'
CO H ome
HH e e
n e
a e
m
y pa I
H y
C OM 0 p H
Tb H n p H
OIO M o p
am e nm
CH
aBI JIB O
m H y
TH I K
OB m o
oo paH a
HH Horo '
e n a H
n pne
p
,
T com o

164 ['11. 6. HeKOTOpble npuMeHeHun HeCKOAbKux xouuenuua’
pnon oépameHnB COCTaBJIﬂJI 24 q. LITOGbI onpenenmb, Ha KaKOM
paCCTOBHBH IIOJI)KEH HaXOIIHTbCH TaKofi cnyTHBK, MO)KHO HCHOJIb30-
BaTb coomomeHne KenJIepa H COHOCTaBHTb pannyc 0p6HTbI cny'r-
HHKa c pannyCOM 0p6HTbI JIyHBI
3 2 3 2
rCHYTH Iknyrn rCHYTH l
3 2 ’ 3 2 '
r Hm T am (384 000) 27
33M€THM, qTo sneer) 06a nepnona BBIpameHBI B cyTKax, 06a pann-
yca — B KHJIOMeT. C 3eMJm MbI BHJIHM, qTo ﬂyHa B03BpamaeTca
B HeKOTopoe HCXOIIHOE nonomenne omocuTe/zbuo 36e36 npnénnsn-
TQJIbHO qepes 27 cyT. (I/IB-Ba KeHHB CBCTeMBI 3eMJIB—JIyHa
BOI‘ Comma .HyHe Tpe6y10TCB eme 0mm cyTKH, qT06BI ﬁTH
B ncxonnoe nonomenne no omomenmo K 3eMJIe H COJIHuy.) I/IMeH-
HO 3T0 BpeMB — 0T HOJIHOJIyHI/Iﬂ no HOJIHOJIyHHB — Mbl 06BI
c
m T e H e p
IIOIO M
0
pam H H BI H
BII J B H
1
u
neﬁ p
a
c e r
o p
ém cyT
H KO
B ) JI IIy e
HC HO JIb
OB Tb

166 FA. 6. Henoropbte npumeneuun Hecrconbrcux xouqenquﬁ
’
——-—
¢I/I1. 6.6. CnyTHHK B pemme «CBOéOILHOl‘O nanemm» no HanpaBneHmo K 36MJI&
HOCKOJI HO
BX
H
O Cb e
M m
p p e
a, o a
y o nm
0 T cn TH
a
. /
1
3
-
p a
x e
nbT
a e K
T o H T
e x aK
e T ,
C

6.3. Momenr umnyxzbb‘a 167
6bl Ha 36MJIIO, eCJm 6B1 ei‘o CKOpOCTb 6bIJIa HenoéTaTotIHoﬁ mm
3eMJm 6bma nnocxoﬁ. Moxmo cunTaTb, qTo CHyTHHK nanaeT Ha
3eMJ1Io, HO HOBHOCTb 3eMJm, noc'Koy 0Ha KpHBOJmHeﬁHa, KaK
6b1 yKJIOHHeTCH OT Cl'lyTHHKau
B npo
c
61 0
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mm
o n o o
H T HH a
. H
on o
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c ny TH
, B
Oo
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o n me
m x eT c
In o H o o
ée
c m
MH y
T HH
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C HIO O
CTB
a H T
er o .
T O n
p ono
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e

168 1‘4. 6. Hercoropbze'npumeueuun necxoxzbtcux rcouqenqua
(DI/IF. 6.7. Hoacnenne onpeneneHnn momeHTa HMIIyJIbca omocmenbno HeKOTopoﬁ
ocn. ﬂame eCJm KoubKoéemeu nepememae'rca no npaMoﬁ .nmmn a He conepmaer
mBoro nBHmeHnn, OH TeM He uenee o6nanaer MOMeHTOM munynbca omocn-
Teo Tomm 0. Beam STOT KOHbK066)KeLI BO3bMeTCH aa pyxn c npyrHM KOHbK0-
demueM, CTOﬂILleM B Totxxe 0, 06a mm HaqHy'r BpamaTbca npyr 0THOCHT8JIbHO
npyra, n MOMeHT Hmnynbca HarmmHo npoaBmeTca.
>Ke, KaK HeCKOJIbKo pacmHyT
a n
n T -
c
xy
ro o p
m y
Jo o H
n nH e
T. H c ee
ya 3
aH I O M
e HT IH
M

169
6.3. Mouem' mung/wed
/ l
(DI/ll. 6.8. Ecmx MOMeH'r HMHyJIbca mvr oc'rae'rca IIOCTOHHHHM, T0, Korna KOMeTa
nBHmeTca no opén're Boxpyr Comma, cxopocn v nonxma memn‘bca.
(DI/ll. 6.9. lIBa MaXOBHKa, Maccm KOToX OlIHHaKOBbI. Macca neBoro Maxonnxa
cocpenomqena Ha oéone, KaK y Benocnnennoro Koneca. Macca npaBoro mam--
a cocpenowouena- 36.11143»! ocu. I'Ipmaecm BO BpameHne mm ocranonmb nenoe
Koneco auaqmenbno zmee,
n aB e B am
a ru
m
xna
O H a K
T
O
eHM I OT
I H Ha O
b e Ma c mH
Oa H I e
KO H
C K H
H
(nr
.

170 FA. 6. Hercoropbte npwueueuux Hecrxux xouuenqua
——-—~
’
li’pymauwi money”: a r x F '
[Mezzo
# r
‘ _/ puqaaa
I, 005
ﬂepneudulrympuax
cum
DI/II. 6.10. Hpncnocoonenne, nosaonmomee Bpama'rb nacmx no I‘OBoﬁ op6n're
nepemeHHoro pannyca. Benn Mb! TﬂHeM mHypox BHHB, TO Ta o
paa o m y
meH bm e Ma nn
y c
H
e J
a
aa c n c
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r a
. H
O C OJI
c nane c
ry e ra.
a
m B I
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nyca
MOe H
T MyJIbca H eM H
e T

6.3. Monet” wuny/wca I71
(DI/Ll. 6.11. Hponanonbnoe (yCJIOBHoe, HO no'JIeanoe) HanpaBJIeHHe momem‘a mu-
nynbca —_ruanpaBneHne 131mm: ocn BpameHHH—onpenenae'rca onenyloumM npa-
BHJIOM: ecnn nanbuu npaBoﬁ pyKn H3OI‘HyTb B HaﬂpaBJIeHHH Bpamemm Koneca,
T0 Gonbmoﬁ naJIen oxameTca HaHpaBJIeHHHM 3110.111: ocn B Hymo cmpony.
ﬂHO H3MeHHTb; 5mm qacmqno OéBHCHHeTCﬂ, noneMy IOBeK
.ynepxmsaeT paBHOBecne Ha myLueh/{ca Benocnnene, HO He MO-
}KeT aToro ClleJIaTb, Korna Benocnnen HenonBHmeH. ECJIH IOBeK
I'IbITaeTCH HaKJIOHHTb Koneco Benocnnena Ha xony, T0 0H HCHbITbI~
BaeT He npoc'ro coupomBJIeHHe TaKoﬁ HOHbITKe—HaﬂpaBJIeHHe
CHJIbI COUPOTHBJIBHHH OKEIBaeTCH nepneHnnK

6.4. yeue 470! norenquanbnoz‘i auepeuu 173
6
. I
p m e
b p
m u n e u au
bo a e p
n
H am
OC HOH
o m
eT o
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a Hn HHO TH
n a
IH oﬁ a nep
nn n o
M
H 110 p a
O O b nn o
OTo e . o c n

174 [‘12. 6. Hexoropbte npwneueuun necrconbrcux xonqenuud
ﬁn)-
<I>Idl‘. 6.13. l'IoaeneHne rpyaa, cmmalomerp npymmy, onpenenae'rca nnyma BH-
naMH no‘TeHuHaoﬁ aneprnnz sneprneﬁ rpaBHTauHH n aHeeﬁ upymmm.
CyMMa EUWJIUM +Eepac. mm
~
am
II.
— E n p m
m
E n a

6.4. eue ¢0l norenquaﬁbuod suepeuu’ I75
g
a
I
~
E u
0 Eu
‘
0
m a e
. n

176 FA. 6.‘Hetcoropbte npwueuenus Hectcoawcux nouqenqua
5mm ' I ﬁ‘ 1'
a
Paanaaecnoe
- paccmoxuue
Urn/namruaauue
+
F > 1'
ﬂpumnatceuue
(DI/IF, 6.16. HpaBnononoénaa Baa norenunanbnoﬁ sneprnn mm CBHSaHHOI‘O
mom (a). Cma, Koropyro PICHbITbIBaeT aTOM npn nepememennn BHyTpH no'ren-
unanbnoﬁ HMbl (6), M0)K8T 65m; Haﬁnena, ecnn nocrpomb rpa H
ano n a
K pH B o
n T e
HHa o ae
pn n BOBe ee
T eq a x .
c
n m
e n u
n B
y x aTOMO HO
b a o
e ac mm e o nna
B OH
H aTb HK T
p H
Ia

Pearoue I77
Pealome
B aToﬁ I‘JIaBe Mbl l'lOJIbBOBaJIHCb BBEHEHHbIMH paHee HOHHTHHMH
HOTeHunaoﬁ aueH H HMHyJIbca H pacmnpnnn 3TH momma.
Mbl BHILEJIPI, l1T0 HCl'lOJIbBOBaHHe HpeIICTaBJIeHHH o n0TeHuHaJIbHoﬁ
aneprnn I‘paBPITaIlHPI HOBBOJIHeT Oé'bﬂCHHTb MHome HBJICHHSI, c1351-
3aHHbIe c paKeTaMH H cnyTHnKaMn. I‘pa H
T eH H a
JIb H
o 3 e
pm u p
a B H Ta n n
HOT po e H
b I
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6
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e
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p e T
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K a

178 1‘4. 6. Hexoropbte ‘npuueneuun' Hecrconbrcux xonuenuuﬁ
BpameHHH. MOMeHT HMnyJIbca HMee’l‘ KaK BeJIHqHHy, TaK H HanpaB‘
JIeHHe. BHyTpH HsoHHpOBaHHoH CHCTeMbI BeHHqHHa H HanpaBJIe~
HHe MOMenTa HMnyJIbca COXpaHHIOTCH. PeaKu-HH Bpamatomeﬁca CH<
CTeMbl Ha BHemHee BosneHCTBHosIBJIHeTca B I‘HpocxoeCKHx
sdxbex'rax.
Fpa¢CKHH MeTOIL oaHHH HOTeHuHaJIbHoﬁ SHepI‘HH CHCTeMH
c ycnexom HpHMeHHETCH H B Tex cnyx, Korna MbI He 3HaeM, 1(3-
1016 CHJIbI HeﬁcyTByIOT Ha Teno. Hamep, ClleJIaB CaMbIe 06111He
npennonomeHHH o TOM, KaK yHepmn‘BaeTCH aTOM 'B TBeOM TeJIe,
MbI momeM npemcxaaa'rb OCHOBHbIe MOMeHTbI ero l'IOBelLeHHH.
OTBETbI HA BOI'IPOCbI
6.1. I'Iocxonbxy CHJIa, neﬁcraylomaﬁ 113 Mini, HpOIIOHOHaJIbHa ero pacc'roa-
mm or ueHTpa Baum H HanpaBngHa K ueH
3M
JI
H M a
61
1
e B e
CTH
e
o
a T a x e H a r p
a H a ar
o HH a B BHH
H Ha m
H e. H
1

Qwem Ha eonpocbt I79
*—
I
yqnmaaa, q'ro 01m Haxona'rcn B paanux cumemax KooHaT n Ha6monalow
cnny Kaxmuﬁ n3 cnoeﬁ CHCTEMhI.
6.6. e Bbumcanu BeIﬁ 14 115111113 CTonéubI TaGJ‘Hﬂlbl, conepmameﬁ
pannycu opém u nepnonu oépamenna nnaHeT. HenHo BHIle'l‘b, q'ro 0THomeHue
r3/T2 mm Bcex nJIaHe'r paBl-IO npnmepno enmmue.
I'
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M e
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0
0
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,
0

180 FA. 6. Hercoropbte npumenenun Hecxonbrcux xouqenqud
O
6.13. BenocnnenHoe Koneco MOI‘JIO 651 Bpama'rbca TOJIbKO c KaKoﬁ-To conep-
meHHo onpeneJIeHHoﬁ qacm'rofd mm c qacm'roﬁ B 113a pa3a Gonbme, mm B Tpn
pasa éonbme H T. n. KpOMe TOI‘O, yron, xapaxrepnayromnﬁ opHeHTaumo ocn K0-
JIeca, M01‘ 611 H3MeHHTbCH TOJIbKO Ha Heéonbmyro nncxpewyro BenHy, Tax qTo
ocs Koneca He moma 651 SaHHMaTb npomemuoro monomemm memny STHMH
ymaMH.
6.14. CBH3aHH08 c npymnnoﬁ TBJIO 6y11eT HaXOIIHTbCﬂ B paBHOBeCHH B To?!
Totlxe, B Ko'ropoﬁ KpHBaH, npenc'raanmomaa cy KHHeTcxoﬁ H I‘IOTeHuHaJIb-
Hoﬁ aHeﬁ, nMeeT HyJIeBoﬁ Harmon. Ho 06e CTOpOHbI 0T Hee Ha Teno neﬁ~
c113 Bo c c aH
anna o mn enn
, C T pe
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pa T H T
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17 parcruttecrcue pagan»: '18!
ﬂycman Kanwpeuan
[ 1’ [j 1
Tpmxopaannoé
_ npauepueame/m
V
¢VIF. 6.17. Hpoc'roe yc'rpoﬁc'rno mm KaqecTBeHHoﬁ ouemm ueHTpotSexmoﬁ cmm.
C'repmenb nm‘ca K Topuy 6mm Jmnxoﬁ JIeHToﬁ.
411:2 z
lleumpodexcnax C'IJJM = m r= 11141
P n mn n e
m a n ﬁa T Te
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a m

182 FA. 6. Hercoropue npwuenenuz necxonucux tcouqenzgud
f—qaCTora (uncno odopomn B ceKyHny). CJIelIOBaTeJIbHO, MOMBHT HMHYJIbCa
Tena, mamxymeroca no oxpyxmocm; paBeH m2nr2/T = 2nmr2f. Ecmx Moment
umnynbca oca‘aeTca HOCTOHHHHML TO panHyc Bpamenna TeJIa nonmeu yBeJmtm-
BaTbCﬂ npu yMeHbmeHHH uacm'm mm Haodopor. '
Hroébl omy'rmb error supper“, canb're Ha Bpamaloumﬁca CTyJI n menneHHo
Bpamaﬁ'recx: c BbITﬁHyTblMH B croponu pyKaMH. BHeaanHo npnmmn're pyKn R my.
3T0 yMeHbIHHT pannyc new name? maccu. 3¢¢exr 3Haqm‘enbno ycmlmca, ecnu
BbI Gyne'rc nepma'rb B BHTHHyTbIX pyxax TOJICTyIO xnnry mm npyroi’i TameJIi
npenme'r. qTOébl BHOBb samezmn'rb eBoe Bpameune, ecnu BbI, Koneqao, eme He
caeTeJm co CTyJIa, 11 core OHHTb pacbTe pyxn.
BHI/IMAHI/IE! ynb're oc'ropomHu, nponenmnaa STOT OllblT. Scptpexr MORE?
6511*}: TaKHM CHJIIM, qTo qenonex mome'r nmepa'rb paBHoaecne n yuaCTb, JIH60
,ynapmbca o Kaxylo-Hnéynb meéeJIb,
TaKoe me HBJIeHHe M0}KHO Haémona'rb c HOMOLIIbIO npocmro ycrpoficrna,
nsoépqmennoro Ha (bur. 6.10. HponeHbTe mHypox qepea Kaxyro-nndo 6xy u
npnxpenm‘e K ero Konuy qTo-Hnéynb Mill‘Koe, Haupnmep nacmx. HOJf53YHCb 6-
K0?! xax pyxoa'rxoﬁ, Bpamaﬁ're nacmx B ropnaomanbnoﬁ nhocxocm c panHycou
-BpameHHa oxono 30 CM. llpyroﬁ pyKoﬁ neTca y‘llepmHBaTb umypox, qTo
o
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300mm 183
)Kezmuﬁ MOMCHT'BblShlBaET nonopor B HaHpaBJIeHHH, nepneunuxympnom ommae-s
momy. Bu mome're omy'rmb 9TH annexing, Korna eng're, He nepmacx: 3a pymx.
Haxnonmecr: B CTOpOHy n HOCMOTpme, Kyna noaepHeT KOJIECO.
ECJIH y Bac ecu: Benocnnennoe K'oneco 6e3 Benocnnemiofi pa, nonBTe
ero Ha npotmoﬁ BepeBKe 3a 0mm Koneu ocn, Kax noxaaauo Ha (pm. 6.19. 11011-
nepmnnaﬁ're KOJIeCO B Bepmxanbnoﬁ IIJIOCKOCTH n 38¢

184 [‘12. 6. Hercoropbze npwueneuun Hecrcojzbrcux xonqenqua
:reca, uro anepeuu apamenun Bbl npunucuaaere npaau/nbuuﬁ snare. 06paTnTe Bnn-
manne Ha T0, qTo )KeCTKOCTb npymnnu k canaana c nocronnnumn apamennn, n60
cnna Ha'rnmennn npymnnu = — ueHTpo6emHan cana,
k _ 4n2
— f — — m 72— f.
k _ m4:n:2
__ T2 .
MmeeT nn nonyqennui’i peayaT CMbIcn? (Oépamre Bnnmanne Ha T0, two man
8131 'rae'r n o r nn
pnn
yc y a py en n
e H
,
bI
3a a Te pa
6
0
y a n e
n o n en e
ue HT o e
H
o ﬁ C HII .
Bn n
6
1
B B

FJIaBa cenbMaa
TenJIOTa, TeMnepaTypa
n coxpaHeHue aaeprnu
Tenepb, HaKOHeu, Mb] IIOJDKHbI OKOTeJIbHo nonBecm morn.
B axcnepHMeHTax c éeryHKaMH Ha Bosnymnoﬁ nonymKe. oun-
caHH
B m
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. b

186 [‘11. 7. Ten/tom, reuneparypa u‘coxpaneuue auepeuu
OHa 06’bHCHSIe‘I‘ H npyrue HBJieH'HH, Tame, KaK B03HHKHOBeHHe
CBeTa mm

7.]. Ten/101a u remneparypa 187
C
Haepeeamenb
(DI/ll. 7.1. Hexoropoe KonnTBo Terma Harpeer Bony B Heéonbmom cmxane,
H0 0H0 He cmome'r sameTHo H3MeHHTb «HarpeTocrb» 301151 B HanonHeHHoﬁ BaHHe.
DI/IF. 7.2. Teopua Tennopona odbacnae'r nepeuoc Tenna cympCTBonaHHeM no--
Toka Hennnnuoﬁ mnxocm, HanpaBneHHoro 0T ropnqero 'reJIa K xonozmomy.
u
c e n
oa Te I e
ﬁa M IC
JI ,
To

188 FA. 7. Ten/tom, Temneparypa u coxpaueuue aHepeuu
Haémonalomeeca pacmnpenne Ten H
a
pea nn O
é
bﬂCH
JI
O b
o oe
H e Te
nn o pna
I
I mn p o
a e me n
a
T n
I pn oﬁ Tep
a e
n
JIOTb I n
T pe
-
O B a
J K
on n T e
H Ia
c e p
me b
l . m
epT JII
y a p e -
pn Te n n
po ab I
I H aec
e T e ,
I n c
0

7.2. Hamepenue reuneparypu 189
4‘.
0
00%?
.
W
/ l
4/
Malaya .00 J
F
I
J
0 ~

190 ['21. 7. Tenmra, reuneparypa u coxpanenue suepeuu
Bonpoc 7.4. ByneM HCXOILPITb n3 TOI‘O, qTo MeTaJIJI, y KOTOpOI‘O
H3M€HeHHe llJIHHbI éonbme, B Harpe'roﬁ 6nmeTaJIJInKoﬁ HJIaCTHH-
Ke Bcerna pacnonomen c BHeIIIHeﬁ CTOpOHbI. LITO nponsoﬁne'r, eCJm
TaK CO T a
H I O
nn
a
c H
Ko x a n
b n
o e n e a
yn a e

7.2. Hauepeuue Temneparypbt 191
a 6 8
8
A
q q Pucm - 100
- 90
- 80
Mewamra 70
~ 60
a 50
- 40
L 30
f - 20
' g: - 10-
g :. o
Kunﬁwaﬂ
306a
(DI/[1. 7.4. a— HexannépOBaHHuﬁ pTYTHbIﬁ TepMOMeTp; 6— Ha many Haneceaa
pncxa, omeqalomaa ypOBeHb pﬁry'm npn Temnepa'rype 'ramma man; a — Ha mxany
HaHBCEHaBTOpaﬂ pncxa, omeqaromaa yponenb pTy'rH npn Temneparype Knnennn
301m; 2— HOJIHOCTbIO orxanuéponannuﬁ Tepmome'rp.
ero rIOKasaHHIP'I MO)KHO yéemu‘bca, nowremaa Tepmome'rp TO B 3a-
Mepsaromyro, TO B Knnamyro Bony; npn STOM p'ry'rb nonmna Ha-
XOIIHTbCH COOTBeTCTBeHHO T0 Ha HyJIeBoﬁ OTMETKe, TO Ha OTMeTKe
100. (cnpya BbICOTy pTyTHOI‘O CTonénxa Ha HIKaJIe, MbI momeM.
namepm‘b 3106 T e H
ea
y y B pn
nx
op ae HH b
l x am
M H
T
a J OH
I
M I T
o t Ia
M H
. B e
CT n e o
m

