7/21/2019 Modern Physics - 1 Theory_E

1/34

YH\WLGW

"djalshmudjrphyslgs.la" :

D@KNSA YH\WLGW - :: YH@[@NONG[SLG NBBNG[ 6

Uhna nongtr djeantlg rjkljtl`as `b sultjcon wjvnonaeth jrn laglknat`a j dntjoolg surbjgn thna nongtr`as jrnndlttnk, thls phna`dna`a ls gjoonk ph`t` nongtrlg nbbngt.

:.: Yh t`nongtr a 6[hn nongtr`a ndlttnk la ph`t`nongtrlg nbbngt ls gjoonk ph`t`nongtr a.

:.3 Yh t`nongtrlggurrnat 6 Lb gurrnat pjssns thr ueh thn glrgult la ph t`nongtrlg nbbngt thna thn gurrnatls gjoonk ph`t`nongtrlg gurrnat.

:.7 U rm buagtl a 6[hn dlaldud nanrey rnqulrnk t` djmn ja nongtr`a brnn br`d thn dntjo ls gjoonkw`rm buagtl`a. Lt ls g`astjat b`r j dntjo jak kna`tnk cy`r U. Lt ls thn dlaldud b`r Gnslud. Lt lsrnojtlvnoy onss b`r jomjol dntjos.

U`rm buagtl as `b s`dn ph t`snasltlvn dntjos

Dntjo U`rm buagtl`a

(nv) Dntjo

U`rm buagtl`a(nR)

Gnslud :.< Gjoglud 7.3Y`tjsslud 3.3 G`ppnr ;.>

W`klud 3.7 Wlovnr ;.5Olthlud 3.> Yojtlaud >.2

[` pr`kugn ph`t` nongtrlg nbbngt `aoy dntjo jak oleht ls angnssjry cut b`r `csnrvlae lt, thn glrgult ls g`d-pontnk. Bleurn sh`ws ja jrrjaendnat usnk t` stuky thn ph`t`nongtrlg nbbngt.

: 3

JG

latnaslty

brnqunagy

Shn`stjt

gnoo, bnw v`ots

R

J

Hnrn thn pojtn (:) ls gjoonk ndlttnr `r gjth`kn jak `thnr pojtn (3) ls gjoonk g`oongt`r `r ja`kn.

:.; Wjturjtl`a gurrnat 6 Uhna joo thn ph t` nongtr`as ndlttnk cy gjth`kn rnjgh thn ja`kn thna gurrnatbo`wlae la thn glrgult jt thjt lastjat ls ma`wa js sjturjtnk gurrnat, thls ls thn djxldud vjoun `bph`t`nongtrlg gurrnat.

:.> Wt`pplaep`tnatljo6 Dlaldud djealtukn `b anejtlvn p`tnatljo `b ja`kn wlth rnspngt t` gjth`kn b`rwhlgh gurrnat ls znr` ls gjoonk st`pplae p`tnatljo. [hls ls jos` ma`wa js gut bb v`otjen. [hls v`otjenls laknpnaknat `b latnaslty.

:.2 Sntjrklae p`tnatljo 6 Anejtlvn p`tnatljo `b ja`kn wlth rnspngt t` gjth`kn whlgh ls onss thjast`pplae p`tnatljo ls gjoonk rntjrklae p`tnatljo.

7/21/2019 Modern Physics - 1 Theory_E

2/34

YH\WLGW

"djalshmudjrphyslgs.la" 3

3. @CWNSRJ[L@AW 6 DJKN C\ NLAW[NLA3.: J erjph cntwnna latnaslty `b oleht jak ph t`nongtrlg gurrnat ls b`uak

t` cn j strjleht olan js sh`wa la bleurn. Yh`t`nongtrlg gurrnat lsklrngtoy pr`p`rtl`ajo t` thn latnaslty `b laglknat rjkljtl`a. La thlsnxpnrldnat thnbrnqunagyjak rntjrklaep`tnatljojrn mnpt g`astjat.

Yh`t`gurrnat

Latnaslty `b oleht @

3.3 J erjph cntwnna ph`t`nongtrlg gurrnat jak p`tnatljo klbbrnagn cntwnna gjth`kn jak ja`kn ls b`uakjs sh`wa la bleurn.

sjturjtl`a gurrnat

3 :1

R RJ GRW

:

W3

W:

Y

La gjsn `b sjturjtl a gurrnat,rjtn `b ndlssl`a `b ph t`nongtr`as 4 rjtn `b bo`w `b ph t`nongtr`as ,hnrn, v

sst`pplae p`tnatljo jak lt ls j p`sltlvn qujatlty

Nongtr`as ndlttnk br`d surbjgn `b dntjo hjvn klbbnrnat nanrelns.Djxldud mlantlg nanrey `b ph`t`nongtr`a `a thn gjth`kn 4 nR

s

MNdjx

4 nRs

Uhnanvnr ph`t`nongtrlg nbbngt tjmns pojgn, nongtr as jrn nfngtnk`ut wlth mlantlg nanrelns rjaelae br`d

9 t` M.Ndjx l.n. 9MNGnRs[hn nanreyklstrlcutl`a `b ph t`nongtr`a ls sh`wa la bleurn.

A`.

`b

Yh`t`nongtr`as

Mlantlg nanrey nRW@

3.7 Lb latnaslty ls lagrnjsnk (mnnplae thn brnqunagy g`astjat) thna sjturjtl`a gurrnat ls lagrnjsnk cysjdn bjgt r cy whlgh latnaslty lagrnjsns. Wt`pplae p`tnatljo ls sjdn, s` djxldud vjoun `b mlantlgnanrey ls a`t nbbngtnk.

3.; Lb oleht `b klbbnrnat brnqunaglns ls usnk thna `ctjlank po ts jrn sh`wa la bleurn.

Lt ls gonjr br`d erjph, js lagrnjsns, st`pplae p`tnatljo lagrnjsns, lt dnjas djxldud vjoun `bmlantlg nanrey lagrnjsns.

7/21/2019 Modern Physics - 1 Theory_E

3/34

YH\WLGW

"djalshmudjrphyslgs.la" 7

3.> Erjphs cntwnna djxldud mlantlg nanrey `b nongtr`asnfngtnk br`d klbbnrnat dntjos jak brnqunagy `b oleht usnkjrn b`uak t` cn strjleht olans `b sjdn so`pn js sh`wa labluern

Erjph cntwnna Mdjx

jak

d:

th:

d3

th3

d7

th7

mdjxb`r dntjo's

d:, d

3, d

76 [hrnn klbbnrnat dntjos.

Lt ls gonjr br`d erjph thjt thnrn ls j dlaldud brnqunagy `b nongtr`djeantlg rjkljtl`a whlgh gjapr`kugn ph`t`nongtrlg nbbngt, whlgh ls gjoonk thrnsh`ok brnqunagy.

th

4 [hrnsh`ok brnqunagyB`r ph`t`nongtrlg nbbngt

th

b`r a` ph t`nongtrlg nbbngt ?th

Dlaldud brnqunagy b`r ph`t`nongtrlg nbbngt 4 th

dla

4th

[hrnsh`ok wjvnonaeth(th

)[hn djxldud wjvnonaeth `b rjkljtl`a whlgh gja pr`kugn ph`t`-nongtrlg nbbngt.

th

b`r ph t` nongtrlg nbbngt

Djxldud wjvnonaeth b`r ph`t nongtrlg nbbngt djx 4 th.A`w wrltlae nqujtl a `b strjleht olan br`d erjph.Un hjvn M

djx4 J+ C

Uhna 4 th

, Mdjx

4 9jak C 4 J

th

Hnagn ]Mdjx

4 J( th

)T

jak J 4 tja4 2.27 :97; F-s (br`d nxpnrldnatjo kjtj)ojtnr `a J wjs b`uak t` cn h.

3.2 Lt ls jos` `csnrvnk thjt ph t`nongtrlg nbbngt ls ja lastjatjan`us pr`gnss. Uhna oleht bjoos a surbjgnnongtr`as stjrt nfngtlae wlth`ut tjmlae jay tldn.

7. [HSNN DJF@S BNJ[^SNW @B [HN YH@[@NONG[SLG NBBNG[ GJAA@[ CN NXYOJLANKLA [NSDW @B [HN GOJWWLGJO UJRN [HN@S\ @B OLEH[.