192 FA. 7. Ten/20m, Teuneparypa u coxpauenue anepeuu
a
r‘ F (DI/IF. 7.5. Hpoc’roﬁ raaonuﬁ TepmomeTp. Bmcora raao-
H mm CTOJIGHKa, Hamepaemaa no HmKHeﬁ nonepxnocm
KanJm pTyTH, nponopnnonamma Hamenenmo 06 bema raaa,
saxmotxennoro B c'reKJIaHHOM Kanmmape.
Illnlull‘
Ifdﬂflﬂ
pmymu
ll .L A‘Uh‘ All:
. l'a3, .
g aazmwvemw
; -3 Rana/map
l
—————>‘
Tl 111.:
0mm H3 TepMOMeTpOB IIOCTHI‘aeT OTMeTKH 50°,
‘fmelrlmmué 3T0 03HaqaeT, I{To T0 CTBKTeJIbHoe K TeM-
‘W’WWP nepaType caoi’icmo, Ha KOTOpOM ocnoaaH
TepMomeTp, xapaKTepnsyeTca 3HaHeM, paB-
HbIM nonoanHe pasnocm ero Bennqnnbl
npn TotIKe KHHeHHH H
1
0 sa
e
pa -
H K
3 1
1
1.
n py oo
T ep
O M
e Tpa pT o
>K eT e
M H paT
pe CB KTe

I .
I
I
I
5‘. Fa: cmuwaemcx l
3 :
E I, l
g l/ I
a / I
x’ I
/ l ——>—-
273°C 0 ’6’
Temnepamypa
(DI/IF. 7.6. Banncnmocm oébema raaa o'r Temnepa'rypu, sxc'rpanonuponannan
K 1‘0, B Ko'ropoﬁ o6beM 6m: 61:! paBeH Hymo.
F °C K
m
212 — 100 — 3 7.1 Z [funemze soda)
.98, 6‘ —— — 3 7 . .310 Hanna/1611a,? mmnepamypa mam var/0mm
7 I, 6‘ — ZZ ——Z.95, Z Odom/{ax KOMHEIIIHJII men/zepamypa
32 —‘ — 0 — 2 7.3, 15 Jauepaaﬂue was!
- 38 —— - 58,9 — 234, I Jauemaﬂue pmymu
- 45.9, 8 — — - Z 73, I5 — 0 Adm/710mm”? b

7.3. Mexauuuecxud ensued/zen? rerma 195
Bonpoc 7.8. Hoxamme, qTo HpaBHJIbHaSI (popMyna mm nepe-
Bona TeMnepaTypBI B rpanycax LIBJIbCHSI B rpanycm' (DapeHreﬁTa
MMeeT Bun: T(°F) = 9/5T(°C) +32. HeMy paBHa lIHCJIeHHaH BeJIH-
qHHa TeMHepaTypbl a6c0JIIOTHoro H
Bl a
I e
(a e Hr e
T a
(
m .
.
7
)

196 FA. 7. Ten/tom, Temneparypa u coxpaHeHue anepauu
1
e%
@
/’7
/ %
%£%%
/cw/
%1:1::D%Ah
% %x
/ ///:
1
(DI/IF. 7.8. VCTpoi’ICTBo mm H3MepeHnB KonnTBeHHoro COOTHOHIeHHﬂ memny
TenJIOToﬁ H mexaecxoﬁ aueprneﬁ. (1/13 KHHI‘H: F. T. Bonner, M. Phillips,
J. Raymond, Principles of Physical Science, 2d ed;, Addison-Wesley, 1971.)
I
BBIpamaB BennBI B JIeBoﬁ qacm ypaBHeHHa B‘ CHCTeMe MKC
(MeTp, KHJIOI‘paMM, ceKyHna), MbI nony
s ne pm
oB m Ko
x
1 1

7.3. Mexanuttecrcuﬁ axeueaneur Ten/la 197
ff
memny KaJIOpHHMPI n mKoyJIBMH. Bce nocnenyroume SKCHepHMeHTbI,
onuparoumecn Ha 3T0 coomomenne, Harm“ comacyroumeca pe-
ByJIbTaTbI. I/ImeHHo TaKoe COBnaneHne pesyJIBTaTOB pa3HB1x axe-
nepnMeHTOB HOllTBUlaeT cymBCTBOBaHHe 3aK0Ha coxpaHeHna
aneprun.
Hemeuxuﬁ qmsnK I‘epMaH I‘eJIBMmJIBu 3HaqHTeJ1bHo pacumpml
Konuenumo aKBHBaJIeHTHOCTH MexaHcxou n TeHJIOBOH aHepmn.
B pesyaTe 6BIJI yCTaHOBJIeH 603% 061mm 3aK0H COXpaHEHHH
aneprnn, pacnpompanmoumnca Ha aneKTpnqecx, MaHym, xn-
ecxyro H Bce npyme BHIIbI aHepmn. STOT 3aK0H MO)KHO npenma-
BHTb B paBHBIx (popMax, HO cymHOCTB ero cocmm B TOM, Ino 0H
0TpnuaeT BOBMOKHOC'PI) yHHqTomeHnﬂ mm cosnamm aHepruu. I'Ipn
£106 n
oue
c
xH p
J o
b
x
Ba H
M Oe
ﬁTH H n ep
ae n
O
I HI‘ B
n a
B B
3
Be T o
n TB e
Ho B B Ba
IH Ho
e Be e H
e a K o-
J én p y oe
e
p

198 1‘ A. 7. Ten/207a, Temneparypa u coxpaueuue anebeuu
<bI/II‘. 7.9. B Bononane 3011a HeCKOJIbKO xononHee BBepxy, a w
a
y
,
e.
a c r
b H BIH
H n H men
n pe B
am a T
aBeH IO
. e

7.4. Hponexzenun aHyTpermed anepeuu 199
7’
Kaxmblﬁ KHJIorpaMM Bonbl' TepHeT HOTeHH-HaJIbHYIO sneprmo
mgh = (l KI‘) (9,8 M/C2) (60 M) = 588 Am. STa I'IOTeI-IIIHaJIbHail
aneprnﬂ nepexonm B KnHeTcxyro a’Heprmo nanatomeﬁ BOllbI, Ko-
Topaﬂ B CBOIO oqepeub npu pe3K0M Topmomeuun BOlIbI y nonHmKBa
Bononana nepexonm B TeIIJIOByIO aHeprmo. KonnTBo BBmeJmB-
mefdca ‘BHyTpeHHeﬁ aneprn'n paBHo 588 11>K/ (4,185 IbK/Kan)=
= 141 KaJI._ECJIH onHa KaJIOPHH y-BeJIHImBaeT TeMnepaTypy onHoro
rpalvma BOILbI Ha 0mm rpanyc HBJIbCPISI, T0 141 KaJI yBeHT TeM-
nepaTypy 1000 r BonBI Ha 141/1000 = 014°C. MaK-OHMaJIbHaﬂ Be-
JIHImHa pasnocm TeMnepaTyp, TaKHM 06pa30M, AT=0,14°C.
ﬂmoynb 6BIJI HaCTOJIBKo nornomen axcnepHMeHTaMH no Hayne-
HHIO nepexona MexaeCKoﬁ aneprnn B TenJIOByIO, L1T0 name Bo
BpEMﬂ CBoero CBaIL66HOI‘O nyTefneCTBmI no IUBeﬁuapHH HpOBepHJI
y Bononana CBOH peTBI (cpnr. 7.9).
B on
p c .
10
.
(a'r
n
K a
H pa

200 FA. 7. T en/zora, reuneparypa u coxpaneuue auepauu
Ty m n s Me
e HH e a
K o -
T o K
M
uH a u
n H
m n
a a MT O B
.
on ne
m an e
p mn
,
H 0
6
O
IH O
m
m H Me eHm IT
M n eaT
y H
a
°C
s a
ra nc
m 0 KO
e CT aB na e

7.4. Hpone/zeuun anyrpeufted snepeuu 201
_
CKOJIbKO 3a6e>KaTB Bnepen n Becm HeKOTOe IlaHHbIe o MBKpo-
CKType BemeCTBa, KOTopofI MbI 6y11eM BaHHMaTbCH B CJIBIIYIOIIIPIX
I‘JIaBaX..I/I3MEHBHHH, KOToe nponcxonm‘ B BemeCTBe
lI OI
JI O
m e n
u e J
O B
o ae pn nH
I T OI
I e m B
1
0
1
.
0
6 13
m

TA. 7. Ten/10m, Teuneparypa u coxpauenue snepeuu
1,0-10'” ~ a
M
~ 6
E 3
‘5 E
E g 0.5-10'” -
Si
sa‘E
0 I00 [000 10000
Teunepamypa, K
ﬂupum . 0'
weer/mm“,
-33 08W?“ M965 (Kant/add”)
‘ 1,0 - 10
to
E
3
§ 5 .23
E S 0.5 '10
E E
5‘3 a:
0 200 400 6'00 800 [000
Temnepamypa, If
/ (DI/IF. 7.10. a —TeMnepaTypHaa saBHCHMOCTb ynenbuoﬁ TBIIJIOBMKOCTH nonopozla
(npn no'cronnnom oéﬁeme), BupameHHaa B Kan/(monexyna orpan). Oépam’re BHH-
Lianne, q'ro mKaJIa Temnepa'rypbl -— norapmpmuqecxaa.
6—ynenbnaa Tel'IJloeMKOCTb HeKOToX TBebIX TeJI. Bonbmnncmo merannon
mueeT npnénuamenbno onHHaKonylo ynemanylo TennoeMKoc‘rb npn KOMHaTHoﬁ
TemnepaType (BOO-K) B ennunuax Kan/(aTom-rpan). (Oépamre, onHaKo, annula-
we 33 noneneHHe éepHJIJmH.)
TeHJloeMKOCTb Bonopona H3M€HH€TCH TOJIbKO H
e
KO I
b K H
OH eI
JI e HI T
eMep a T pax
Be TH
pe r pHo
c
—
n

7.4. ﬂponaneuun anyrpetmed aHepeuu 203
#—
BaTeJIbHo, IIJIOTHOCTb )KI/IIIKOCTH, 06pa30BaBmeﬁcs1 npn nJIaBJIeHKK,
ﬁonbme nmomocm TBepnoro BemecTBa. Ho STOﬁ nKHe .1161]. Ima-
Baer B Bone, a TBepnBIﬁ BKCMyT -— B paIaBJIeHHOM BHCMyTe. ECJIH
IIOIIBOIIHTI) sneprmo K Bone, Haxonameﬁca npn 0°C, 06’beM 8011b!
6yneT yMeHbIﬂaj‘bCH 110 Tex nop, n0Ka ee TeMHepaTypa He IIOCTHI‘HeT
4°C. BbIIlIe STOﬁ TeMHepaTypBI Bona BeIIET ce6H HopMaJIbHO, 'r. e.
pacumpsie'rcsi npn IIOILBelleHHH TenJIa.
ECJIH TenJIo nocrynaeT B ra3, Haxonﬂmnﬁcsi npK HOCTOHHHOM
naBJIeHKK, T0 06'beM rasa Bcerna yBeJIKqKBaemH. B T0 BpeMﬂ KaK
omocmenbnoe yBeJIHKe o6'beMa y TBepIIbIX TeJI H )KKBKOCTeﬁ
o‘B Mano, y ra30B 0H0 oneHB BeJmKo. 3aK0HBI sToro pacmnpenna
OﬂPlcaHbI B WI. 10, H0 mm cpaBHEHHH OTMeTHM, q'ro npK HOBbImeHKK
TeMnepaTypBI pTyTn Ha 1°C ee 06’beM yBeKBaeTCB Bcero Ha
0,01%. TaKoe >Ke HOBbImeHHe TeMHepaTyr asa, Haxonﬂmeroca
npn I‘IOCTOHHHOM IlaBJIEHI/IH, BbI3QB€T K3MeHeHKe 06’b€M3 Ha 0,40/0.
OTHoeJIbHoe H3M€HeHHe o6BeMa y rasa npKMepHo B 40 pas
éonbme, y
p T T
. 0
613m nn
nne n e H
K T e n
JI a K B
me T B
Te
M n
e a T
y a no
-
ne ne o o
pa
T a e T OI
H a
K O B B
y
c ny a a
s
T o
r o M
0K T He p on

204 1‘4. 7. Ten/101a,. remneparypa u coxpaHeHue anepeuu
K Bosneﬁcmmo TenJIOBoﬁ anepmu Ha BemBCTBo. MB1 CﬂeJIaEM 310
c HOMomBIO npenJIaraeMoﬁ qMoneJm, KOTopaH OCHOBbIBaeTCH Ha
aTOMHoﬁ MHKpOCKType BemBCTBa.
7.5. Mone.'.1B MHKpOCKTypH BemecTBa
Comacno MoneJm, KOTOpaﬂ 6y11eT nanomena B cnenymmeﬁ
I‘JIaBe, BceBemBCTBa, KaK TBepIIbIe Tena, Tax 11 mnnxocm mm ra3B1,
cocmm‘ 113 Meaﬁmnx qacmu, Ha3bIBaeMbIX aTOMaMH. B pane
cnyqaeB HBCKOJIbKO TaKHX aTOMOB MOI‘yT 06pa30BB1BaTB CTaénJIBHBIB
KOM6HHaLlHH, 11a3B1BaeMB1e MonexynaMn. HpH OﬂpelleJIeHHbIX ycno-
BHHX MoneKyJIBI HI‘paIO’I‘ ponB OCHOBHbIX cyéqacmu 11 HeT HnKaKoﬁ
HeoéxonnMocm BIBaTB ’I‘O, l110 01111 cocmm 113 eme éonee Men-
KHX qacmu. KaKne pasMepBI 110.11>KHBI HMeTB aTOMbI, I1'106B1 Ha111a
MOIIeJIb COI‘JIaCOBbIBaJIaCb c sxcnepHMeHTa'nBHBIMn IlaHHbIMH? Ko-
He, aTOMbI nonxmBl 6BITB HaCTOJIbKO MaJIbIMH, qTo yBHIleTb 11x
HeBoopymeHHBIM rJIa30M 11.1111 name B MHKpOCKOl‘I HeBosMomno. Ca-
MBIﬁ CPIJIbl-Iblﬁ MHKpOCKOH He B COCTOHHHI/I 06H_apy>1mTB 06yCJ10BJ1eH-
Hy10 aTOMaMH BepHHCTOCTb CKTy M
T pH H a H
M e H
B
m I IeI
M e TK TO
H M O
KH
y B 1
1 e T B
11
M 1 1 B
1 M n
po c o na
B - I
HO MB e e,
Me
e T pa
M
e p
1 1011 0
1111 0
MH p
O eT pa ,
T e

7.5. Mode/lb uuxpocrpyrcrypbt semecraa 205
Z
l
l
l
l
(DI/IF. 7.11. IIByxaTOMHaa MoneKyJIa M0)K€T nomomaTb aneprmo, KOTopan pac-
xonyeTca Ha KoneéaHHa H Ha BpameHKe.
BeCTHO o T'enJIOTe. Korna K may HOILBOIII/ITCH TenJIO, 0H0 npeoépa-
syeTcsI B KKHeTCK
3H e
p r
o
a O
MOB .
T
M I H a
KH ITe -
I a
b
C I
bI
Te e
n K
T O
OH
na e K K
JIbH

206 ‘ 1‘21. 7. Ten/20m, remneparypa u cpxpauenue anepeuu
sneprna. Kamnaa MOJIeKyJIa TaKOI‘O rasa COCTOHTJ‘IB nByx CBHSaH-
HbIX memny c0601? aTOMOB. Sneprnﬂ, nomomaemaa 1101106110191 cu.-
CTeMoﬁ, pacxonyeTca He TOJIbKO Ha HOBbIUJeHHe cxopocm xaomqe-
cxoro HOCTynaTeJIbHoro KeHmI, H0 11 Ha KoneéaHnH, H Ha Bpa-
meHHe (qmr. 7.11). HOCKOJI T e He
p Tya e CTb
e a
pn
H e
K
H e T
CK o a e
r nOCT
HaT
JI
HO
O B m
e
HH .
110 0
1
1 CC T M I
M O I
K y J I ,
n JIb a He
r me K
O T I

7.5. Moaezzb uurcpocrpytcrypbt semecma 207
Tar/o A TanaB
(DI/II“. 7.12. I/Isodpaxenne KHHeTHKH BoauuKHOBeHBa «no'roxa Terma». Korna nBa
TeJIa Baxonmca B Kon'rax're, monexynm ropaqero TBJIa (6enue xpymm) nepe-
nalo'r sneprmo MOJIeKyJIaM xononnoro Tena (nepHBIe xcxn) HyTeM Memone-
KpHBIx cronxnoaeanﬁ.
aTOMHbIe I‘a3bI. CJICIIOBaTeJIbHO, Ha BHyTp HHHe

17A. 7. Ten/tom, remneparypa u coxpauenue suepeuu
ﬂomeuuua/mi.
anepzuz
+
j
, r
A, / /
‘ _ /
(DHF. 7.13. CpenHee nonomenne aToma (nyHKTHpI-Iaﬂ manna) B acnmmeTHoﬁ
no'reHuHaJIbHoﬁ ame HameHaeTca npn H3MeHeHHH KHHeTCKoﬁ (KoneéaTenBHoﬁ)
sneprnn H, CJICILOBaTEJIbHO, H
Me e H
H T e m
e a
r
y b
.
e np Tp
aT e O
IO e I nn
n m a
aTB
OJI e éa T
e
I H
IOH
p m o
H
O
C K O JI
3 1
1
6 b a
O b
H M OI

7.5. Mode/2b murcpocrpyrcrypbz semecrea 209
KHHeTCKoﬁ 3Heprnu KoneéaHuﬁ. HOCJIeIIHﬂﬂ aneprnﬂ (ecmd ctm-
Ta’l‘b, qTo Bce aTOMbI BeﬂleCTBa nonm OIIHHaKOByIO nopumo
aHeH) HpOﬂBJIHETCH B yBeJIHtIeHHu TemuepaTypBI Ba 1 °C. ,
Hama aTOMHaB Monenb HOBBOJIﬂeT 06'bH‘CHHTb 11 npyrne TeIIJIO-
BbIe BBJTeHHB, r10 KpaﬁHeﬁ MBpe‘ KaTBeHHo. KaK cxeMaTcxu
nsoépameno Ha (bur. 7.13, Kaxmblﬁ aTOM HaXOIIHTCH B acummer‘puw-
H011 BOTeHunaJIbHoﬁ ﬂMe. Korna KoneéaHHB YCHJIHBaIOTCH, aTOMbI
KOJIe6J110TCB yme He OKOJIO 11x nepBOHaIBHBIx paBHOBecnblx nono-
meHHﬁ. KaK BHIIHO 113 (bur. 7.13, c yBeJIHueM aMrIJIHTyllbI Kone-
63mm cpeBHee paCCTOHHHe Memny aTOMaMH BospaCTaeT. I/IMeHHo
3THM Oé'bHCHHETCH T0T (paKT, qTo épnbmnHCTBo BBLuBCTB pacumpa-
eTCH 11pm HOBbIIHeHHH TeMBepaTypBI. Pacmnpenne He/ﬂ 0633c-
HHTb npocm yBennneM pasmaxa Koneéannﬁ. I10 Tex nop noxa’
paBHOBeCHbIe paccmmma He H3MeHHTCH, 06BeM BemBCTBa OCTaeTca
HeHBMeHHBIM. TOJIBKO aCHMMeTpHH HOTeHunaJIBHoﬁ HMbI 06yCJ10BJ1H-
BaeT oénapymnBaeMoe HaMH pacmupeHHe.
Hoqemy me Toma 06'beM JIbIIa 14 BucmyTa ymeHBmaeTCH, Korna
01m HJIaBﬂTCH, 11 name nponomxaeT yMEHbHIaTbCH B Heéonbmofi 06-
JIaCTH TeMnepaTyp Bblme ToneK nnamenna?‘ B COOTBeTCTBHH c Ha-
meﬁ Monenbro MbI I10JI)KHbI upennonommb, I1T0 B aToi’T 06JIaCTH
aTOMbI PI MOJIEKyJIbI HepeCTpaI/IBaIOTCH B HOBbIe K0H¢Hrypa11nm me
HOTeHuHaJIBHbIe ﬂMbI HMeIOT npyryro ¢opmy. B npouecce TaKoﬁ ne-
pBCTpoﬁKn BHyTpeHHBB 3Heprna MO}K6T HOI‘JIOIIIaTbCH mm BbICBO-
éomnaTBca B BaBHCHMOCTH 0T TOI‘O, KaKOBa HaIBHaB n KoneqHasI
CKTypa. BéJmsn TH IIJIaBJIEHHH TBepnoro TeJIa [IOIIBOIL 110110.11-
HnTeJIBHoro KOJIHlIeCTBa TeIIJIa He BBIBBIBaeT- yBeJIHHH aMBJIM-
TyIlbI Koneéannﬁ aT0M0B, H0 cosnaeT BHyTpeHmoro sneprmo, He06-
XOILHMyIO 11.1151 paBpBIBa HeKOTopblx CBBBeﬁ, KOTOe ynepmnBaJI'H
aTOMbI mm MOJIeKyJIbI B (pHKcnpOBaHH non
me
n a,
aK
T0
1
0JI K
O
6IB B T BeI
O Te e
B O JI
I
J HT B Oe e T
B 1111
1
1

210 FA. 7. T endow, reunepgrypa u cox‘paueuue suepeuu
7.6. Tennosaa aneprna u BBpOﬁTHOCTb
1/13 Hameﬁ KOHIleIlIIHH TenJIOTbI H monenn MHKpOCTpYKTy
B
I -
e a
O C p H H
IeC I Cl
CTHH
,
n aM
l pa e
m n
a e
M
,
q
ro
n o n
cx om
ceae
x ﬁ
a n e p ne
ﬁ ,
3 a aM
0

7.6. Ten/wean amepaus u eeponmocn 211
1
moccpepnoro. B 11% B KamﬂOM BBIGpaHHOM HaI'IpaBJIeHHH KeTca
TaKoe )Ke qncno aTOMOB mm MOJIeKyJ'I, KaK H B JIIoGOM npymM Ha-
npaBJIeHHH. CymeCTByeT HeKoe pacnpenenenne CKopOCTefi omocn-
TeJIBHo KaKoﬁ-To cpenHeﬁ CKOpOCTH, BeJIHqHHa KOTopoﬁ 3aBHCHT 01'
TeMBepaTypBI. OéBBCHHTe, KaKHM 06pa30M H3 aToro xaoca MO}KHO
11

7.6. Ten/106a}: auepewz u eepomnocrb 213-
Ecnn 6B1 Mbl 3ax0'rem1 BepHyTb mamnHy B HCXOILHOB 0001051-
H11e, MbI 110JI>1111B1 61311111 6b1 TOJIKaTb nopmeHb B 06paTH0M HanpaB-
neH1111, npn Ta
x I 1 06
1 1 T no
y
omo 11 u
nm m p
a aH T e a c
e
Be MH
O
T Ba JI
a C b 11
pm ne B H a
a b n
o T e nepa
T p . Ha
pa m e I
a B IH
He
O
’ e M

214 1‘ A. 7. Ten/10m, reuneparypa u coxpauenue suepeuu
B onHoe BOCTOBHKe. KonnTBo TeHJIa, npeBpaTKBmeeca B me-
xaHCK pa o
T
y Ta
K
K
M
0
6 pa 0 , a BH
o
(
,
— 2)

7.6. Ten/106a}: suepeun u aepoamocrb 215
B T2— a6comomaa TeMnepaTypa, npn KOTopoﬁ qaCTB TeHJIa npn-
xonm‘ca BB16paCB1BaTB 6’e3B03BpaTHo. /
VB nocnenHHe I‘OIIbI Bospoc Hmepec K TeHJIOBOMy sarpaaneumo
oxpymalomeﬁ cpenbl, T: e. K ﬂOBbIHleHHIO TeMnepaTypBI Haumx peK
PI osep, BbI3BaHHOMy lIBHTEJIbHOCTbIO IOBeKa. 3Ta npoénema 0851-
33113 c HBJICHHHMH, KOTOe Mbl TOJIbKO qTo paccmo'rpeJIH. y Hamnx
snexrpocranunﬁ TemnepaTypa T1 eCTb TeMHepaTypa napa BbICOKOI‘O
naBneHBB, nonyqaemoro aa cqe'r CI‘OpaHHﬂ KaMBHHoro yum, mm-
KOI‘O TOHJIHBa mm I e I eHH
s ep
I
s
3a B I
OK
O ‘
O
llaBJIeH
IH I K opo
no n n u
x C B
o CB ee
p e r
o o np a e ae
ne a T pa e
no xn an p B
B ITB 60
0C mm

216 [‘11. 7. Ten/101a, reuneparypa u coxpaueuue auepeuu
(DI/11‘. 7.15. Mm mm ronbcba, nanalomuﬁ B BmBK c necxom. C06bITHH [myr
B Toﬁ HOCJIelLOBaTEJIbHOCTH, KaK 3T0 noxasaBo, HQ B 06paTHOM nopsmxe 01m
HILTH Be MOI‘yT.
Tax HpOCT; OH MO)K€T 6bITb BameH HBCKOJIBKHMH cnocoéaMH; Bce
OHH paBHOLIeHHbI, xom 9T0 PI He TaK OHILHO. OnHa H3 (popM-
pOBOK BTOpOI‘O 3aK0Ha TaKOBa: eCJm—CBCTeMa HMeeT BOSMOXHOCTb
H3M€HHTb CBoe COCTOHHHe paBJIbIMH nyTBMH, TO 0Ha B Konue
KOHHOB npune'r B Hauéonee Bepom‘Hoe H3 Bcex BO3MO}KHbIX coc'ron-
HHI'FI. HaMep, TeHJIO Bcerna 6y11eT nepexonmb H3 60JIee Harpe-
Toﬁ oénacm B 60.11% xononH.
Bo
p o
. 1
. a oe
O K
T
H eTomo e
n e
B p a To
c
Ha p a Je
H e B
OT
pM p n c om
nee H o
ce
n JI a

Pesroue 21 T
nmeeT Mecm BoxmeHHe: anepmﬂ, Haxon

218 1' A. 7. T en/tom, reuneparypa u coxpaneuue auepauu
vCKOpOCTﬂMH, ynpyro coynapmo'rca Memny coéoﬁ a co CTeHKaMPI
cocyna. Korna K raay nonBonmca KaKoe-To Konnqeo Terma, 0H0
no Kpaﬁneﬁ Mepe qaCHo nepexonm B KnHeTcxyro aHep-
.rmo aTOMOB. ECJm ra3 cocrom‘ H3 MOJIEKyJI, T0 HBKOTOpaH qaCTB
anepmn M0)K€T nepexonmb BO BHyTpeHHHe Koneéanmi H Bpa-
meHne MoneKyJI. CJIeIlOBaTEJIbHO, yneaH TennoeMKoc'rb rasoB,
cocm‘oamnx n3 CJIO)KHbIX MOJIeKyJI, Beer-Ba 60J1bme,
y ona
TM
1
1 I
a O B.
nn n l Tene
M o me
e CB e
J m HH
B
a K H
I B a o-
p ym
H MO
I e
K yJI
y ma
T O M
PI
a

OTeeTbl Ha aonpocu 219'
OCBooonnTbca. (Oémcnenna, nonoénble STOMy, B CBoe BpeMﬁ npennarannw
Bnonne cepbeano.)
7.3. Oé'beM mapnxa Ha Konne Tepmome'rpa énaqmenbno 60.11
0 6
B e aa n n na
a , c O T
O M n c e nn
n . Bo pa
c a n e ob
e a
OB
J
I
ﬂ T C B
a e 'r
H

‘220 ['22. 7. Ten/tom, Teuneparypa u coxpaueuue aHepeuu
7.11. Her! Kanopna Bb16paHa TaKHM 06pa30M, qroébl ylLeJIbHaﬂ TenJIOeMKOCTb
3011131 éblna paBHa ellHHHlle.
l
7.12. ylleJIbHaﬂ TeHJloeMKOCTb meTaJIJIOB, BblpameHHaB B Kan/rpanycoepaMM,
ymenbmae'rca c pOCTOM nnornocm. YMHomaa yneJIBHyro TennoeMKOCTb Ha Maccy
aToma MeTaJIJIa, Bblpameunylo B rpammax, nonyqaeM mnnoemxocn B Kan/rpa-
nye-arom. Bra Tel'IJloeMKOCTb, KaK BHlIHO H3 CTonéua 5 T86JI. 7.1, Hmeer GJm-
SHTeJO OILHHaKOByIO BeHHy mm Bcex meTaJmoa. 3Haqemm B CTonéue 1 no-
nyqarorca B pesyaTe yMHomeHHa 3HaHﬁ cronéua 5 Ha BeHHy, OépaTI-IYIO
macce aToma, BameHHoﬁ B rpaMMax. HpH yMHomeHHH Ha Maccy aroma nony-
qaeTca nocrommaa BenHa. Hocxonbxy Bce snana CJIlx TennoeMKo-
creﬁ, BameHHble B Kan/rpanyc-CM3, notrrn OILHHaKI, Kaxmblﬁ Kyénqecxnﬁ
caHTnmeTp 'naHHoro MeTaJIJIa conepmm npnénusmenbno OllPIHaKOBoe tmcno aTQ-
MOB. CneJmBaTeJIBHo, ILHaMel amx aTOMOB Mano OTaIO'rca npyr 01‘ npyra.
7.13. ECJIH BlIOJlb Kamnoﬁ CTOpOHbI Kyéa pacnonomeHo 103 aTOMOB, TO FIX
oémee no B Ky6e COCTaBJIHeT (103)3 = 1024.
7.14. Monexynapnble ynenbnme TermoeMKocm oé

17 parcwttecrcue W60”: 22]
6y11yT Koneéa'rbca c OJIHHaKOBOﬁ amnnmynoﬁ, npOMemyTOi'i Mexmy éonbmoﬁ
H manoﬁ aMnJIHTaMH, cyLueCTBOBaMH BHaqane. TenJIOTa nepeuma OT Harpe-
Toﬁ qacm K xononHoﬁ. Ob MaJIOBepOHTHO, qToébI Bce aTOMbI Ha OJIHOM Konue
crepmm, nmee BHaqane onnHaKdB T e
ne a y p
y
B
p r a
a non ea T b
a
60
e e H
T H
HH O, a
r
M bH n pyo
K o u e
, o
mc e
m aa H pr
m B T
M n
y ae
CT a
I aC
6H e a
me
H o .
I I
P KII
I
C K I
I

222 FA. 7. Ten/10m, remneparypa u coxpaﬂenue auepeuu
cBepxy. Hpexme non an nm na e
enn , ne n
c a m e o
m n eMb ﬁe s
y a T
T
e JIO ,
.
n T e p
H HOe
o
p
se
ﬁ ono ﬁ

3aaaqu 223
Kucnowy: B omomennn 10:1; [00:1 mm B KaKOM-Jméo npy'l‘om? €11
c e n
-
a e rac Bon oﬁ
u c
1
3 nn e n
x u e
o p a
y e
r . n e no n aK
C J
I
O
T a o
r m
H
3
JI H H H
b
x
O JI ey I (
C
17 H
3C O
H
) c e c
o
HM c nemn ecx
m n , H
no e
s H

224 1‘11. 7. Ten/107a, reuneparypa u coxpauenue auepeuu
8. OG'BBCHHTe, nmemy B npexume BpeMeHa mpuqnonmeﬁmnxn oéHapymnnH,
two 0
M r T nn
y
m ' r
b H
aH Te
IH
o
.

(Dur. 8.12. Henpepbisiibii’i crIeKrp nsnyueiimi Harperoi’r Bonbrppamosoii JICHTbI 8 BH—
mrmoii 06.71am“ (BBepxy) ii (CBepxy BBL/13) Jiiiiiei’itiarbie cneKrpbr aTOMOB BOILOpOJa,
aromoa remm H aTOMOB pTyTu. Bulimiasr qacrb enexrpa J1€)KHT B HHTepBaJIe 11mm
BOJIH or 7000 A (KpaCHaH oénacrb) 110 4000 A (cpnoneTOBaH oénacrb). )Kemo—
opamKeBoii oénacrn oreeqaer ,rmmia BOJIHbI 6000 A, CHHe-ronyéoi’i—nnmia 130mm
4000A; l A (aHrcrpeM)_-10‘10M. (IIBa BCpXHHX cnexrpa 133mm H3 KHHI‘H:
Chemistry—311 Experimental Science, ed. G. C. Pimentel, Copyright 1963 by
W. H. Freeman and C0.: 113a HmKHHx -—n3 KHHrH: E. R. Hardwi'ck, C. Knobler,
Chemistry: Man and Matter, Ginn., 1970.)

FJIaBa Bocsman
ATOMbI
u nepnonnqecxan Taémma
B nByx npenbmymnx I‘JIaBaX Mb] BCTaJIH nepen HCOGXOIIPIMOCTBIO
npennommb KaK-Jméo Monenb BHyTpeHHero CTpoeHHﬂ BemeCTBa.
yIIOBJIeTBOpHTEJIbHoe oébncnenne nonmnﬁ TeMnepaTypBI 14 Terms»
MbI Hamnn, I'IOJIb3yﬂCb HpEllCTaBJIeHI/IEM o cy6MnKpOCKonnqecxnx
qacmuax, KOToe MOI‘yT 0T6HpaTb sneprmo Ha BBmKeHne, a Tax-
me Ha pacmmenne H cmame nx B3aHMHbIX CBﬂseﬁ. L11‘06131 nony-
B nanbneﬁmee HpeIICTaBJIEHI/Ie 06 smx HBJIBHHHX, a Taxme
o MnomeCTBe npyrnx BsanMoneﬁCTBnﬁ, KOToe CBH3aHbI c H3MeHe-
HHHMH CTpoeHHH BemeCTBa, paCCMOTpHM 60JIee nonpoéno npnpony
MHKpOCKTy.
Hpmbeccop apn (DeﬁHMaH, JIaypeaT HoéeneBCKoﬁ npeMHH 14
0mm n3 caMbIX BbIIIaIOIIIHXCH @43

226 ”. 8. Aroma u nepuoauuecrcan Ta6/zuua
npnMepHo K V BeKy 110 H. 3., OIIHaKO neﬁCTBHTeJIbHOCTB TaKOBa, qTo
TOJIbKO B HameM CToneTnH aTOMHaﬂ Teopml nonla Bceoémee
npusuanne.
8.1. ATOMHaﬁ Teopml IlaJIbToua
LIecrb HOCTpOEHHH OCHOBHoﬁ MOIIBJII/I, H3 KOTopoﬁ BOCJIH Baum
COBpeMeHHble HpeILCTaBJIEHPIﬂ 06 aTOMHoﬁ pone BemeCTBa, npn-
Hannemm aHrJIHfICKOMy LUKOJIbHOMy emo, CTaBmeMy XHMHKOM,
ﬂmony ﬂaJIbTony. HOJIHoe H3JIO)K€HP1€ CBoefi Teopmi OH onyéo-
Ban B 1808 r. B Knnre, osamaBJIeHHoﬁ «HOBaﬂ cncreMa (pmococpnn
XHMHH». OILHaKO llaJIBmH npnoépen HBBBCTHOCTB c0BceM He now-
My, L1T0 OH HKOGBI nepBbIM BbICKaBaJI MbICJIb o cymeCTBOBaHBH aTo-
MOB. Fpeqecxne qmnococpbr JIeBKnnn, HeMoxpm H Snnxyp, a TaKme
'raKHe 3HaMeBnTBIe ytIeHbIe XVII n XVIII CTOJIeTHﬁ, Kax P06epT
Boﬁnb H I/IcaaK HbIOTOH, HCHOBeIIOBaJIH Bepy B aTOMHCTCKn
pnpony BemeCTBa. IIaJIbTOHy BbIIIaJIa sanaqa— pas
H a
aea TM H
T
C
n
x
n nT
e IO

228 FA. 8. Ammo; u nepuoauuecxaﬂ Ta6/zuqa
(DI/IF. 8.2. Saxon xpaTH o
'r om
H H
ﬁ
. ne
eT b I
H B
0 6
pa
3
I
T OIIH H
H 3 y
:3
1 1 03.
K a a
aoe x
na o nn H e
H a I onp
mm ‘ T n a
T O a

8.2. Knaccuuecrcue .uoae/zu crpoenun aroma 231
~ -’ {I} W{;‘,‘”‘x‘7‘-e.
‘ '. - . ,.;._;.;:'.:;-Z ﬂowmumemyo
' .-.. ;.-.-..1-‘ JapﬂJfCEHHaﬂ
’ ' mud/racmb
(DI/IF. 8.4. Monenb aTOMa Tuna «HyIUIHHI‘a c HSIOMOM». >Knnxoc1‘b HmeeT nono-
mm‘enbuuﬁ sapsm, 1‘0 He
'rpna
y
on
or u ua
rnn
bm
a pmo p
y
x e
H H B
He a n e'rp o
n a .
a m

8.3. «Hoaaﬂ ¢u3urca» u coepeuennan mode/lb aroma 233
8.3. «Honan «Manna» n cospemeuuan MOIICJIb aToma
I'IepBBIfi pemalomni’l mar B HanpaBneHnH pasBmmi Tex upen-
CTaBJIeHHIP’I o MOLLCJIH aroma, KOTopBIe HHTbI B HaCToamee Bpe-
MH, 6BIJ1 cneJIaH HPIJOM BopOM, ﬂaTCKHM yBIM, KOTopBIﬁ
BKJIIO‘JHJICH B pa60TB1 naéopaTopHn Pesepdmpna KaK pas B T0
BpeMH, Korna HOHBHJIHCB nyénnxaunn 06 SKCHepHMeHTaJIbHOM non-
TBepmneHHn cymeCTBOBaHHH aTOMHOI‘O a. I‘Ipemne n
n C
T
yK
H
MC
IH IO K JI
I a
C e Ia H
o oB
o O
M H
0
X OI
PI OB
p a
T e
o a pa KTe pB
Oa
r
B m e
pao T IKO O
e B e m
K e pb e BHIM
nr a BH OH a H H
H c

234 FA. 8. Aroma: u nepuoauuecxan rats/mud
S
(DHF. 8.7. Harpe'raa mm, B namnouxe Haxannaanna, Kax n Bcaxoe npyroe Harpe-
Toe TCJIO, usnyqae'r sueprmo B Bane snexrpomarnumux BOJIH.
MaI‘HH’I‘HOI‘O HsJIyHa H npncymne HM Bennqnnm A. B neﬁcrsn-
Tenbnocm Bce 3TH nanyqeuna CBﬂaaHbI c oMH 14 TCM )Ke (ppm:-
KnMn HBJICHHHMH. M131 pasnnqaeM Bunnmylo O6JIaCTb, yJIb'rpa«
(bl/IOJIBTOBOB usnyqenne H peHTreHOe JI
T
JI
KO m
m m
y, q
r
M
b B C
‘ IH H -
H MaeM
H

8.3. «Hogan dmaurca» u coepemeunan moae/zb aroma 235
I .
I
I
l
“ I
I
I
.< I
<1 I _
I I
g I I
w I I
g I I
% I_ '
at} : Anal“. 3500 N
l 3000]!
I
Z5001?
2000K
I L—
0 I.__.: 10 2-10‘
Batht
a
d
ac
m
, d
u m
B O I H
bI ,
H c
pe
u

236 FA. 8. Ammo; u nepuoauqecrcaﬂ 1116

238 FA. 8. ATOMbl u nepuoauuecxan Ta6nuua
‘1
Hpn tIaCTOTax, MeHbUJHX v0 (qaCTOTa, npn KOTopoﬁ hvo:—-q)),
SJICKTPOHbI Booéme He SMHTTIOTCH, nocxoy Toma sneprua
¢0T0Ha meHBme 3Heprnn, He06xonnMoﬁ mm npeononenna n0TeH-
unanBHoro éapbepa (p. Hpn nsnyqennn, qacrora KOTOpOI‘O 60JIbIlle
v0, MaKCHMaJIbHaH sneprna SMHTTHpOBaHHOI‘O sneKTpona onncm-
BaeTCH ypaBHeHneM (8.3). Ecnn, KaK 3T0 upennonomml 3ﬁH~
UlTeI/IH, qncno TOHOB naHHoﬁ lIaCTOTbI, nanaroumx Ha MeTaJmntIe-
CK HO B
HOT b n
pno p
u n n ab
o
He
B o mn
J I
y m IT o
a TaH BHTHB
H O IH
e
l o
m e c
xo
b CH
M o H
a m ona e
M a axnepnm e Ta
oH
OH OH HOH JIH
O
T M e m
y He HHH
O CTIH B
I yH Bn

8.3. «Hoaaﬂ dmawca» u coapemeunan mam aroma 239
HeﬂpeBeH, BoséymneHHbIe aTOMbI rasa HBaIOT cnoxmylo cepmo
Ko BameHH
Ce T p
a JI I
JI
H H
I P
I , Ka mon 3
O T o
X o
0
T B
e T T Be
c 1
0 o
np nn
e n
na 'r T a
qm
r
.
.
1

240 1‘ A. 8. Aroma: u nepuoauqecrcan ra6/zuqa
no I‘OBoﬁ opéme, B ueHTpe KOTopoﬁ pacnonomeno 0THOCHT€JIb-
H0 TmKeJIoe smpo oezmnuIM nonomnTebIM sapsmOM.
Bop OTKJI, qTo Bce CBoﬁCTBa aTOMa, HaémonaeMbIe sxcnepw
MEHTaJIbHO, 1310110 l ea JI H
c
I eK
r a
n JI
y
n, no ny o I
O JIH
B oém cu n
ne e n up
nn o n m
m
b ,
T o
m a o
M
O e

8.3. «Hoean ¢u3wca» u coapemenuan moae/zb aroma 241
Pemaa 3TH ypaBHeI-IPIH 0THOCHTeJIbHO r, HpHXOlLHM K cnenyxomeMy
pesyJIbTaTy:
2/12 _ —kqlq2
4n2mr3 _ r2 ’
n2}:2
r2 —4nzm,3 )= — 164142.
n2}:2
W = — WW2:
r2211?
W = - k414i.
n2h2/(4n2m) _ r
[34142 ’
n2h2
_ '_ r.
BBeIIH HOByIO HOCTOHHHYIO ao = —(h2/kq1q24n2m), MO}KHO ne«
penncaTb ypaBHeHne (8.8) B Bnne
= n2a0. (8.9)
OTCIOILa cﬂenyeT, Inc B 60pOBCKoﬁ MoneJm aTOMa Bonopona
panuycm yCToi’mIx I‘OBbIX Op6HT SJIGKTpOHa 110JI>KHb1 6bITb
nHCTHbIMH BeJmaMH: do, 400, 9%, 16ao,...; 3T0 COOTBeTCTByeT
3HanaM KBaHTOBOI‘O tmcna n, paBHbIM l, 2, 3, 4, . . . , ((pnr. 8.13).
B
n p
c
.
1
1 .
I IO
a
m

242 ['21. 8. Aroma u nepuoauuecrcan raénuqa
E
<DI/II‘. 8.13. Paspemeunue xpyroaue 0p6HTbI exempoua B dopoacxoﬁ MOJICJIPI
nonoponnoro aToma, coorne'rc'rnyxomne COCTOﬁHHHM, Ko'ropue onpenenmo'rca 311a-
qenmmn n, paBI-IHMH l. 2, 3, 4,. ..
l'IoncraBJIHH nocnenHee paBeHcmo B ypaBHe'Hne (8.10), HaXOIIHM
E=%mw+kﬂﬂ,
f
__1_ —kq142) M7142)
5 2 ( r + ( r ’
hag).
k
E=%’£. (8.11)
ECJIH Tenepb nonm‘asmb BameHHe mm r H3 ypaBHEHHH (8.9),
T0 HOJIM
E = k 44—2— (8.12)
2 (nzao) '

8.3. «Hoean dmaurca» u coapenerman M03611!) aroma 243
TaKHM nyTeM Bop npnmen K Monenn aToma Bonopona, B KOTO-
poﬁ sneKTpon nsnme'rca no 0p6PITe H M0)K€T HaXOIIHTbCH TOJIbKO
B onpeneneH c o
m
m na
cor a
e
HbM a 6 p
M
q en n
, a
mn e n
3
K
T
O
X C

244 [‘12. 8. Aroma; u nepuoauqecrcan Mei/mud
Cocmmuue n=l; l=0 Cocmomue n=Z; [=0 Cacmaﬁﬂue n= 2; [=1
(DI/ll. 8.14. HPOCTpaHCTBeHHOC pacnpeneneHHe BepOﬂTHOCTH 11ml SJIeKTPOHOB
B HeCKOJIbKHX HepBbIX KBaH'I‘OBbIX COCTOHHHHX. (H3 KHHrH: Chemistry— an Expe-
rimental Science, ed. G. C. Pimentel, Copyright 1963 by W. H. Freeman
and Co.)
HaCTHuaMH, BmKneTca Ha nax npymx OCHOBOHOJIOMHHKOB HOBoi’I
(pHsHKH: BepHepa FeﬁseHéepra, SpBHHa IllpeHH-Hrepa, Bonbcpram‘a
HayJIH, JIyH He Bpoi’ma, MaKca BopHa H HOJIH llnpaKa. K KOH-
Herman KBaHTOBaHHH 3Hepr1m H nMnyJIBca 6mm 1106aBJIEHbI mm-
mm rne Konuenunn, KOTOe MoryT noxasaTBCH CTpaHHbIMH
BceM, KTO Bee BpeMH HMeJI ILEJIO TOJIbKO c (pHBHKoﬁ MaKpOCKOHH-
HeCKHx CHCTeM. Hanpnmep, Hacmubl, TaKHe MaJIbIe, KaK SJIBKTPOH,
He MoryT, KaK OKa3bIBaeTCH, OIIHOBpeMEHHO H sanumaTB Tot-1H0 on-
peneneHHoe monomeHue, H HMeTb 1‘0
o npn ee
H
b
ﬁ
HM H
y I B
c He c
me TB e , a
0

8.4. ﬂepuoauqnocrb a nape aromas 245
MeHT, yI‘JIOByIO BaBHCHMOCTb HpOCTpaHCTBeHHOI‘O pacnpeneJIeHmI, a
Taxme (mm Bcex aTOMOB, -KpOMe Bonopona) nm B BBLpameHnH,
onpenenmoume aneprmo SJIeKTpOHOB. TpeTBe KBa'HTOBoe qncno,
06Ho 0603HaqaeMoe ml, 0TpamaeT, KaKoe BosnefICTBne Ha naHHoe
cocmmme Momer OKaBaTb BHemHee MaTHoe none. 3T0 qncno
MO)K€T HpHHHMaTb 3Ha'Hﬂ OT — I no +1. pOJIb nocnenHero KBaH-
TOBOI‘O Lmena, ms, M0}KHO HOCTa'IOqHO Harnanno HpCIlCTﬂBHTb, ecm-I
HpHHHTb, qTo SJIeKTPOH eCTB MHHnaTIoxﬁ rnpocxon, Koropblﬁ Bpa-
maeTca 0THOCHTeJIbHO CBoeﬁ ocn JIH60 no lIaCOBOIP'I CTpeJIKe (m8 =
= +1/2), JIH60 npomB qaCOBoﬁ CTpeJIKPI (ms = —1/2). HarJIsmHoe
HpeILCTaBJIEHHe o HpOCTpaHCTBeHHOM pacnpenenennn aneKTpOHOB
B HeKOTOX COCTOHHHﬂX nae'r (pm. 8.14. B cnenyromeM pasnene
MbI zmM, KaKHM 06pa30M Ha OCHOBe smx upencraBJIeHHﬁ yna‘
eTCH 06’bHCHHTb qmecxne n

246 1‘ .4. 8. Aroma u nepuoduuecxan ruff/tuna
KOTopoe Mo
H a
B a
JI om
;
no e p m T e
ep H Be
T I I
O, T
oT
0e
JIe
n n p
BH qcn
HO I
O
K T eI I I
O aa
e HHH O
T OHO B aOH
O B ne
m n ocxo
yT O
a e T
p
n e c
ne T a-
. e H
, q
n n y TH
a TJI
I

8.4. ﬂepuoautmocrb 8 nape aronoa 247
. 2
femzu
He
10
Heat! Ne
18
Apeay Ar
36
mo”
ll'pun Kr
(DI/ll. 8.15. Snemen'm: reunﬁ, neon, apron, KpHI‘ITOH, 54
xceHon n panon upenc'raanmo'r codoﬁ nnepmue Keenan Xe »
raau. (H8 KHHI‘H: Chemistry—an Experimental
Science, ed. G. C. Pimentel, Copyrlght 1963 by Pam)” 86 L
W. H. Freeman and Co.) R11
1 2
H Ho
3 4 5 6 7 8 9 10,
Li 8e 8 c N o F No
11 12 13 14 15 16 17 18
Na Mg AI Si P 8 CI A!
1920 2122 23 24 25 26 27 282930 31-32 333435 36’
KCaScTivcymroCoNiCuaceAsSoerKrE
373838404142434445484748495051525354
RbSr 1! 21M) Mo Tc Ru Rh Pd Aged In Sn'SbTo I x.
55 56 57 72 73 74 75 76 77 78 '79 80 81 82 83 84 85 BBL
c. 8. 'La Hf To 1111 a. o: 1: Pt Au Hg Tl Pb Bi Po At Rn
87 88 89
Fr R8 tAc
5859606162636465666768697071
CoPrNSmETbDyHoEtTmYbLu'

84. Hepuoautmocrb 3 Mupe aromoe 249'
I —' a --3,- (:2
r n 4' l = 0 10 weir/71p
Z l
e
rmpﬂa
—
n =
3
l =
I n
3
l

‘250 FA. 8. Aroma; u nepuoauttecxan 1062mm
n3 BaMHeﬁmnx CBoﬁCTB aroma—auepeuro uonusauuu. H011 He]?! no-
HHMaETCH Ta MHHHMaJIbHaH sneH, KOTOpaﬂ Heoéxozmma mm
TOI‘O, qTOéBI HOJIHOCTbIO OTopBaTb 0T IlaHHOI‘O aTOMa BHemHnﬁ snex-
TpOH. HonyHoe B pesyJIBTaTe aToﬁ onepaunn 06pa30BaHne nMeeT
sneKTpuKnﬁ sapsw. +1 n Ha3bIBaeTCH uouou. SHeB Honnsa-
nun eCTb Mepa TOI‘O, HaCKOJIbKO upotIHo 3JIeKTpOH CBHBaH c aTOMOM.
ConocraBmm Bonopon n rennﬁ, MbI HaXOIIPIM, qTo y nocnenHero
anempmecxnﬁ sapsm Bnpa B nBa pa3a éonbme. Kamnblﬁ aJIeK-
TpOH B aTOMe remm <<omyu1aeT>> npmameune co CTopOHBI sapsula
anpa, paBHoro +2. CJIellOBaTeJIbHO, anepmﬂ nonnsaunn ream;
MHOI‘O BbIHIe aHeprpm Bonnsaunn Bonopona. ECJIH neperaTBca
IlaJIbIIle, K ammo, MbI HaﬁneM, two 321
i ma
B o pa
Ta T n o
( +
,
O
lH
KO ane T p
O H Ha
n
on mea
epe
i

Peatome 25t
200— ' . Ca
Li N, A' K
11 l l l l I l l l l l l l l_L LI
6 8 10 12 14 16 18 20 22
Amommzi HUMP]?
011
02
Juapeun uomzsauuu, man/M0175
l
4
(DI/II. 8.1/8. Uepnonnqnocrb B Beamtmne aneprpm nonnaaunn nepBux nBanua'm
anemeHTon. (H3 KHHI‘H: Chemistry —an Experimental Science, ed. G. C. Pimen-
tel, Copyright 1963 by W. H. Freeman and Co.)
B pe3yJ1bTaTe TaKoﬁ neperpynOBKn pearnpyroumii aTOM M0>Ker
HOJIHOCO mm qacrnqno norepm‘b Hanéonee anepbIe aneK-
TpOHbI. L{em BbIIlle aneprnn Honnsaunn, TeM n-Hee ynanmb sneK-
Tpon. OTHOCHTeJIbHaH n-HepTHocrb SJIeMeHTOB c aTOMHbIMH HOMe-
paMn 2, 10, 18, 36, 54 H 86 qaCTH
c a a H a
T eM, qo He
p nnH OI
IB a
H H
y
B
nn a
B
T O K
B peH
b CO
a H
p ea u o
na Hn
conocrb ne a J
I e Kn e

252 [‘22. 8. ATOMbt u nepuoduttecrcan Tab/mud
qacmuBI HOJI}KHbI Becm ce611 aHaJIoru BO
JIH a M a B
TOB B eB
O IH bI
O J KH
IBe c
c e
61 aao H o
acm a M
.
1a O a
K a
H
OBH T o
p m e TO
JI
b O
Be a
K osnH o
0 e
11 B 111
110 T B
O p H o
ﬁ O
Ie IH a
T O
a, 1 1
1 O '
b
C
H I a

Oreerbt Ha BonpOCbl 253
8.4. ECJIH qacmua, nBHmymaaca no opéme, nsnyqae'r 3Heprmo, ee 06mm
aHea B COOTBeTCTBHH c 3aK0H0M coxpaHeHna aneprnn n Maccm nonxma ymenb-
maTbca. KaK 6mm noxaaaHo B m. 6, ymeHbmeHHe aneprnn Tena, mymeroca
no opém‘e, BbIBOBeT yMeHbmeHHe panHyca 0p6HTbl. TaKHM oépaaoM, e
a n e
-
rpon
6 n
e r non
o
nm a b H an y
a r
an
epr o
, T 0
on n onn
p a
n
n

254 r11. 8. Aromu u nepuoauttecrcan Ta6/mqa
8.9. OTHomeHne maccu 6eﬁc60nbuoro Mina (1,5-10—1 Kr) K macce 3JIeKTp0Ha
(9-10“31 Kr) paBHo npuMe H0 1030:]. TaKHM oépaaoM, HaM Hymen 06mm,
macca KOTOpOI‘O nopsmxa 1 0 K1. Taxoﬁ 06'beKT—3TO Comme, macca KOTopOI‘O
2-1030 KI‘. (Macca 3eMJIH npnmepno 6-1024 KF—COBepIHeHHO oneBHnHo, Inc B
llaHHOM cnyqae 9T0 Ob manol)
8.10. I
1 1
_ = n 7 —_ — _ =
A (1,097 10 ) (22 42)
= 2,057 - 106 M—1,
2. = 4,862 ~ 10-7 M,
, 3
v = f. M= 6,166 .1014 c-l.
9. 4,862.10
8.11.
[:2
a0 = — —— .
kqlqg4nzm
HOnCTaBHM snaqeuna h, k, q1, q2, n, Toma BCHOMHHaH, q'ro q; = —qz, nonyqaeM
_ (6,625 - 10-3“)2
(8,988 - 109) (— 1,602 . 10-19) (1,602 - 10-19) - 4 . (3.14.2)2 . (9,109 - 10—31)
= 5,29 ~10—“M.
l'locxonbxy 3T0 p1 ecrb pannyc aneKTpOHHoﬁ Op6HTbI B 06b1tIH0M Bonoponnom
aTome npn KOMHaTHoﬁ TeMnepaType, nname'rp a'rOMa paBeH npnMepHo 10-10-1‘,
mm 10-10 M. KaK COI‘JIacyIOTCﬂ pesyJIbTaTbI a'rnx peTOB c axcnepnmeHTaoﬁ
oueHKofd paaMepa aToma, cnenaHHoﬁ B NI. 7?
8.12.
kqnaz (8,988-109)(—1,602-1b‘°)(1,602-109) 7 -1
= _34 10 _“ =—1,o97-10 M ,
hc~2ao (6,625-10 )(2,988-10 )(2)(5,29.10 )
8.13. Has! n = 2 KBaHTOBoe qHCJIo l momeT HMeTb anaqemm TOJIbKO 0 mm 1.
[Duo He mome'r npeauma'rb (n—' 1).] Hm I = O Kaamonoe qncno mz Mome'r
613m: paBHo TOJIbKO Hymo. [hm 1= 1 qucno m1 mome'r 6bITb paBHO —l, 0 mm
+1. 11m: Kamnoro H3 BosMoxm
3 a e u
4 l m a m om
mo e 'r
6 m pa BH
o
1
2

ﬂpaxruttecrcue pa6OTbl 255
4.1'Ipn apeHnH KHCJIOTbI 06pa3y10'rca emme napu HCl. Pa601‘y mena-
TeJIBHo ﬂpOHBBOIlPITb non. BBITBMHBIM Konnaxom. ‘Ecnn TaKOBOI‘O He HMEETCH, T0
Momno HpOBOJIHTb OHbIT Ha xopomo BeHTHJIeMOM MeCTe y oxna. Ecnn me na-
p0B HCl HaxannHBaeTca CTOJIbKO, qTo OHH HaqHHT BbISblBaTb omyTHMoe pas-
npamenne mas mm nerxnx, HeMellJIeHHO y6epme pac'rBopu c HarpeBaTeJIIx
HpH60pOB H ynaJmTe moneﬁ n3 nopameHHoro HOMemeHHH.
3aK0H KpaTHbIX omomennﬁ M0)KHO nponeMOHCTpHPOBaTb, y6enHBmHCB BTOM,
q'ro Bec0Boe coomomenue IIHHKa H xnopa, KOTOe, COBlIHHﬂHCb, oépasylor xno-
pHCTBIﬁ 11mm, aBJIaeTca 1‘0 on
pene eH b
m . 3
n a HI
e M O
K H n on bHa
6 o n
a ae ax n
e To mo
em e
H ooo n T Ba
n H a c H B
e CTb I
M
O JI
H -
TB
O M a
CTB p a o
mo
ﬁ H
JIT b
l HO
l I K
T a M a
o p a K
611
y
' r a

256 PA. 8. Aroma: u nepuoduttecrcan Ta6/zuqa
CKOJIbKO KeHHﬁ nanbua BbI neJIaeTe B onHy ceKyHny. HonpaKTBKyﬁT 1
1 0T
e np n x
a He n c
m r n meo
ro
, r
o a
'r Ta 6
y
1 e
'r n
0 CT aT
0
n o
c
'r a Ho
B C O
CTa BJ

3a0auu 257
opeamm macca aTOMOB naHHoro anemeHTa B TOM ero Bane, B KaKOM on BCTpe-
qaeTca B pone, nocronmta. Moxmo JIH, HMeﬂ To'Ie naHHme o KpaTH m
mH ome T e
HH om me nx o np
m m b
T
0
pa
nq
e
4
. m
m B e T
p
a IH u a om ca
o r pu
ae mx apm nn
e K
T p
o H Bn o
nm a 6 m a
Ba I
JIO

FnaBa HEBﬁTaﬂ
MOJIeKyJIbI
u XHMCKHe peaKuHH
B upenbmymeﬁ I‘JIaBe MbI paCCMOTpeJm UpeILCTaBJIeHPIe 0-6 am-
Me, a mum nmyro B HaCToamee BpeMﬂ'Monenb ero CTpoe-
mm. CBOﬁCTBa BemeCTBa npaKTuKH HEJIBSH HOHHTI), ecnn -
TaTbCH HpEﬂCTaBHTb em) KaK Haéop cna60 BBaHMOHEBCTByKHHHX
aTOMOB. Tax, HanpnMep, Bona cocmm ncxnroqmenbno P13 aTOMOB
Bonopona n Kncnopona,-0nHaK0 ee caoﬁcma HP! B KoeM CJIyqae He
HBJIHIOTCH npocmﬁ cyMMoi’i mm me CpellHHM n3 CBOBCTB amx nByx
a'I‘OMOB. I'Ipmmna 000mm B cneumeCKOM, HeHOBTOpHMOM Bsau-
Moneﬁcmnn, K0T0p0e npoucxonm Me‘y a’I‘OMaMH pasn

9.1. M mercy/2a 6060p00a 259
f
HpeIICTaBJIeHPIe o éonee CJIO}KHbIX aTOMaX co MHOI‘HMH sneKTpo-
HaMPI, MbI ILCTaJIbHO H3m npomeﬁmnﬁ aTOM Bono‘pona. T011110
TaK me 11.1151 OGBBCHBHHH xumnqecxux eBaseﬁ B coenHHeHuax, co-
Bepmamnx éonbmoe qncno aTOMOB, MbI cumaeM HOJICSHbIM pac-
CMOTpeTb upo-CTeﬁume MOJIeKyJIbI.
9.1. MoneK'a Bonopona
HpOCTeﬁmei’d HefiTpaJoi’I MOJIeKyJIoﬁ HBJISIeTCiI MoneKyna BO-
nopona. OHa cocmm H3 nByx HpOTOHOB (Bnpa aTOMOB Bonopona)
n yx aneKTpOHOB aTOMOB .Bonopona, KOTOe ynepmnBaroTcsI
CHJIBHOIP’I nqecxoﬁ CBHBbIO. llaJIbmH He HpeILCTaBJIﬂJI, qTo raso-
oépasnmﬁ 3011013011, a Taxme HeKOTOe npyrne aneMBHTale ra3b1
COCTOSIT n3 Monexyn, Kamnaa H3 KOTOX BKJIIOqaeT nBa Merl-
HbIX aTOMa. Korna STOT (ham 6BIJI yCTaHOBJIeH, HepBbIe npnBep-
)KeHHbI aTOMHoﬁ Teoppm 6mm BeCBMa osanaBI: IIJIH
6 II
O a a
n
b

9.] . MoaeKy/za eoaopoaa E
/
/
/
‘~V A
I
/ o
/
/
/
a ---- ———— —— a
A
/
I 1 Q
’4 ‘ u'
I
/
(DI/IF. 9.2. BO3M0)KHbIe BsanMoneﬁcmHa Memny HpOTOHaMH, HecymHMH sapsm + e,
n aneonaMH, HecymnMH sapanbl — e, B monexyne nonopona.
Bblpamerme mm nonHoﬁ norenunanbnoﬁ aHeprnn mayx aTOMOB
Bonopona, yllaJIeHHbIX IIPYI‘ OT npyra Ha éonbmoe pa-CCTOHHHe,
MO}KHO nonb H3 Bblpameunﬂ (9.3) cnenyroumM 06pa30M.
B I'IpeILEJIbHOM cnyqae, Ko-ma aI ynaJIeHbI npyr OT npyra Ha
6eCK0He

262 FA. 9. Moxzexy/tbt u xuuuuecrcup pearcquu
(DI/IF. 9.3. Cxemamqecxoe H306pax<eHHe pacnpenenenna anemponnoﬁ HJIOTHOCTH
mm nByx aTOMOB Bonopona, Haxonaumxca Ha oueub MaJIOM paccmauun (a), H
mm Monexynm Bonopona (6). ATOMbI H Monexyna Haxonmca B HHBIIIEM aHepre-
ecxom coc'roamm. Membanepnme paCCTOHHHH B cnyqaax a n 6 onnnaxoau,
Tnpyroumfi 0TpnuaTeJI1ﬁ BKJIaII B BeJIHy noreHunaoﬁ
snepmu Gyne'r 60J1bIHHM.
B on o
c
.
. MB I noa r a
e en nM M b I r
o
p
e r a -
B
m a u
H HH Ie
H
I b
I
K T O
e
y
a
CTB
I OT B o p
O aH

9.2. yaue monexcy/zbt 263
DI/IF. 9.4. Cxemamqecxoe BsoépameHBe pacnpeneneuna aneKTpOHHoﬁ nnomocm
B moneKyJIe H2 B CJlellHLEM nocne HHSIIJEI‘O cocmmmn c 60nee BBIcoxoﬁ
HOTeHunaoﬁ snepmeﬁ. HsoépameHBoe cocromme HBJIHETCH aHTBCBasbIBmBM.
Mexnaanepﬂoe paCCTOﬂHHe HMeeT Taxyxo )Ke BeHHy, Kax PI Ha (par. 9.3.
memny aTOMHbIMH BnpaMn, B pesyJIBTaTe I{ero 06pa3yeTCB HOTeH-
IlPIaJIbHaH HMa. OILHaKO paaBmaB Teopua

92. ,yeue MOAeKy/lbl 265
z?
5: F:6:F HIE!
a 0’ a
.. H
HINZH 11:6: H:5:5:H
a z? e
(DI/IF. 9.6. CBHBH, ocymeCTBJmeMbIe qepes BaneHTHbIe SJICKTpOHbI, HHOl‘Ila H30-
6pa}KaIOTCH TOqKaMH, Koropbxe COOTBeTCTBYIOT SJIeKTpOHaM. “penCTaBJIEHbI CBHBH
B MOJIeKyJIaX QJTopa (a),

266 1‘ A. 9. MOJleKbl u xumuqecrcue pearmuu
sHaqmeJIBHo 60J1ee BbICOKyIO aneprmo. Teopnn SJICKTPOHH
c
o
CT
HH n ﬁ B
O
JIKyJIa n n
O
B H H
HH
I IT a n
I H o m O
T T
O B a -
IHH I
x
ne T OOB
a n py I
T
cs I a
T M en
on me
n
. I I HO
B e Me
H o
o
C H e
H JI HTa B
o éa
m n K o
ﬁ
1
m 3HH
, p a

268 F-z. 9. Moxzcrcy/zbz u xummemuc pearczguu
dIVII. 9.7. PacnonomeHue HOIIOB xnopa (CBembIe mapHKH) H HOHOB K'dJIPIH (TQM-
I-Ible mapuKn) B Kpnc'ranne xnoppICToro Kamm. (Durypa Bsma n3 omioﬁ :43 pan-
p a
o
T Ba am aa
p noy
.
IIKH I I I
L
. a
u
i
n
, e e
a l
C
em
s

9.3. Tunbt ceasez‘i 269
(DI/IF. 9.8. Cxemamqecxoe TIPEILCTaBJIEHHe MOJIEKyJIbI Bonopona (exam) 14 M0-
nexym cpTopa (cnpaBa), B KOToX BaJIEHTI-Ible SJIEKTPOHbI paCHpeILEJIeHbI l'IOpOBHy
Memny aTOMaMH, a Taxme MOJIEKyJIbI ¢>TopHCToro Bonopona (B cepemme), B K0-
Topoﬁ SJIEKTPOHbI pacnpenenenbl He l'IOpOBHy.
.‘
-
. _.
I. ..
'
-
.
r
.
'
.
‘

270 FA. 9. MOJleKy/ uuu ercu
perc q
u
épa
s e r c a C B
H b . e
ny mm
I
B M
II e I
JI I MH n
ya
a MH
c
m e
CB e
H ep e BH

9.4. HOAﬂle u Henoxmpubte MOAelcy/lbl 271
épasyer Tpu JIOKaJIHBOBaHI-Iblx CBHBH, nocxoy 0H HMeeT oéume
napbl SJIeKTpOHOB c KaxmbIM H3 nByx cocemmx aTOMO-B, a Taxme
c aTOMOM Bonopona. Kpome TOI‘O, meCTB SJIeKTpOI-IOB IleJIOKaJIH30-
BaHbI—OHH Haxonmca Ha MoneKyH
o p
m
a l
x K
O TO
e a cne e
I HBI n o
Be m
KJI B y
n m
e
cm a
O O y e
on a K a no
a aHo
H a mr .
9..
.
. onn p ue
l He no a
p nue MOJIeK b
Ha K
e
cn Boon
B ya T MH o
M o e Ke, a
m o
l e -
H
l e MM
OJIe K y
JI

272 1‘ A. 9. Monercy/zbt u xunuuecxue pearcuuu
ﬂunwzwué ﬂunamuuiz @ﬂé
MaMeHm mm mameum 0mm 8“ E
(—— ——> 3‘: §
E §
g: :2
EQ
'0
g E
3, §
8 E
K 3
‘b {/
(DI/IF. 9.10. B Jmneﬁnoﬁ MOJIeKyJIe ILBYOKHCH yrnepona (cneBa) ,IlHIIOJIIe M0-
MeHTbI canseﬁ BsaHMHO Komnencnpyxo'rca. B Hennneﬁnoﬁ Monexyne H20 (cnpana)
,tLHnobIe MOMEHTbI cnaaeﬁ cxnanbmaro'rca n 06pa3y10'r peaynbmpylomnﬁ m1-
nobIﬁ momem MOJIeKyJIbI.
6
ﬂ
Q
Q
“$3
a ’
Ewgéx
~

9.5. XuMuttecrcue pearcquu u xuuuuecrcue ypaaueuuﬂ 273
pona H Bonopona, Roma qepes Hee npocxaKHBaeT aneKTpnKaH
ncxpa. Ilpyrne

274 FA. 9. Monercy/zbt u xwuuttecrcue pearcquu
Tax, KonnTBo aTOMOB Bonopona caeBa H cnpaBa B IlaHHOM
cnyqae paBHo

9.5. Xumuqecrcue pearcquu u xumuqecrcue ypaeueuua 275
_4
M'OJIeKyJIa HPEIICTaBJIﬂeT coéoﬁ COBOKyHHOCTb onpeae/zennoeo KOJIPI-
TBa aTOMOB. YnoéHee npmepmnBaTBca éonee orpaHHHoro
onpenenenna MOJICKyJIbI, a HOHHbIe KpHCTaJIJIbI (TaKne, KaK com)
me OTHOCHTb K Knaccy BemBCTB, HOCTpoeHH
nM OJIeKyJI
. Be e CT
a KO
Ba e TH
B I M B
CBHBHMH a me o
rT 6 I b H e
M O
I e K yJIBp H I
MI . o
n B M
e
( p e
m K
O O

276 FA. 9. MOAeKy/lbl u xuMuqecrcue pearcuuu
TO Mbl HeﬂpaBHJIbHO OTpaSHM cpaKecxoe COCTOHHHe Rena, no-
CKOJI
Ag
N
O a ,
a
C
l H a
03H H
P
c
T T BOB
a IH
1

9.6. Aromwte u monercy/mpnbte Beca 277
n npoueHTnoe conepmanne Kamnoro aneMBHTa no Becy B coenn-
Hennn.
UpennonomnM, HaM HBBCCTHO, HanpnMep,’ qTo Monexyna HeKO-
Toporo coennnennn cocmm n3 onnoro aTOMa yrnepona n onnoro
aTOMa Kncnopona. yCTaHOBJIeHO, Ino no Becy 3T0 coennnenne co-
nepxm'r 42,8691) yrnepona 11 57,14% Kncnopona. TaKnM 06pa30M,
oopaseu, nmeiomnﬁ Maccy 100 r, conepmm‘ 42,86 r yrnepona n
57,14 1‘ Kncnopona. He HMCH npeLLCTaBneHnn o TOM, KaKoe oomee
KonnTBo a’I‘OMOB conepmmcn B oopasue, Mb] 3HaeM, qTo B neM
paBHbLe KonnTBa aTOMOB yrnepona n Kncnopona. H03T0My 0T-
Homenne 42,86: 57,14 nomxno 6BITB paBHo omomenmo mace mum-
Bnnyanbnmx aTOMOB yrnepona H Kncnopona!
B KaTBe BTopOI‘O npnMepa BOSbMeM Bony. UponeHTnoe c001“-
Homenne Bec0B B neﬁ: 11,11% Bonopona n 88,890/0 Kncnopona.
B oopasne Inaccoﬁ 100 r, CJICIIOBaTeJO, conepmmcn 11,11 r B0-
,uopona n 88,89 r Kncnopona. LIncno aTOMOB Bonopona B nBa pa3a
oonbme qncna aTOMOB Kncnopona, HOCKOJI

278 FA. 9. Monercy/zbt u xuMuttecrcue pearcuuu
Macca a'IoMa llaHHOI‘O aneMenTa, Bblpamennan B aTOMHbIX enn-
Hnnax MaCCbI, ooblqno Ha3bIBaETCﬂ aTOMHbIM BeCOM naHHoro sne-
MeHTa. TaK Bonopon, yrnepon n Kncnopon HMCIOT aTOMHbIe Beca,
paBHbIe COOTBeTCTBeHHo 1, 12 n 16. HpnMeHeHne TepMnHa «Bee»
BMeCTo «Macca» BMa Heynaqno, OIIHaKO Hymno npnsnaTb, I{To
yqenble qaCTeHbKo rpemaT HepﬂﬂlJIHBOCTbIO mm H6C006pa3HO-CTb10
T6pMPIHOJ10I‘HPI. Upnqnna aToro — HCTopnKne npeneneHTbI n ma-
Amman 1).
B n p
c
. 3
. C O
T B T
TB
IT n npnBne H
I e
‘
3
1
s aq nn
aOM H
M acc oo ona
, nn p na
n r n eo
a TM n
o o cn
T e
I
I

Ta6/zuz4a 9.3
Cnmnounqecme 0603Haqeuna, a'romme Homepa n cpemme a'romuue
omocmenbnue maccu anemen'ron,
Bupaxenuue B aromuux enmmuax maccu
N9 Snemem CHMBOJI Aflgnggﬁ 21931:: gzlégﬁu
l A301“ N 7 14,0067
2 AKTHHHFI Ac 89 (227)
3 A1110M11H11i’1 Al 13 26,9815
4 AMepnuuﬁ Am 95 (243)
5 Apron Ar 18 39,948
6 ACTaTHH At 85 (210)
7 Bapm‘i Ba 56 137,34
3 Bepnmmﬁ Be 4 9,0122
9 Bepmnﬁ Bk 97 (247)
10 Bop B 5 10,81 1
l 1 BpOM Br 35 79,904
12 BaHaJIHﬁ V 23 50,942
13 B050 p011. H 1 1,00797
14 Bonb¢1paM w 74 183,85
15 BHCMyT Bi 83 208,980
16 I‘anonmmﬁ Gd 64 157,25
l7 ramnun Hf 72 178,49
18 I‘ammﬁ Ga 31 69,72
19 I‘eJmﬁ He 2 4,0026
20 I‘epmaHHﬁ Ge 32 72,59
21 FonbMHﬁ Ho 57 164,930
22 HHCHpOBHﬁ_ DY 66 162,50
23 EBponnﬁ Eu 63 151,96
24 )Keneso Fe 26 55,847
25 30.11010 Au 79 195,957
26 143111411 In 49 114,82
27 “on I 53 126,9044
23 I/Ipunuﬁ Ir 77 192.2
29 I/ITTepénﬁ Yb 70 173,04
30 PITTpHiI Y 39 88,905
31 Kanmﬁ Cd 48 112,40
32 Kanuﬁ K 19 39,102
33 Kanmbopnnﬁ Cf 98 (252)
34 Kanblmﬁ Ca 20 40,08
35 Kncnopon O 8 15,9994
36 Koéanb'r Co 27 58,9332
37 MHuﬁ Si 14 28,086

9.6. ATOMHble u monexg/mpnbze aeca _ 281
Hpodomrcenue
N9 anemenr CHMBOJI Aggnggn 8232!: ac: T5222: ’1.
78 Cepe6po Ag 47 107,868
79 Gene}! S e 34 78,96
80 CKaHnnﬁ Sc 21 44,956
81 CTpOHuHi’I S r 38 87,62
82 Cypbma Sb 51 121.75
83 Tammi! T1 81 204,37
84 TaHTaJI Ta 73 1 80,948
85 TeJIJIyp Te ~ 52 127,60
86 Tepénﬁ Tb 65 158,924
87 Texneunﬁ Te 43 (99)
88 THTaH Ti 22 47,90
89 TopHn Th 90 232,038
90 Tﬁ Tm 69 168,934
91 yrnepon C 6 12,01115
92 YpaH U 92 238,03
93 (DepMHfi Fm 100 (257)
94 <Doc¢op P 15 30,9738
95 (Dpanunﬁ Fr 87 (223)
96 (IJTop F 9 18,9984
97 Xnop C1 17 35,453
98 X pom Cr 24 51,996
99 Heanﬁ Cs 55 132,905
100 Hepnﬁ Ce 58 140,12
101 uHHK Zn 30 65,37
102 Ilnpxonuﬁ Zr 40 91,22
103 SﬁHmTeﬁHHﬁ Es 99 (254)
104 3p6uﬁ Br 68 167,26
B a nn u an
ee
nu e o
o p ey T
r m m B
o o r
n 'r c '

282 ['11. 9. Monercy/tbt u xumuuecrcue peaxquu
Bonpoc 9.14. y éonbmHHCTBa nerKHx aneMeHTOB aTOMHble mac-
CbI BblpamaIOTca HeJIbIMH tmcnaMH; 3T0 CBHﬂeTeJIbCTByET OTOM,‘~ITO
OHM cocrom npammecxn H3 OILHOI‘O H30Tona. Oé’bﬂCHHTe 3T0.
Macca monexynbl eCTb npocm ca mace COCTaBJImoe e
a’I‘OMOB. Ecnn MbI cnomnM omocmeJIIe aTOMHbIe Maccm Bcex
aTOMOB, KOTOe nm B monexyny, TO nonM omocuTe/zbnyto
moxzeicy/mpnyto maccy. TaK, omocmenbnaa MoneKpHaH Macca
130
p
aHa
8 (2
- , 0
1
,
0 1 ,
0
. K

9.7. Xumuttecxan apuqbuewrca 283
L11‘06131 onpenenmb, CKOJIbKO TOI‘O mm HHOI‘O nponyKTa M0)K€T
6bITb nonyo B pe3yJIbTaTe nqecxoﬁ peaKunn, mo ocyme-.
CTBHTb cnenyromyro HOCJIeIIOBaTEJIbHOCTb onepaunﬁ:
1) 3aHHC3Tb céaJInpOBaHHoe ypaBHeHHe npouecca;
2) onpeneJ
JIH
MT nyo n pe
areHT
3
H aO H
B H
Hpa HHI Ha
I T H
, a
o e
O J
HI eCTB
o p
on K
T a
M O
K
T B
1 Tn ny o nn
a
H
O M o
m e
T B e
I H M
HTIO H em - p
e a eTa
.

Pesroue 285
Peswme
MbI I/ICCJIeILOBaJIM npupony nqecxoﬁ c3913}: B MOJIBKyJIe BOIIO-
pona, H60, raK me KaK H B cnyqae aTOMa, nsyHe STOﬁ upOCTeﬁ-
meﬁ MOJIEKyJIbI C03IL3€T OCHOBy mm HOHI/IMaHHH 60JIee CJIO)KHbIX
cnyqaeB. MBI yCTaHOBHJIPI, tITo Te KBaHTOBbIe COCTOSIHI/Iﬂ MOJIeKyJI,
B KOT0X SJICKTpOHHaH I‘IJIOTHOCTb nMeeT Hanéonbmyro BeJIHy
B HpOCTpaHCTBe Memny ﬁllpaMH, SIBJIHIOTCH CBHBbIBaIOIHHMH COCTOH-
HI/IHMI/I B np0TnB0n0JI0>KHOCTB aHTHCBBBBIBumM COCTOHHHHM, K0-
rna SJIBKTIJOHHaH I‘IJIOTHOCTb cocpenomqena I‘JIaBHbIM 06pa30M BHe
MBMBBnepHoro HpOCTpaHCTBa. HpHMEHHB npnnunn I'Ia
K OI e
K y
JI a M
, Mb I m
m n 06
b
C I
/T
b n
one MMe
a O HBI
e BHH ppn -
p I
T H T
JIK O T oa K
or
n a n e
T
OH I B O
I
K J
Ie M o r
Ta
HT b B H
b Ba IO HH e
C O T O H
II
.

286 TA. 9. Monar

Oreerbt Ha eonpocu 287
non yI‘JIOM 120° npyr omocmenbuo npyra ((1)111: F
9.12). I'IpH TaKOM pacnonomeHnH Kamnblﬁ mmonb- 1
HM?! MOMeHT '10
KO H
e H
C
e TH
IB y
M
I p
y
I I
H M H .
c on
HeHH H
N
3
m o n
H
ep a
n
oa a ro ra
I
B 011111 n o
c x cm O TpH
ae o a p a
e H b e I a O
M bI ¢Topa 0
6pa
3y 0

288 FA. 9. Monercy/wt u xumuuecrcue pearcquu
9.16._
2H2 + 02 -'= 2H20,
10,0
—2,0—2- — 4,95 Mona H2,
30.0
m- — MOJIH 02.
Ha Kaxmyro ennunuy 02 npnxonmca 60J1ee 11
3
e m
u m
H
. a KM
o 6a -
0
M , I H
H T
I
O
I I
H pe a
I‘e T OH B I e
C
H
0. M
bI on
M

ﬂparcruqecxue paéom
289
ﬂoaropme 3KCHepHMeHT B TOM )Ke Bummuom
mxatby mm xopomo BeHTHyeMOM HOMeIlIeHHPI
c llpyI‘HMH )KHJIKOCTHMH: 3THJIOBbIM Cl'IHpTOM, 6e11-
30JIOM, AHMeTHJITHOHHJIOM n 3THJIeHI‘JIHKOJIeM (aHTH-
dapHaoM). Kaxaa n3 amx xmnxocreﬁ cocmm n3
nonapnmx MOJIeKyJI? KaKne H3 HCHbITaHHbIX BaMH
Monexyn MO)KHO cquTaTb Hauéonee HOJIﬂIMH? l'Io-
n‘e Jm Bbl. npyroﬁ peayaT, ecnn 6y11eTe HOJIb-
BOBaTbCﬂ B oTe nonommenbno sapameHHmM
HpellMeTOM?
2. HOHI-tbte u KOBCl/leHTl-tble 06ﬂ3u
BHI/IMAHHE! ECJIH anemponu npnéopa 11M
nsMepeHHa aneKTpnqecxoﬁ HpOBOlIPIMOCTH axmotleHbl
B ceTb, TO OCTeperaﬁT K
a c
a b cn
, T a
K
a B bI
O K BT
e o
n u
b np
a eTu
e
c TK
O MH o
me ba
II ep
n
M I
T e a e
KTpo no nB
n
c n -
n o a
H
o
d
on nc eK a noro
O bIaH 3 -
B
b B

Flt. QMOJIeKy/lbl u xumuttecxue peaicquu
lllmencenwaz JlaMnawra
swim ' :0 Ham/mama”
e 930
alert/7,0065] H '1, ‘0
(DI/II“. 9.14. Hpoc'roe yc'rpoﬁCTBo mm oénapymexma anex'rponpononnocm.
3aTeM n0MecmTe HeKOTopoe KOJIHlIeCTBO conn (mopncroro HHﬂ) B THI‘eJIb
n HarpeBaﬁTe ee, noxa oua He pacnnanmca. I'IpOBee, npononm Jm aneKTe-
cxnﬁ TOK pacnnaBJIeHHaa noeapeHHaa COJIb. HOBTOPHTe axcnepnmem c caxapOM,
HarpeBaa ero OCTopomuo, trroébl OH IIJIaBHJICH, H0 He nonropaJI.
Oébacnme nonyHbIe pesyaTbI. Race 113 PICHbITaHHbIX lIHCTbIX BemeCTB
“MEET Honuyro CKTypy? HeKOTOe HeHOHHbIe BemeCTBa, HanpnMep ycnaa
KHCJIOTa, npn paCTBopeHHH B Bone pacnanTca Ha norm. KaK M0)KHO yCTaHo-
BHTb, HMeeT Jm nomi C
K T
p
q HC
a aeH o n n
a en b B
ye Me
m a b, To
n n
ap HH a
O
JIb H B
I H
T
H un
o
' I
OH
b
IB e
e
T

3a6atm 291
6. I'IpOBee cnenyromHe XHMCHHe ypaBHeHHH H céanaHCHTe Te H3
HHx, B KOTOX dan H
a
pu e H a
CI , C
1
2
+C,

FJIaBa necmaa
COCTOHHHH B€LLL€CTBa
B NI. 1 OTMeIOCb, qTo npn Tex 3%

10.]. Farm 293
ﬂaaﬂeﬂue ——>
ﬂame/we —>
0639M ——> I/Oo’zeM
¢I/Il‘. 10.1. 035131: Mexmy JIaBJIeHHeM n 06'beMOM y ra-3013.
ape
( aM
. py
a a q a
CT HH eH e a
H n H
n

294 FA. 10. Cocrosmun semecrea
3116Cb b — Hem'ropaa nocroannaﬂ. Bemmnna b BaBHCHT OT KOJI-
CTBa rasa, ero ﬂaBJIEHHSI, a name OT emmnu, B KOToX H3MepHIOT
06'beM n TemnepaTypy.
B p
c
1.
.
K M
y 1 e
r bI
‘
JIH Ile T
ypa B eH, BIa
m
me a
O H
la p
m
, C
J T
e n pa
T
ypa ae
ca HK a JIeH n
b m , H
aKe m
B m aJI
e

10.1. 1 dab; 295
ﬁﬁwy
B 080 35’
do (96 6); go
LP 8 °° 6:4 1§° 08° 3’) °_§J
P1v1 REV;z
H2=T—§_ n~H3=—T?
2
(DI/II“. 10.2. ECJIH P1 = P2, T1 = T2 11 Vl = V2, TO 11H2 = nNHa. HOCKOJI
unno M
JeKyJ
no o p n
na
n b
n o , 1
apa H
I 0
6 Be apa
q
B x a ao a
on m
c ne
p ma TB pBH
I e K
n n TB
M J I K yJI
.
e
J
I
Bo O T
K
T H
e I e

10.]. F031;: 297
MoneKyHoﬁ MaCCbI rasooépasnoro BemeCTBa nyT-em H3Mep6HHﬂ
ero IIJIOTHOCTPI (Macca, neJIeHHaH Ha 06’beM) npn KaKHX-JIH60 3a-
llaHHbIX naBneHuu n TeMHepaType. qTOébI yéemn‘bcsl B cnpaBeJum-
30cm aToro yTBepxmeHHH, npexme Bcero npeoépasyeM ypaBHeHne
(10.4) K may
n P
7—-R—T. (10.5)
SaTeM yMHomnM 06e qacm 3Toro ypaBHEHHH Ha MOJIeKyJIHpHyIO
maccy Wm nccnenyeMoro raaa:
Wm-n _ PW,
V — RT '
I'Iocxoy nponssenenne omocmenbnoﬁ MoneKyJIHoﬁ Maccm Ha
qHCJIO Moneﬁ paBHo macce 06pa3ua, B JIeBoﬁ qacm 31‘01‘0 ypaBHe-
mm CTOHT Macca, LleJIeHHaH Ha 06’beM, T_. e. HJIOTHOCTb 6:
(10.6)
PW,
(5—7. (10.7)
OTcrona nonyqaeM ypaBHeHne mm omocmenbnoﬁ MoneKpHoﬁ
MaCCbI
PWm=6RT,
Wm: 61:] . (10.8)
B n. 1 pa311eJ1a «Hpaxmqecxne paéo'rbl» B Koaue HaCToameﬁ
l‘JIaBbI OHHCﬁH sxcnepnMeHTablﬁ METOII onpenenenna MoneKp-
HbIX mace, ocnoeaHHbIﬁ Ha ypaBHeHnn (10.8). 3T0 coomomenne
HaBeJIO CTaHao HH3Sap0, yHKa ABoranpo, Ha MbICJIb o
meTone onpenenenm aTOMHbIX Macc H ycranoanenna (popMyJI Mone-
KyJI. Bean 3131 3HaeTe MOJIEKyJIﬂpHyIO maccy IlaHHOI‘O COQIIHHEHHH H
ero npoueHTHbm cocraB, BbI MO)K€T€ mm KamnomaneMeHTa B Mone-
KyJIe Haﬁm Imono, KOTOpoe I'IpeIICTaBJIHET coéoﬁ nponssenenne
aTOMHofi Maccm Ha qncno aTOMOB STOI‘O aneMeHTa B coennHeHnH.
HanpnMep, B COCTaB amnosoro crmpTa, omocmenbuaa MoneKp-
Hail macca KOTOpOI‘O paBHa 46,1, 3 (pOpmyJIa HmeeT Bun C2H50,
nm 13,10/0 Bonopona, 34,8% Kncnopona 14 52,1% ymepona. 3T0
osnaqaeT, qTo 13,10/0 0T 46,1, T. 6. 6,05, COCTaBJmeT tIaCTb MOJIeKy-
Jmpnoﬁ Maccm MOJIeKyJIbI crmp'ra, npnxonamytoca Ha aTOMbI BOIIO-
pena. HoaTOMy BenHa 6,05 ILOJI)KHa 6bITb paBHa ‘IPICJIy aTOMOB
Bonopona B 3THJIOBOM crmp're, yMHomeHHOMy Ha aTOMHyIO maccy
Bonopona (6X 1,008: 6,05). AHaJIoro 34,8% 0T 46,] COCTaB<
JmeT Benny 16,0, KOTOpaﬂ B c3010 ouepenb paBHa Lmcny aTOMOB
Kncnopona B 9THJIOBOM cnupTe, yMHomeHHOMy Ha aTOMHyIO Maccy
Kncnopona (1 X 16,0 = 16,0), 3 52,1% OT 46,1 COCTaBJIHeT Benny
24,0, paBHyro qncny aTOMOB ymepona, yMHomeHHomy Ha aTOMHym
maccy yrnepoua (2X12,0=24,0). (Ha (pm. 10.3 HpenCTaBJIeHbI 3TH
COOTHOLHeHHH.)

298 FA. 10. Cocronuun semecrea
.1 0 060' 6:615? @060 oia < 6 -
15'; 735:]: 1:) p 6' - 1,008 e/mom amomoa MOM“ “mamas H
‘l I
41,6 3 (0'13
34,8% 11' d
CZHBO w H5108 ﬂue/70pm: 4 [MW/b amama 0
( 0.348)(46; I a) ‘1-16' 5 /MOJ16 amomoe
°/.
rafza/fe”¢oda
I M0176 6176/ 24,03 yamjooia 5 2410.0}! amomoa C
Z ' IZ a/mm amome
(DI/11‘. 10.3. OTHocmeoe Beconoe conepmarme Hexo'roporo snemeHTa B MOJIe-
xyne, yMHomeHHoe Ha 0THOCHTeJIbHy10 monexynapnym maccy monexynbl, paBHo qncny
aTOMOB aroro SJIEMeHTa B MOJIEKYJIe, yMHomeHHomy Ha omocmeylo aTOMHyIO
maccy aneMeHTa. Tax KaK MOJIH nponopunonanbnu 0THOCHTeJhIM monexynap¢
HbIM mm aTOMHbIM maccaM, 311 y
a sa HH O
T
l
eJIIe Mon ey
n
b
, MO
JI. H penonom n
M , qo BaMH n
Be
m a
T
O MH a
Ha
c a JI
pa
.
OI

10.1. F (13m 299
L L L
(H) =61] <60
pl P2 P3
Pas] [bag [7133
L
(i=0
P=pl 471241.),
(DI/IF. 10.4. Benn l‘aBbI, conepxcanmeca B 'rpex Konéax paBHoro oéseMa, nepe-
Kab B qe'rBep'rylo Konéy Taxoro >Ke oébeMa, TO llaBJIeHHe B 3T0?! Konée 6y11e'r
paBHo cyMMe naBJIeHHﬁ raaoB B Kamoﬁ H3 KOJ16 no nepexaqKH.
pacnonarae're coennHeHHeM, KOTopoe conepxm'r TOJIbKO 0mm aTOM
xnopa, TO BHOJIHe oéoCHOBaHHo nonaraTb, qTo HaH60JIbH1HM 061mm
neJmTeJIeM GyneT aTOMHbIﬁ Bec xnopa. IIaHHbIe Ta6JI. 10.1 HJIJIIOCT-
pIOT meTon. I/ImeHHo TaKaH npouenypa 6bma upemlomena LIan-
Hnssapo mm onpenenenna aTOMHbIX Macc HeKomx H3 HanéoJIee
nerxnx SJIeMEHTOB.
Bp c
10.. II pBee
nn a
, p
B eeH I
e
B
T n
ée I
IO TH
O
CT e

300 [‘11. 10. Cocrommn aemecma
paBHo cyMMe HX napqua/zbubtx daeneuua. HapunabIM name-
HneM rasa HasbIBaeTCﬂ IlaBJleHHe, KOTopoe cosnaeT naHHbIﬁ KOMIIO-
Hem rasoBoﬁ CMeCH, Korna TOJIbKO 0H OIIPIH Haxonm‘ca B cocyne.
llToébl Hal‘JlﬂllHO I‘IpeIICTaBHTb ce6e CMbICJI aToro yTBepmneHnH,
npennonomnM, qTo nmeeTca HeCKOJIbKO cocynon OIIHHaKOBOI‘O 0613‘
eMa, B KOTOX 3aKJIIot1eHbI pastime I‘a3bI npn paSHbIX name
P 1 ,
P2 14
3 .
C IIB e
T H
a b n p
e a b B
0 m
1
c o y n
o s
T
O o m e l
a JIeHH eHM
y e p a
B o y M
e 1

10.]. Fast): 301
3”“ (r1 H r2) JIIoéBIx nByx I‘aSOB CBHBaHbI c HX MOJIeKyJIHpI-IbIMH Be-
caMH (WMl H WM?) ypaBHeHHeM
'1 WM,
WM' . (10.9)
Bonpoc 10.7. Ormmme axenepnmeHT, c nomommo KOToporo B
aynmopnn Mo>KHo HOJIyKOJIHIIECTBeHHO npoBeMOHCTpnpOBaTB COOT-
HomeHHe Mexmy CKOpOCTbIO nmpqwsun rasa H ero MOJIeKpHBIM
Bec0M.
me OILHO HHTepeCHoe HBJIeHHe M0}KHO oéuapymm‘b, ecnn qepea
MHKpOCKOH c H66OJIbIIIHM yBeeHBeM HaémonaTB, KaK TaHuyror
B3BemeHHB1e B HEHOIIBHKHOM Bosnyxe KpomeqHBIe qacn nbma
(0T qKH mm curapeTBI). BHILHMbIMH 3TH qacu CTaHOBHTCﬂ
B ocrpo HaHpaBJIeHHOM ﬂpKOM CBeTOBOM JIyqe. AHrJIHﬁCKHﬁ 60Ta-
HHK PoéepT BpoyB nsyqan aHanoHoe xaomqecxoe meHne
Kpomeqnmx Bacmu uBeToImoﬁ nBIJIBuBI, B3BeIIJeHHbIX B Bone. BHa-
Ie 0H nonaran, qTo meHHe sepeH IIbIJIbIlbI KaKHM-TO 06pa30M
MO}KHO CBHBaTb c TeM, qTo I'IbIJIbIla UpHHaIIJIeHﬂ/IT K mnBoﬁ mare-
pHH. OﬂHaKO BHOCJIeIICTBHH OH oénapyxmn, Ino moéoe BemeCTBo
TaHuyeT HTb He xyme, ecnn ero xopomeHBKo BBMeJITB n pac-
CMHBaTb ero BBB
B Bo n
x em
m B
ne .
e opn a KO
o a HC T
a BH CB e ﬁ B a
ae o ém e
O
6 b
HC H
HHH OC I e
H H
r 3 0
B 1

[‘A. 10. Cocronnun Bezqecma
(DI/11‘. 10.5. BpoyHoacxoe manmenne. CHJIbHO yBeeHHoe n306pax<enne 'rpaeK-
Topnﬁ Tpex BSBeIIIeHHbIX B Bone MaJIEHbKHX qac'mu, nonomexme KOTOx (11pm-
cnponanocb qepea Kaxmue 30 c. (Flo )K. HeppeHy.)
KOTopoi’I MOJIeKyJIbI OTTaJIKHBaIOT npyr npyra c cnnoﬁ, 06paTHo
nponopunonanbnoﬁ paccmsmmo memny HHMH, momeT Oé’bHCHHTb
06paTHn ponopunona

’r§‘ (DI/IF. 10.6. BepHyJIJIH oémcmm naBneHHe raaa Henpe-
Ix BHbIMPI CTOJIKHOBeHHHMH Meai’i C
J
P
CPI
,
J a
T H
u
asco T e
K a M H
o
ya
.
C BH CHeH
e M
po n ITe
n
I OT
BI o e M
I ye
O
B OH
I
I B
I .
7)
y T
H
OBIH
I e
M
KHB JI eTH O
CH en

FA. 10. Cocroanun eemecrea
(DI/IF. 10.7. Bursarooépasnuﬁ ny'rb MOJIeKyJIbI raaa. Kamnoe uaMeHeHHe Hanpa-
anemia oéycnomeno CTOJIKHOBeHHeM c npyrofi MOJIeIoﬁ.
11) B cpedueM cromcnoaeuuﬂ newcay monexy/zauu u monercyn co cremcamu
cocyaa neuron}: a/zbno ynpyeumu.
COI‘JIaCHO onpeneneumo, Koropoe 6mm mm B NI. 2, ynpyroe CTOJIKHOBe-
HHe—STO TaKoe c'ronxnoaenne, npn KOTopOM nonHaa KHHeTHHecxaa aHea co-
ynapmomuxca qacmu coxpaHaeTca HensMeHHoﬁ. H806XOIIPIMOCTI: Taxoro noc'ry<
naTa CTaHeT ouesnnnoﬁ, ecnn Mb] HOCMOTpHM, q'ro nponsoumo 651, earn: 611 CTOJIK-
HOBBHHH MOJIeKyJI HpHBOlIHJIH K ymenbmeumo KnHeTcxoﬁ aneH, nyCTb name
IIOCTeHEHHOMy. I'lpn TaKHX oécmmenbcmax cpenHaa cxopocrb MOJIeKyJI rasa
nonxma 6mm 61:! Taxme IIOCTeHeHHO YMeHbHIaTbCﬂ. Bo Bcex Gonee TOHKHX KHHe-
ecxnx monenax coxpaHeHo npenCTaBJIeHHe BepHyJum o TOM, qTo JIaBJIeHHe
raaa eon: cnenc'rane CTonKHoneHnﬁ moneKyJI. ECJIH 6H cpemma cxopocn: monexyn
ymeHbmanaCb, T0 llaBJIEHPIe B SaMKHyTOM T6HJIOH30JIHpOBal-IHOM cocyne nonxmo
6131.110 61:1 nana'rb. Ho aToro He Haémonae'rca, OTKylla cnenye'r BblBOJI o cnpaBen-
JIHBOCTPI nocnennero HOCTyJIaTa. (B JIIO60M CTOJI’KHOBeHHPI qacrb KHHeTCKoﬁ
SHepmH M0}KeT GET]: napacxononana Ha Boséymnenne BHyTpeHHero nnnmeuna B
MOJIeKyJIax. OnHaKo B cnenyromeM CTOJIKHOBeI-IHH snepma BoséymneHHoro co-
CTOﬂHHH aToﬁ Monexynbl CHOBa Mome'r nepeﬁm B KHHeTCKyro aneprmo 03.1101”!
113 coynapmomnxca MOJIeKyJI. B' pesynb'ra're B cpenHeM n0Tepb KHHeTuqecxoi’a
3HepI‘HH He nponcxonm.)
B
no c
.
.
B penb y
m IJIa B
a M
I
CTaOB HIH
I IO
T O
I K
H
O B HH a
e e m ya n o
e e T Be

I -
Tl F 'L‘P
‘ /4 (nl ,L‘
(V H
(DI/IF. 10.8. Paccmorpeauaa B TeKCTe MO- | ,x’ 0%) w -' £
/
nenb. Pas cocrom‘ 143 N MOJIeKyJI, Kamnaa «L «
n3 Ko'ropux nmee'r maccy m n unnmerca | ‘Ym, ,, a
co cpenneﬁ cxopocnno :7 no cnyqaﬁHmM ,5” v ’4! (Eli
HanpaanennaMB Kydnqecxom cocyne c mm- ’| - (m, ’/
Hoﬁ pe6pa l. I bx,’ I:
k ————_. —. —_
/
k g, —>
93’ '
I I
ﬂ @3
I/ ’l / I
/ /
r / £77)
I
(DI/11‘. 10.9. omemiaa M011r aa: 1/3 N MOJIeKyJI namxe'rca Bnepen H Ha-
san nepneHnuxynapHo Kamnoﬁ nape napaJIJIeJIIX c'reHox Kyénqecxoro cocy11a.
I—__
/ '
+MI7
(DI/IF. 10.10. MoneKyJIa, ImeBmaa nepen
CTOJIKHOBeHHeM co CTeHKOI71 HMHyJIbc
+ M6, nocne CTOJIKHOBeHHﬂ nMee'r HM-
HYJIbC — M :7.
-MI7

306 1‘11. 10. Cocronnun aeugecraa
ypaBHeHne (10.4). TaKoﬁ 131313011 aHanorn aa m
y
, n e
n n m en
H om y I
K o eM
. a
C
O Tp H
r a 3
c o
m
mn
ﬁ
1
3
u n H
H
l
M
OI KJIK am
-
n a a H
K T0

10.]. Fast»
TepBaJI BpeMeHn At COCTaBHT
_ pacc'romme _ _l_
a .
B TeHe aToro HHTepBaJIa qHCJIo IKHOBeHnﬁ c Kamnoﬁ CTeH-
Koﬁ paBHo HOJIHOMy uncny MoneKyJI, KOToe B Hameﬁ monenn 113n-
ma Memny llByMH npomBononoIMn CTeHKaMH. 3T0 qncno
(‘OCTaBJIﬂeT 1/3 Bcex MoneKyJI, Haxonaumxca B cocyne, T. e. paBHO
N/3. HOCKOJI K
a me CTJI
H Be H H e e
e
r n
se eH oH
M n y
JI
b ca Hae
JI H HH
y 2
M
, o m e
H
MeH e
H He HHJIb

1‘11. 10. Cocrommn aezqecraa
06bIKHOBeHHoe qHCJIo, MbI MomeM 0603HaqHTb ero JIIOGbIM CHMBO-
JIOM, KaKoﬁ HaM HOHpaBHTCH. B npyrnx pa60'rax 6131.110 noxasaHo‘,
qTo HMeIOTCH BeCKne npnbI (CBHBaHHbIe c npnponoﬁ TOI‘O upOCT-
pnBa, B KOTOpOM, KaK MbI nonaraeM, cymeCTByIOT Haum
MOJIeKyJIbI) Bu'épa'rb B KaTBe MHommeJm nponopuuonanhHo-cm,
CBHSbIBaIOIJleI‘O KHHeTcxyIO aneprmo MOJIeK c
a
c OJI OH
o T e n pa
T
p o
, e I M IH y
3
/2 12
12
3
lICOI
b y H
TT o ne
n nﬁ O
T JIaH HO
H B
O
HO T e T
CTB
yO
m
y o OI T
a HO
B Ky

10. I. 1‘ dab: 309
rnqecxoi’i MOIIeJIH. YK‘peruIeHmo BepBI B KnBeecxyro Teopmo cno-
C06CTBOBaJIa Taxme Ta JIeI‘KOCTb, c KaKoﬁ aTa Teopmi HOSBOJISIeT
06'bHCHHTb npyrne BBJIeHmI B rasax. paCCMOTpHM, Hanpnmep, 0613-
HCHeHHe 3aK0Ha FpexaMa (10.9).
PaByMHo npennonommb, LITO CKOpOCTb mupcpysnn rasa nponop-
unonanbna cpeBHeﬁ cxopocm LLBmKeHnH ero MoneKyJI. CTporoe
paCCMOTpeHHe llHHaMHKH rasa, B KOTOpOM HpHHHMaETCH, Inc 11811-
)Kyumeca CTaJIKHBaIOHlHeCH qacmubl c0Bepma10T Tax HasbIBaeMoe
c/zyttaduoe 6/2yoicaanue, KaK MbI upelmonommln B Hameﬁ Kn-Hemqe-
CKoﬁ MoneJm (CM. (pm: 10.7), nomBepxmaeT TaK HTy
IIB H In
o r
a n x y .
CJIeI O
a e
JII
I
, B
yaB
e H n
e 1
0.) ,
B I
p mmee a
KOH px a
aB e T
o o
en
c o
p OCT ﬁ nm
b p
y nr

310 FA. 10. Cocroanuﬂ semecrea
I'Ide

10.]. fast»: 311
Q;
3 §
§ e
K) 3 ‘
k T k
3 23
E 1‘ E
3:, Q Mewmwzezrympyoe pace/770mm —>
0 1
j §
§ 7‘ m 4 . A
.. 3 I 1
l 1% ' '
E Paccmoﬂﬂue mewcdy Pacemmnue memdy
a mane/rynamu a madam/nu mama e Managua/m;
.§~ (Um a maepdom mane e ease
(DI/ll. 10.13. 3aBMoc1'b peaynbmpyromeﬁ Memmonexynapuoﬂ CHJIbI OT pac-
cros‘mna Memy MOJIeKyJIaMH. (H3 KHHI‘H: G. Holton, D. H. D. Roller. Founda-
tions of Modern Physical Science, Addison-Wesley, 1958.)
HeJIbBH nepeBeCTH B mnnxoe cocmmme npn TeMnepaTypax BbIIJIe
-— 147°C, a COg—UPH TeMnepaTypax Bblme 31°C). Honommenb-
HbIe OTKJIOHeHHH (peaJIbHaﬂ Kpmaaa npoxonm‘ BbILIIe mneanbnoﬁ npa-
M0171) y peaJIlx rasoB He ob 3aMeTHhI, BHJIOTb no naBJIeHnﬁ
200 aTM H BbIIIIe.
B n o c
1010
K a K
b I n oa ae
e ,
y K a K
I O
Hn e pe
q nn e
H b
x H u
ea o npny
as a
H o
T e
m ne
pTyp e y n
TH a
m on
ab a TH o e
JIb oo n me

10.2. )Kuarcocru 313
10.2. )Kmumcm
BBOﬂHbIe KbI (pnsmm 06131 c
n e ma
neTa J
I H e o
n c a
H eTB ep
x enH a
o B
To a a
KK IKO M
co c mm o
K
K n
pa BH
J Oy e
m e
c a e
H b meH H
a H HH e
CJ m
H Bo me
no mn a T
-
c
1 I I
e M
T
0
M 0
KHO

10.2. )Kudrcocru 315-
Oé'beM mnnxocm CpaBHHTeJIbHO mano saBn
O Te
M e a
T
p b n I
a J e H
ﬂH
aM e
p e
C IH

316 1‘4. 10. Cocronuun semecrea
HamepeHHa BHBKOCTH ncnonbsyro'rcn pa3H006pa3Hb1e MeTOﬂbl, 0mm
n3 KOToX BaKJIaeTCB B H3MepeHHH cxopocm nanemm MeTaJIJIH-
qecxoro maa B éxe, sanonHeHHoﬁ nccnenyemoﬁ )KHIIKOCTbIO.
CMaSOIe pBOﬁCTBa MaCeJI PI CMa3OK caMbIM TBCHBIM 06pa30M CBS!-
BaHBI c Hx BHSKOCTHMH. HPOHHKaIOLHee Macao, Koropoe MeHmor
npn 0TBopaaHHn BapmaBex 60JITOB, n0J1>KHo HMeTB oB
HHBKyIO BHSKOCTb. C npyroﬁ CTOpOHbI, CMasBIe Macna mm ra-
-'reJIeﬁ IlOJIKHbI oénanaTB BeebMa BbIcoxoi'x BHSKOCTbIO, qT06BI 01m
He BbIMHMaJIHCb n3 3a30p0B Mexmy KyumMnca qacmMn.
IV éoHHCTBa )KHILKOCTeﬁ c pOCTOM TeMHepaTypBI BHBKOCTb 3a-
'MeTHO yMeHbIIJaETCH.
Bon p
c 0 .
1
.
T OJII
o
ne
J m
B HH e
pe H
06 I

10.2. )Kudxocw 317'
QO
0
a 6
(DI/IF. 10.16. IlByMeIe monenn rasa (a) H mnnxocm (6).
OHH xaomqecxn mamxyTCH r10 paBHbIM HanpaBJIEHHﬂM, noq'rn TaK
)Ke, KaK MoneKyJIbI ra3a. OnHaKo cpenHee paccrosmne, KOTopoe
MoneKyJIbI npoxonm mexmy ﬂByMﬂ CTOJIKHOBeHnHMH (mu/(Ha c130-
6011HOI‘0 npoéera), B mnnxocm COCTaBJIHeT TOJIbKO Hecxoo 11e-
CHTbIX aoneﬁ aHFCTpema, Toma KaK B rasax npn oébblx IlaBJIe-
HHHX aTa 11JIHHa nocmraeT COTeH aHI‘CTPEM.
Xaomqecxoe KeHne B mnnxocm MomeT HaTOJIKHyTb Ha-
MblCJIb o TOM, Ino B mnnxocm He cCTBYET—KaKOﬁ-HHGO ynopsl-
noHocm mm onpeneneHHoﬁ CKTy. B ﬂeﬁCTBHTeJIbHOCTH )Ke-
llaHHbIe no paccemimo peHTreHOnx qeﬁ B mnnxocmx noxa-
3blBaIOT, ‘ITO B Kamnblﬁ naHHbIﬁ MOMeHT B pacnonomeHnH MOJIEKyJI'
nmee'r MeCTO BbICOKaﬂ CTeHeHb perpHocm H CKTy. OnHaKO-
TaKaa ynopﬂn0HOCTb cymeCTByeT TOJIbKO JIOKaJIbHO (Tax Ha3b1-
BaeMbIﬁ <<6mm<Hnﬁ>> HOpﬂIIOK). llByMepHaH Kap'mHa, noncnmomaa,
q'no nonpasyMeBaeTcn non 6J1H)KHHM HOPHIIKOM, npenCTaBJleHa Ha-
qmr. 10.16, 6. BHILHO, ‘H‘O 6OJIbLHHHCTBO C(pepnqecxnx MOJIeKyJI 0K-
pymeHo IlleCTbIO IlpyI‘HMH, mm H cosnaeTca JIOKaJIIﬁ IIOpﬂlIOK.
B 6J1mKHeﬁ 06JIaCTH, HeKOToe H3 3THX MoneKyJI (mmeuennme
mTpHXOBKoﬁ) oxpymeHbI TOJIbKO HHTbIO MOJIeKyJIaMH. 3TH Mme--
KyJIbI COOTBeTCTByIOT netbem‘aM, KOTOe CO3IIaIOT nanbmoro Heyno-
pﬂIIO‘IEHHOCTb. Bnaronapﬂ HenpeBHbIM 6bICIM cmemeHHHM-
TpexmeIx necpeKTOB BHyTpH mmmocm ee MoneKyJIbI oénauT
BbIcoxoﬁ nonsnmnom‘bro. Hpn nosbuuennn TeMnepaTy m
n o m
CTe
le HH
e
ﬂ o p
ﬂ o
H
CTH n

318 FA. 10. Cocroauun semecrea
B MHKpOCKOH 6p0yHOBCKoe KeHHe uBeTOﬁ HbIJIbubl mm npy-
rnx Mnxpocxonnqecxnx qacmu, B3B€IIJeHHbIX B mnnxocm. ybIe
MHOI‘O paéoTamT Han TeM, qToébI pacmnpmb KaTBeHHbIe upen-
CTaBJIeHmI 06 amx n npymx HBJIEHHHX B mnnxoﬁ (base, CTpEMHCb
.noﬁm no TaKOI‘O ypomm HOHHMaHHH, Korna MO)KHO GyneT nepeﬁm
K uonymo KonnTBeHH
c
o
om e Hnﬁ.
0
3
.
Kpc m
m ue
c x
eB e pn ee
J a Bp eT
e JI
a a a K
T p
n
y
O Ta , a
Ka e
m
o
,
K CT OCT
I. r p
KT
y
B
np o
m oo o ao
cmT ee ma o B n

(DI/11‘. 10.17. (DopMa KpHCTaJIJIOB noaapeuuoﬁ coma sasncm 0T ycnonnﬁ, B KOTO-
X OHH BaHleHbI. (P13 KHHI‘H: B. H. Mahan, University Chemistry, 2d ed.,.
Addison-Wesley, 1969.)

320 1‘22. 10. COCTOﬂHuﬂ eeugecraa
(DI/IF. 10.20. Oéoanauennn pe6ep (a, b, c) :4 I03
((1, B, y) B TotiKe nepeceqemm pe6ep 11m: aJIe-
MeHTapHoi’i aqei’ixn Kyénqecxoﬁ peme'rKH.
~ ‘
a
a
b

10.3. Kpucm/uzuttecrcue reepabte Te/ta 321
HCTHHHOI‘O TBepnoro TeJIa. OCHOBHoi’i CTponTebIﬁ «Knpnnq» 3T0?!
CKTy H
a B B BI
Tae e na
p
o ﬁ
t e
r
o ﬁ H
O T
O HH T
C K
T
y
Ie
I
I
IHH
I b
I n n e

(DI/IF. 10.22. BonopoIe caasn B B0116. Hapsmy c cnoﬁ nonapnoﬁ CBHBbIO 0—H
cymeCTByro'r 60J1ee cnaéble Bonoponnue c3331! 0 H, oépasyroumeca Memzy
OTpHuaTeJIIMH aTOMaMH Kncnopona H nonomHTebIMH aTOMaMH Bonopona.

10.3. KpucTa/mwtecrcue Taepabze mm 323
OCHOBaHHaH Ha TOM, qTo KpHCTaJIJl xapamepnsyror no TeM CHJIaM,
KOToe CBHBbIBaIOT ero qacmubl. I'IpH TaKOM nonxone paannqaro'r
BIpe Tuna KpHCTaJIJIOB—MOJIeKyJIﬂIe, KOBaJIeHTHBIe, HOHHbIe
H meTaJIJICKHe.
Monetcy/mpnbte Teepabte Te/za COCTOHT B3 OTIleJIIX MOJleKyJI
mm aTOMOB, KOTOe ynepmnBaroTca CHJIaMH Ban-nep-Baanbca,
a B cnyqae I'IOJIHIX MOJIBKYJI—ILHIIOJIb-ILHIIOJIIMH BsanMoneﬁ-
CTBHBMH. HpnmepaMH MOI‘yT cnyB H011, cepa, cyxoﬁ nen (TBep-
nan IeKHCJIOTa C02) PI HHepTHbIe rasbl B TBePIIOM COCTOHHHH.
Bnaronapa OTHOCHTeJIbHO cnaébm memmonexynapHmM emaM KPH-
CTaJIJIbI sToro Bnna HMeIOT Hnsxyro TeMnepaTypy nJIaBJIeHmI.
Kpome TOI‘O, HOCKOJI 3 HCH
JII 6
3
1
He H B JIIOTCH CTp
m H an
aB Ie
H BMH M
ne K
JIBI
c
.
11 a 0
C
OpO H B I H
O I
C H e
é
on m nM
c
eI H HH H n
ono e

324 1‘ ll. 10. Cocronuun semecrea
(DI/II. 10.24. CKTypa rpatpma. Ko-
BaJIeI-ITHO cnaaannue aTOMbI yrnepona
06pa3y101' nByMepHme cnon c rexca-
ronanbnoﬁ CKTypoﬁ; memny CJIOHMH
neﬁCTBylo'r cnaébxe Monexynnpnble
c1393. (H3 Knnrn: Chemistry: An
Experimental Science, ed. G. C. Pi-
. mentel, Copyright 1963 by W. H. Free-
W man and Co.)
Knacca HpeIICTaBJIHIOT coéoﬁ Hanéonee TBepe BemeCTBa c oneHb
BbICOKHMH TeMnepaTypaMn nnasnennn.
TpeTnﬁ Tnn KpHCTaJIJIOB, uounbte ICpuCTa/l/lbl, COCTOSIT n3 nono-
mnTe

10.3. KpucraA/zuttecrcue Teepdbte Tena 325
IIJIaBJIe-HHSI MBTaJIJIOB nemaT B Ob umpOKOM ananasoHe 0T Ob
Hnsxoﬁ (pTyTb nnaamca npu —38,9 °C) no men!) Bblcoxoﬁ (30m:-
(ppaM HJIaBHTCH npn 3380 °C). KpOMe TOI‘O, KpPICTaJIJIbI MOI‘yT 6bITb
MHI‘KHMH n KOBKHMH mm me TBepMH n XpyIIKHMH.
B TaéJI'. 10.3 l'IpHBelleHbI OCHOBHbIe xapaKTepnn

326 FA. 10. Cocrwmun semecrea
% . g
B aKuﬁ Memioysmwué ﬂue/101mm}!
(770M
DI/IF. 10.25. TpH Tuna neQJeKTOB B KpHCTaJIJIaX.
ﬂpyroﬁ Knacc ne¢eKTOB CBBBaH c npncyTCTBneM npnMeceI‘i.
Tomno MaJIbIe KOJIH‘JECTBa npnMeceﬁ cnoc06HbI KaTaCTpocpnqe-
CKH H3MeHBTB TaKne CBofICTBa KpHCTaJIJIOB, KaK SJICKTpOHpOBOII-
HOCTb n HHOCTb. KOHTpOJmpyeMoe BBeILEHHe Meceﬁ c HBJIbIO
nonynB MaTepHaJIOB c OﬂpeIIEJIEHHbIMH CBOﬁCTBaMI/l mnpoxo
ncnonbsyeTCB B HpOH3BOﬂCTBe HOJIyHPOBOILHHKOB, npnMeHmoumxca
B aneKTpOHHKe.
10.4. Hameﬂemm cocmmmn
Bona BBJIBeTCB eIIHHCTBeHHbIM BemeCTBOM, co BceMH TpEMﬂ qm-
ecn COCTOHHHHMH KOToporo mom: CTaJIKHBalOTCH B HOBce-
nBeBHoﬁ mnsnn. MbI HaM nsyne nsMeHeHnﬁ COCTOBHHBCOHH-
caHnB MaKpOCKonnqecxn HaémonaeMBIx upeBpameHHﬁ, KOTOe
nponcxonm c STEM oémensBeCTHBIM BemeCTBOM, a BMW paCCMOT-
pPlM, KaKHM 06pa30M oémee BBJIeHne nepexona n3 OIIHOI‘O COCTOH-
mm B roe M0)K€T 6131Tb CBBBaHo c MHKpOCKTypoﬁ BemBCTBa.
HOMBCTHM Kyc0 JIbI
Ia BCT
K a n H a
p o eMe oT K
I HH I M
O I HK OM
q
m r
10
.

10.4. Hsmeueuuﬂ cocronuun 327
[Tl
(DI/IF. 10.26. LlaBJIeHHe napOB B01113! 11011 KOJIHaKOM, cosnaBaseMOe JIblIOM B c'ra-
Kane npn TeMnepaType —10°C, paBHo 2,8-10— aTM.
‘
KOMHaTHoﬁ TeMHepaTy

328 {'12. 10. Cocronuuﬂ semecrea
Bosnyx B K0JI6e e To}?! Totnm, 11pm Koropoﬁ OH 6BIJ1 HOJIHOCTbIO
HaCBImeH Bonoﬁ, noaTOMy na B O
l b
C O H ECH
O Ba
I I Cb
. O T
Ome
H e Hp
Ha
JI H I
OI aB
JIe HH n a OB
O
ﬂbI
B B on
x KI
L I B
IH
II H a
B m e
H BI
n p
B n n
aH o
T en ea T y eH
aB I B a T H
o
m o c
u -
Te

10.4. Hameuenuﬂ cocroxmuﬂ 329
antiwar/791761109 A’UJIZZW’C'MEU Ara/zany.”
§
~~——_—
KuHemuz/eczraﬂ ayepauz Ha odﬂy Nil/7811’

O
O
E (DI/11‘. 10.28. Korna JIOCTI/II‘HYTO paBHOBecuoe name-
m we napa, CKOPOCTb KonneHcaunu CTaHOBHTCH paB-
Hon cxopocm ncnapeHHa.
HeoéxonHMblﬁ mm CTaénocm KpHCTaJIJIa. 3T0 Bonm‘ K pas-
pymeHmo CKTy p e eT B
Bep
I O
I
OTea
HH e T H
u JI a B I
e
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o
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10
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0

332 1‘ J2. 10. Cocronnun eewecraa
/
yompozicmea 01m uJMPpP/ﬂlﬂ
x mmnepamypu, ﬂea/mm}? 11m. 0.
(DI/11‘. 10.29. LInc'roe BemeCTBo B He c nopmHeM.
~
~_
/
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3
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u

10.4. Hamenenuﬂ cocronnua 333
TeMnepamypa, °C’
50 100 [50 200 2.50 300
l I I l I T
104 __
103 — .
2
5 1 g
4).. § at q, JfCaﬁzrae /
g g g é, g 00017101111119
5 [0‘3 ,— 2 § ‘5 Q
3 1% 5 3E
:1 a ‘3‘ a .
[0,4 _ g 1mm 8.
n 0119115
aeJIuKo
-6 I‘aaoadpwﬂoe ' 1‘
10 - 00017101111118
4 l l L L
llpeao’ﬂadaromue K011111111 6,, b’napoz/enmle 116112;
470]: m. 9. ~ 8,,-
¢HF.10.3I. <1>a303a11 nnarpaMma cep31, KOTOpaH CYHIECTByeT 3 HeCKOJIbKHX
TBepx monncb11xau1111x.
Bone samepsHyib. E01111 631 11e11 He 63111 11erqe 301131, T0 MHOFHé
Haum 03epa 11 pyqbn npomep3a1111 631 110 1111a, c1103313as1 Bee >1111331e
cymeCTBa, 11x Hacenmoume.
HEKOTOe semeCTBa' 3 3a311011M001‘11 0T TeMnepaTy 1
1 a e 11111 OI
yTy e
T
B OB aT
He
3111 011 ,
a
HeCK O
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334 F A. 10. Cocroxmun eemecrea
HOI‘O 0101111e1111H 116 631110, TaK I110 3 ceBep331x Kpaax, me 0pra111131e
631 3 TeHeHHe 1111H1e113110r0 3peMeHH HaXOIIHJIHCb
TeH
ep
a T
p e
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0 1 1 03 0
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l
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31M H
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Pearome 335
ﬁ
xapamepncmqecxux CBoﬁCTB. )Knnxocm He pacmnpmoma 14 He 3a-
[IOJIHHIOT BeCB l'IpeILOCTaBJIeHHbIﬁ HM oébeM'. OHH 3HaqHTeJIbHo 60-
.nee IIJIOTI-Ibl, tIeM I‘a3bI. OéBeM )KHILKOCTH H3MeHHeTCﬂ c TeMnep‘aTy-
poﬁ mm IlaBJIeHHEM mum: Hesnaqmenbuo. He Bce mnnxocm eme-
IHHBaIOTCH Mexmy coéoﬁ B Juoéblx nponopumlx. 3HaH§I Basxocm
(cuna, HpEHﬁTCTBYIOIIIaﬂ Temo )KHIIKOCTH) sameTHo pasnnqa-
[OTCSI y paBHbIX MHJLKOCTeﬁ H B. 60JIbIHHHCTBe cnyqaeB 6BICTpo
yMeHbUJaIOTCH c pOCTOM TeMHepaTypBI.
K comaJIeHmo, 11.1151 mnuxomeﬁ noxa He yCTaHOBJIeHbI yHnBep-
caJIBHBIe coomomennﬂ, nonoénble 3aK0Hy uneaJI-BHoro rasa. Monenb
mnnxoro COCTOHHHH noxoma Ha Monenb rasa TOJIbKO B TOM 0THO-
memm, qTo MOJIeKyJIbI mnnxoucm Haxonmca B UOCTOHHHOM BBmKe-
HHPI. MoneKyJIBI )KPUIKOCTPI Haxonmca B HenocpeBCTBeHHoﬁ 6Jm30-
cm npyr OT npyra, HO upn STOM OCTaIOTCH BocraTotIHo noK-
HbIMH. HBCMOTpﬂ Ha TaKn oKHOCTB, B nonomennﬂx MoneKyJI
B mnnxocm HaémonaeTCH xopomo BameHHBIf/‘i 6J1H>KHnﬁ nopsmox.
Korna )KPIIIKOCTI) nepexonm B KpHCTaJIecxoe TBepnoe COCTOHHHe,
JIOKaJIBHBIﬁ nopﬂnox, xapaKTepHBIii mm ee CKTy, nepexonm
B nanbnnfi HOpHILOK npommeHHoﬁ meCTKoﬁ BblcoxoynopﬂnoHoﬁ
CKTy. HOBTopeHHe reOMeTpnKoro pacnonomenna Mone-
KyJI, COCTaBJmIomero MHKpOCKTypy KpHCTaJIeCKoro Beme-
CTBa, 06yCJIOBJmBaeT peryHOCTB H CHMMeTpHIO BHemHei’i (popMBI
KpHCTaJIJIOB. MOJIeKyJIbI B KpHCTaJIJIaX saxpenneHBI ropasno npoq-
nee, B
aa x mnn
x o
c m
x , HBe eH
M I T
OB OH CT
b o
n
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Oreerbt Ha BonpOCbt 337'
_“
10.4. 06p'a3y101n111’1cs1 ra3 conep
TO 1
e
n c no M011ey1111 0
11 on n m 0
p 3
e
u
2, O
K
O
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b
K

338 ['11. 10. Cocronuun acmecrea
10.10. Bonbmoe OTpHuaTeJIbHoe OTKJIOHeHHe 6¥neT 11a6111ona'rbca 'I‘OJIbKO y 30-
O 0
mmux napon 11pm 110 C. y Kncnopona 11pm 50 C n y renmi
—0

0130101 11a aonpocbt 339
10.14. 063011 1 11 1130311311010 1333, 11M03111010 10M110p31ypy 20 °C-11 1133110-
11110 1 31M, 11p11 03111110111111 TeMnepa1yp31 11.0 10°C yMe113111301011 110 3113110111111
283
V —- ﬂ — JI,
3 11p11 y301111110111111 1133110111111 110 2,00 31111 0630111 yMe113111301011 110 3113110111111
V= (1,00) =0,50 11.
10.15. .11111p011011113113301111311 0M33113 11011111113 0611311313 1111311011 311311001310,
1101113 113111310113 x01101111311'1, 1110631 010 M0)KHO 631110 030603110‘11p030p311113313.
B 10 1110 3p0M11 0113 11011111113 111110113 1100131011110 60113111y10 3113110013 11p11 rop11q0M
113111310110, I110631 63101p0 11311111y1u110011 I130111 300 3peM11 6311111 no11p31131 0M331101’1.
Kp0M0 1010, 011133113 11011111113 63113

1‘11. 10. Cocronnuﬂ eetqecraa
10.21.
1,4.10-2
2,8-10—2
10.22. Hpn BnamHocm 98% Boanyx 110
H a m e n
0
1 0
? H
C OO CT
uc a p HHHo r a
an a.
ITo m
IOB
e K
CB O a
JI e ao p o
o
1 1T
a c m
e nna pa T
b a b
I

17 paxruuecxue p060Tbl 341
CHHMHTe napymnylo anromnnnenyro (ponbry. ﬂpocymme n Baaecme Kon6y,
(ponbry n peannonylo neHTy. Bblq'rme n3 nonyqennoro nepBonaqayro maccy n
onpenenme Maccy cxonnencnpoaannoro mnnxoro nnxnopa'rana. CnnMn're (bonbry
c omepcmem n HanoTe Konoy no camoro Bepxa Bonoﬁ. HepeneﬁTe aTy Bony
B MeIﬁ unnnnnp, qToébI naﬁTH oébeM xon6b1.
Tenepb BbI .pacnonarae're Bceﬁ HeoéxonHMoﬁ nmbopManHeﬁ! Macca mnnxoro
nnxnopa'rana, nenennan Ha 06'beM KOJ16b1, ecrb IIJIOTHOCTb raaa npn 373 K n
nannennn 1,0 am. (Heoonbmnmn KoneoannnMH Bnemnero nannennn MO}KHO npe-
Heépeqb, no ecnn naMepeHnn nponanonn'rcn Ha éonbmoﬁ BblCOTe, onenyeT nc-
HOJIbSOBaTb 6ap0MeTpnqecxoe naBneHHe, Bblpamennoe B aTM0c¢epax.) C no-
M011 y p a
H H H n
10 .
) on
en nn e oo cen
n yo o
ne
x n
pn r o a
cnn xn o
p r a a
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y
n n nn o a a H
a H e T
B H
I C H
C
l . K
a xnae o nc rnan
oomenbn a n one
y
n
na n a c
a
K a on a
c ona c erc
a ca m

342 FA. 10. Cocronnun semecrea
BospMuTe Heéonbmoi’i Kyc0qex cyxoro .nbna. C IIOMOLIO MHnnnmeTpOBoﬁ
JIHHeﬁKH n

Saaauu 343
llaBJIeHHe, xo'ra Knnemqecxaa aneprna monexyn OCTaJIaCb Tog”! )Ke camoﬁ? (I'Ipn
0TBeTe Ha 31‘01‘ Bonpoc oépawme BHPIMaHHe Ba TO, Ha Kaxnx aranaBona
ra30Boro saxona H3 KHHeTuuecxoﬁ Teopml onenye'r ThIBaTb yMeHbmeBne 0.61:-
ema cocyna.)
9. ﬂame onepaunonaoe onpeneneHHe CBOﬁCTB, OTJIHlIaIOIllliX )KHIIKOCTb or
raaa.
10. Kaxan n3 nepeqncneHHblx e nByMeIx qmryp MomeT 6bl'l‘b PIC-
nonbsonana mm BOCTpoeBHa nBymepHoﬁ pemeTKH, aanonHmomeﬁ BCIO HJIOCKOCTb:
KBaaTbI, rn, paBHOCTopOHHne TpeYI‘OJIbHHKH, HpaBHJIbI-Ible namyronbnnxn,
npaBHJble mecmyronbnnxn? Mome'r Jm 6bITb HCIIOJIbBOBaI-Ia mm more npa-
BHJIbHaH ¢Hrypa c 60J1ee
me T I
O r p n Mn
l. T
K
HI
‘ amo
a e Ta BO
M ,
T
o Be ne
T e J I oar
p e am no TM e a-
r p b r
H e
CO I
K m
a ee To

I'IpmtmkeHHé nepBoe
“peﬂCTaBJIeHI/Ie queen
B (popMe CTeneHeﬁ necsmd
paCCMOTpHM B Kaqecme Mepa OlIeHb npocmﬁ pacueT. HaﬁneM‘ BpeMﬁ, sad
TpaqHBaeMoe Ha npoxomneune onpeneneunoro paccmmma, ecam cxopoc'n, H3-
BeCTHa. HOCKOJI C
K p O T
v
=
x
/

ﬂpedcraexzeuue twee/1 a ¢op1ue creneued aecnru 345
11 CMeCTHTe sanm‘ylo 11p0611 Ha ueTe 110311111111 BnpaBo. Honyqn'rca 10 000,0. [[1151
101 sanm‘aa CMemaeTca 11a 01111y 110311111110 BnpaBo: 101 = 10,0. £11151 10° sansrraa
1111Ky11a He CMemaeTca: 10° = 1,0. 111111 10-1 3a11111‘as1 cmemae'rca 11a 01111y 110311111110
BJIeBO: 10I = 0,1. BOSbMeM, Haxoueu, 10—3: 311
s a
n a nc
ema e r a
1aT p 1101111111 1
B
JI B
OI
1 0'=00011
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pa y 1
1 1110 , 11 0
a a y
CH
CTe M
311 1
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Ha H e
0 o pa m e
re CT , e
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11 Me 11 . 1
11 anncn 1
110 1
61 o nH a

346 17 puaoacenue I
HonbsyHCB 31011 0110'reM01'1, Mb! 1110111011 HpOHBBOIlPITb yMBomeHne 11 nenenne
11106b1x queen.
Bce I111011a, HCIIOJIb3yeMbIe B nanuoﬁ sanaqe, Hymno npenc'raBuTb B (popme
nponsaenenna M1101K11're1111 c 0111101'1 umppoﬁ no 3an11'1011 11 cooraeTCTByIOmeﬁ 01e-
neHn 110011111. 3a1~eM Moxmo 110111111: 111111 yMHomaTB 1111<pp0Bb1e anaqenmi 11 BbI‘IPI-
TaTb 111111 CKJIallhIBaTb CTel'IeHH 11e011111.
E01111 BepHyTbca 11 Bameﬁ nepBo1'1 aanaqe, me HaM Hymuo 6b1110 11311111,
CKOJIbKO BpemeHn no'rpe6ye'rcs1 CBeTy, t1106111 npoﬁ'm paceroanne, paBHoe 1111a-
Me'rpy npo'rona, TO 1110111110 3a11110a1-B
l - 10‘15 M l -23 —'24
m—E-IO 01:33-10 0.
311cm: Mhl npeo6paaoBa1111 11110111310111) TaKHM o6paaoM, 1110611 B 110M 110 611110
npoéeﬁ, noa'romy noxasaTeJIB CTeneHn 11p111111100b yMeHbIIIPITb 11a onHy enmmuy:
c 10—23 110 10—“. Taxoro aaxona, q'ro MaomnTeJIb 110JI}KBH HMeTb onHy umppy no
3311111011, HeT. 310 npoc'ro y1106110, x0111 111101113 yno6Hee npyraa 331111013.
Bo'r 11001100 HpHMepOB BblllHCJIeHHﬁ 0 HCHOJIb3OBaHHeM CHCTEMbI CTeneHeﬁ
110011111:
684 _ 6,84-102 _ 6,84
_ _ . la, . 1=
1) 21 2.1.101 2’] 10 3,3 10 33.
0,0084 3110‘3 _7
2) 42000: 4,2-104 =2’0'10 ’
3) 045-3352 = 4,5.10-1-8352403 _ 45.3.4402 z
73 . 0,0006 7,3-101.6-10—4 7,3 - 6- 10-3
~ 37 . 5 ~ 5— 4
~ 4510 ~0,310 —8 10.
O6paTHTe BHPIMaHHe 113 TO, 1110 110 xony neﬁCTBHa B npnmepe 3 11110110 8352
651110 oxpymeHo 110 8,4-103. H00K011B11y 0111111 113 MHOJKPITEJIeﬁ, 0,0006, conepmm‘
10115110 onHy snaqamym umppy, 6, He Hmee'r CMbICJIa yBeJIHqHBaTb l1110110 3Haqa-
11111x umpp B npouecce Bblq11011011111’1. B K011011H0M pesyaTe 1111001 01151011 TOJIbKO
onHa gnaqamaa 1111(ppa. Home TOI‘O KaK I1110110 I‘IpHBelleI-IO 11 TaKOMy Buny, 1101113
no sana'roﬁ Hmee'rca 01111a 1111¢pa 11 31311101101111 Bce crenezm 110011111, 1110111110 «113
r11a30x» 11p11111111y'rb Koneqnblﬁ pesynb'ra'r. 0613111110 0 3mm momma HpOHBBOlIﬂTCﬂ
601100 Totmble Bblq11011e111111, Hanpnmep c 110M01ub10 110rap11cpM11qecxo1’1 1111110121111.
K0Het1111>1ﬁ pesyJIBTaT MO}KHO 611110 611 OCTaBHTb B B11110 0,8-105. OIIHaKO MbI
0MeCT111111 sana'ryro BnpaBo 11a 0111111 311aK, noaTOMy creneHB 11e011111 mo 6B1110
ymeHBmmb Ha ‘en111111uy.
B 60115u1111101Be peTon, KOTOe BCTpeqamTca B 11301011111011 111111re, Tax
1110, Kax 11 B 6011b1HHHCTBe Haumx n0B0011HeBHBIX pacue'rOB, Mb] B11011He momeM
yn0B11eTBop111b011 01111011 111111 nByMﬂ 3Haqau11111111 umppaMu. HoaTOMy pa0B1
0111mm o611erqa101011, e01111 Bce I111011a saUHCbIBaTb c HOMOHLbEO c'reneHeﬁ 110011111.
Bb1n01111111~e Bce npoc'rb1e ap11¢MeT11qecx110 neﬁHa Tax, KaK 310 651110 0110113110
B Mepe 3. HpousBenme Heo6xon11MBIe 01101110111111 11 35111113111111 01011011011 ne-
011111, a saw B yme 11011011111a1°11~e 11110110 0 1011110011310 no 01111011 3H3t1amei1
1111(11. Taxoﬁ OTBeT 11011101 613111: B1101111e yAOBJIETBopi/ITGJIIJHHM. E01111 ma
6011ee Bblcoxaa TO‘JHOCTb, TO 110110111:3yi’1*re norapmpecxym 1111He1’111y 111111 npo-
nenaﬁ're Bce apndmemqecxne 110110181111 11a 6yMare. OllHaKO umppa, HaﬁneHHan
BaMH np11 nonct1eTe B yme, 6y11eT 1100131011110 611113Ka K TOqHOMy pesyaTy.
E01111 310 He Tax, 11p0Bep'BTe 0B011 1101101101131. BbI Haﬁne're 111111 apmpMeecxyIO
0111116Ky 111111 HenpaB1111bHoe nonomenne 3a11111‘01°1 B 01111011 113 AecaTHlx 11p06e1’1.

Upnnomenne BTopoe
ﬂHOCTH, TOllHOCTb
H snpaBbu‘i CMbl'CJl
JIIOJIH qaCTo nyMaIOT, I{To ¢H3KKa—3To HayKa Bblcoxnx TotIHocreﬁ, a 3T0
06b1
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BBe T a
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348 O 17 pu/zoarcenue 2
MHorBe (baKTopbl, B HaCTHOCTH, He acao, HaCKOJIbKO paBHOMepHO pacnpenenaeTca
JICIl B Bone. OJIHaKO 0H nosmnaer OXBaTHTb BCIO npoGneMy B nepcneKTHBe.
LIac1'o pacue'rbl Taxoro BHlla nalor B03M0>KH0CTB cxasaTB, qTo Kaxoe-To C06bITPIe
onpeneJIeHHo npousoﬁneT, mm, H3060p0T, onpeneneBHo He nponaoﬁne'r, H Gonee
Totmble pacueTu y>Ke OKaSBIBaIOTCH HeHyMHuMH. ﬂame B Tex cnyqaax, Korna
pacue'rbl He nator onHosﬂaro orBeTa, onn noaBomuoT yCTaHOBHTB, Kaxne (pax-
To m n Hb e n nye
T H
T b o
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q oéu
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auocru, Totmocrb u aapaebtd wow/1 349
p:
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011m: munnuou necmb ueTI
KaxuM 06paaoM Bhl yanaJm 3T0? —IIecsm. .ne'r Haaan npyroﬁ yqenbm pacema-
TpHBaJI s'ry cxany n cxaaan MHe, q'ro eﬁ
mnnnuoa .ner.
(DI/IF. H2.l. 1000 000 +10 = l 000 000.
Haxonmca 400 qenoaek (T. e. TaM MO)K€T 613m. or, 350 no 450 qenonex); Torna-
Bama oueHKa He HBMeHHTCﬂ, ecnn TpH qenoaexa yﬁny'r. Onuaxo,,c npyroﬁ cro-
pOHbI, e H a a
m
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M T
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a

350 17 pu/zoalcenue 2
Hume npusonm‘ca HeCKOJO npnMepoa.
r. _ ,
x 5,243 x 3,1 _ 16 %1 =4
52 5,243 X 0,003] = 0,016
156 37
—_ -—=4,l
16,12 =16 9,1
l'Ipn yMHOX{eHHH mm AeneHHH ooHo Jmmmm snaqamaa umppa 0T6pacm-
norm :4 omer coome'rcmyromnM oopaaoM oxpyrnaeTca.
d>yHKuu0HaJan sanucumocn. Bo MHOI‘HX cnyqaax, KaK B noacenHeBHoﬁ
)KH3HH, Tax H B HayKe, Mb] HHTepecyeMca sanncnmocrbzo mexmy HeKOToMH
nepeMeHHb, He 3360mm: 06 xx uncnoamx sliauax. HaMep, Bonpoc—
yMeHbmHTca nu BpEMH Bameﬁ noesnKH 311.808,. ecmi 3131 311306 yBeJIHqHTe cxo-
pOCTb aBTOMO6HJIﬂ?—OTHOCHTCH K oénacm (pyHKuHOHaJIIx 3aBHCHMOCTeﬁ. I10-
HyCTHM, qTo Bennqnnm x n y CBHBaHbI Memny coéoﬁ Hexoropoﬁ saBHCHMOCTbIO.
Kaxona '3Ta sannocrb? MomeT 651m, x=Ky? I/IJm x=K/y? I/IJm me
x = Kyz? Ob qacro HmpopMauna 0 Blue SaBHCHMOCTH 3HalIIdTeJIbHO oonee no-
JIesna,
3 H a
H eTo
m x B e H
H T OI
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b l a
B
a x uo
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m ne
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Ta ne n p
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o om e
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I'IPEIIMETHbIP’I YKA3ATEJIb
A6comoTHb1ﬁ HYJIb 193
Anoranpo AManeo 283
Anoranpo runo‘Tesa 294
Anoranpo uncno 283
AJIJIOTpoeCKHe monnaunn 333
AJIbq>a-qacmuh1 230
AHTHCBasuBmee cocroaHue 264
ACTpOHOMHa IIpeBHeﬁ Fpeunn 20
Amoapepa (enmmua llaBJIeHHﬂ) 293
ATOMHaﬂ enHHHua Maccm 277
ATOMHaa Teopna 225
ATOMHbIe CHMBOJIbl 229
ATOM’d Bec
—- — onpeneneHue 277, 282
-- — — MeTonOM Hanunssapo 297
ATOMHbIﬁ HOMep 244
ATOMbI 200, 201, 204, 225
— maccu 276
—- paamepbl 204
- coxpaHeHHe B XHMcxnx peaxunax
273
— CTpoeHue, 11011061106 ConHeuHoﬁ ca-
CTeMe 232
-— aneKTpOHHme COCTOﬂHHﬂ 248
Area A6e PeHe 318
Banbmep I/IoraHH 239
BeryHKOB CTOJIKHOBeHHe 47
Bensona Monexyna 269
BepHyJIJIH 113mm 302
Bep'rone KJIOJIT 226
Boﬁnb P06epT 292, 302
Boﬁna saxon 292
BonbumaH Jhomanr 303
Bop HHJIbC 233, 238, 243
BopH MaKC 244
BpoyHOoe nBHmeHHe 301, 315
Bpoyn P06epT 301
BaJIeHTHbIe SJIeKTpOHbI 265
BaneHTHhIx‘ cnaseﬁ Myron 266
Ban-nep-Baanbca cmm 311, 323
Earl“ 88
BepOﬂTHOCTb H coxpanenne
210
Bec 127 ,
BemeCTB Knaccncpnxauna 22
—— MHKpOCKTypa 26, 185, 201
— COCTOHHPIH 22
BsanMoneﬁcmHe 22
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— rpaBnTauHOHHoe 25
— nByx Ten 42
-— CPIJIbH0e smepHoe 27
— cnaéoe smepHoe 26, 27
—'—- aneKTpOMarHHTHoe 25, 26
— aneKTpocraTcxoe 145
BJIa}KHOCTb omocmenbnaa 328
Bona, nnnonbablﬁ MOMeHT Monexynu
271, 272 ’
Bonopona aTOM
— — Monenb Bopa 239
— — Cl'leKTp 238, 243
-— MOJIeKYJIa 259, 260
— -— 06paBOBaHHe caaseﬁ 323
Bonoponnaa c3331: 323
BOJIHOBaH MexaHHKa 246
BOJIHbI, nsMepeHHe napameTpOB 255
BceJIeHHaa, nuanason pasmepon n pace
CTOHHHﬁ l4
-— MoneJm 14
— CJIO)KHOCTb 21
suepnm
1‘ asoB an
294
FasoBbIe SaKOHbI, 1313113011 H3 KHHeT-
cxoﬁ monenn 306
— — pacue'm Ha ux ocnone 296
raSOBbIﬁ saxoa yHHBepcabIﬁ 294
Fasbl
— KHHeTcxaa monenb 301
—- OTKJIOHeHHe 0T uneanbnoro nonene-
HRH 309
nocmmmaa yHHBepcaam

352
17 peamembu‘i yrcasare/zb
1‘asb1, cxopocn: nu¢¢>y3nn 300
-— coomomeune 06’beMOB, BCTYHalomHX
B peaxumo 294
-— CTaecxaa monenb 301
fanaxmxa Aome
1
5
M
e
I
ﬁ
l
y: 15
a a
x
m
u
O
I
E
I
b 31
I ‘a
J
JI e
ﬁ a
JIH
JI
e
o 1
0
2

ﬂpeamemmﬁ yrcasaTe/zb
353
MeﬂneneeB ﬂMHTpHﬁ 245
MeT-p 14
MeTecxaa CHCTeMa 14, 85
Mosnu Fn 245
Monexynu, KoneéaTeoe H Bpama-
TeJIbHoe ABHmeHHe 205, 207, 209
— maccbx 282
— — onpeneneHHe no nnomocm raaa
297, 340
— nonaIe H HenonaIe 271, 288
— paamepbl 222
—— cxemamqecxoe H306pa>KeHHe 265
Monexynapuux opémaneﬁ meTon 266
MOJIb, HCHOJIbSOBaHHe B xnmnqecxnx
pécueTax 284
— onpeneneane 284
MOMEHT HMnyJIbca 167
— — KBaHTOBaHHe 240
M10011 80
HeBBCOMOCTb 166
HbIOTOHa saxon THI‘OTeHHH 141
— nepBbIﬁ saxon 40
HbIOTOH (enmmua CHJIbI) 126
OKTeTa IIpaBPIJIO 263
Onepaunonannam 24
Drama 77
OTHOCHTeJIbHOB nBHmeHHe Team a na-
6mona'rena 42
OTa cxopocrb 157
ﬂaynn Bonbcpranr 244
I'Ia
u p
i a
nea
28, 24
e
p no
ne
cx
a a
a mm
a
2
7
e
n onno
n

17 peamembtﬁ yrcaaaTe/zb
Tennonposomocrb 208
Termopona Teopmi 187, 195
Tennora 186, 195
— neﬁCTBHe Ha BeLueCTBo 201, 203
-— apemm 331
-- MexaHcxnﬁ axnnaaneHT 196
— onpeneneHHe 186
— HJIaBJIeHHH 330
—— npeoépasoBaHHe
pa60Ty 195, 210
TepMOllHHaMHKa 215
TepMOMeI 188
—— rpanynponxa 190, 191
TOMCOH DJK. 11m. 230
TpHaHryJIauna 19, 31
TpoﬁHaH “roux? 331
B MexaHcx
y ne
pn a
ll y
O
H
b ,
nn onn
e n
a
n 2
7
1pB
neH
ne
H
M
C
opa
m
,
6 3
n
n
p
O

OFHABJIEHI/IE
Upenncnoane penax'ropa nepeBona
Upenncnoaue
I‘JIaBa nepaaa. I'IOCTI/IHb BCEJIEHHYIO
1.]. BceneHHaa Kax 06mm Hccnenoaanua
1.2. HoKH «110mm.» BceJIeHH
1
.
. o
nee
n m y
p
a HHa
e
r H
e ua
m
e m
H
a
Ta e

Oe/zae/zenue
356
4.3. MaI‘HHTHaH HOTeHuHaJIbHaa anepmn
4.4. Ilpyrne (poI HOTeHuHaoﬁ sueprnn
Pesiome
Omen): Ha Bonpocm
Hpaxmqecxne paéoTbI
3anaqn
TJIaBa nmaa. CI/IJIbI.
5.1.
5.2.
5.3.
5.4.
5.5.
5.6.
OnpeneneHHe cum
CHJIa, pasnyaaeMaa npyoﬁ
Cnna memn‘y unmnnpnqecxumn marumamu
Cobmomeuue memny paéo'roﬁ n aHeprnei’l
Eme 0mm 33mm Ha norenunanbnyro sneprmo rpaBHTa
E
e m
m
B
H JB
aH
oe
C
TI I

Oenaenenue 357
I‘JIaBa BOCbMaH. ATOMbI [/1 HEPVIOIIW—IECKAH TABJIIAHA 225
8.1. ATOMHaa TeopHa IIaJIbmHa 226
8.2. Knaccnqecxne moneJm CTpOEHHﬂ aTOMa 230
8.3. «Honaa ¢H3nxa>> n COBpeMeHHaﬂ monenb aroma 233
8.4. Hepnonnqnom‘b B MHpe aTOMOB 245
1388 251
OTBeTbl Ha Bonpocm 252
Upaxmqecxne paéom 254
Banana . 256
I‘JIaBa neBsn‘aa. MOJIEKYJIbI I/I XI/IMWJECKI/IE PEAKLII/II/I . 258
9.1. MoneKyJIa Bonopona . 259
9.2. Ilpyme Monexynbl , 262
9.3. THHbI eBasefi 266
9.4. I'lomIe PI Henonapnme monexym 271
9.5. XHMCKHe peaxunn n

YBAKAEMHH 'IHTATEJIb!
Baum sameqamm o conepmamm KHHI‘H, ee o¢0p‘
MJIeHPIH, KaTBe nepenona H npyrne npocnm nocm-
JlaTb no ampecy: 129820, Mocxna, 14-110, I‘CU,
l-ﬁ cxni’i nep., 2, nan-Bo «Map».

I/IB N9 418
K. Msapu, T. FonbmbapG
I'IOI/ICKH BAKOHOMEPHOCTEPI
B cpuEcKOM MI/IPE“
Penax'rop H. I‘. Haxnmcou
Xynoxumx PI. PI. Kanemm
Xynoxcec-raenauﬁ penam‘op B. 14. Hlanoaanoa
Texunqecxnﬁ penaK-rop E. C. I'IoraneHKona
KoppeK'rop JI. Ll. I'IaHoaa
CnaHo B Ha6op l3/VIII 1976 r. l'IolmncaHo K neqém 6/1 1977 r.
ByM. Tun. N9 2 60X90‘/|e=ll,316yM. JI. 22,63 yen. next. 11. B T/q 0,07 un. mm.
V‘L‘HBJI. 11. 22.72. P1311. N2 2/8615. LleHa l p.45 K. Sax. 285
H31LaTeJIbCTBO «Map»
Mocxaa. l-KPHMCKHH nep., 2
Opneaa nonoro Kpacuoro 3Hameuu
JIeHHHrpancxan mnorpacbna N2 2
nMeHu EBremm Coxonoaoﬁ Coroanonurpadmpoma
npn FOCapCTBeHl-IOM KOMHTeTe Coaera Mnunc'rpon CCCP
no nenaM Hanarenbcm. nonnrpacbnn
u xunmuoﬁ TOpI‘OBJIH.
198052, JIeHum‘pan, JI-52. I/Iamaﬁnoncxuﬁ np., 29

K CBeIIEHPIIO qHTaTeneﬁ
B MOCKOBCKOM IIOME KHI/II‘I/I
OTKPbITA (DI/IPMEHHAH CEKHI/IH
HO I'IPOIIAXE KHI/II‘
I/I3IIATEJ1bCTBA «MI/1P»
BII
U C
C
a B
Ie H
HH
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