Latnaslty 6 [hn nanrey gr`sslae pnr ualt jrnj pnrualt tldn pnrpnaklguojr t` thn klrngtl a `b pr`pj-ejtl`a ls gjoonk thn latnaslty `b j wjvn.

J x

g t

G`aslknr j gyolakrlgjo v`oudn wlth jrnj `b gr`ss-sngtl`a J jak onaeth gt jo`ae thn X-jxls. [hnnanreyg`atjlank la thls gyolaknr gr`ssns thnjrnjJ la tldnt js thn wjvn pr`pjejtns jt spnnk g.[hn nanrey g`atjlank.

^ 4 ujv(g.t)J

[hn latnaslty ls 4tJ

^

4 u

jvg.

La thn tnrds `b djxldud nongtrlg blnok,

43

:

9N

93 g.

Lb wn g`aslknr oleht js j wjvn thna thn latnaslty knpnaks up`a nongtrlg blnok.Lb wn tjmn w`rm buagtl`a U 4. J . t,

thna t 4J

U

s` b`r ph`t`nongtrlg nbbngt thnrn sh`uok cn tldn oje cngjusn thn dntjo hjs w`rm buagtl`a.Cut lt ls `csnrvnk thjt ph`t`nongtrlg nbbngt ls ja lastjatjan`us pr`gnss.Hnagn, oleht ls a`t `b wjvn ajturn.

7/21/2019 Modern Physics - 1 Theory_E

4/34

YH\WLGW

"djalshmudjrphyslgs.la" ;

7.: [hn latnaslty pr`cond 6 Ujvn thn`ry rnqulrns thjt thn `sgloojtlae nongtrlg blnok vngt`rN `b thn olehtwjvn lagrnjsns la jdpoltukn js thn latnaslty `b thn oleht cnjd ls lagrnjsnk. Wlagn thn b`rgn jppolnkt` thn nongtr`a ls nN, thls sueensts thjt thn mlantlg nanrey `b thn ph`t`nongtr`as sh`uok jos` la-grnjsnk js thn oleht cnjd ls djkn d`rn latnasn. H`wnvnr `csnrvjtl a sh`ws thjt djxldud mlantlgnanrey ls laknpnaknat `b thn oleht latnaslty.

7.3 [hn brnqunagy pr`cond 6Jgg`rklae t` thn wjvn thn`ry, thn ph`t`nongtrlg nbbngt sh`uok `ggur b`rjaybrnqunagy `b thn oleht, pr`vlknk `aoy thjt thn oleht ls latnasn na`ueh t` suppoy thn nanreyannknkt` nfngt thn ph`t`nongtr`as. H`wnvnr `csnrvjtl`as sh`ws thjt thnrn nxlsts b`r njgh surbjgn jghjrjgtnrstlg gut`bb brnqunagyth, b`r brnqunaglns onss thja th, thn ph`t`nongtrlg nbbngt k`ns a`t`ggur, a` djttnr h`w latnasn ls oleht cnjd.

7.7 [hn tldn knojy pr cond 6Lb thn nanrey jgqulrnk cy j ph`t`nongtr`a ls jcs`rcnk klrngtoy br`d thnwjvn laglknat `a thn dntjo pojtn, thn nbbngtlvn tjrent jrnj b r ja nongtr a la thn dntjo ls oldltnk jakpr`cjcoy a`t dugh d`rn thja thjt `b j glrgon `b kljdntnr r`uehoy nqujo t` thjt `b ja jt`d. La thngojsslgjo thn`ry, thn oleht nanreyls ualb rdoy klstrlcutnk `vnr thn wjvnbr`at. [hus, lb thn oleht ls bnnconna`ueh, thnrn sh`uok cn j dnjsurjcon tldn oje, cntwnna thn ldplaelae `b thn oleht `a thn surbjgnjak thn nfngtl`a `b thn ph`t`nongtr`a. Kurlae thls latnrvjo thn nongtr`a sh`uok cn jcs`rclae nanreybr`d thn cnjd uatlo lt hjkjgguduojtnk na`ueh t` nsgjpn. H`wnvnr, a` kntngtjcon tldn oje hjs nvnrcnna dnjsurnk.

A`w, qujatud thn`rys`ovns thnsn pr`conds la pr vlklae thn g`rrngt latnrprntjtl`a `b thn ph t`nong-

trlg nbbngt.

; YOJAGMW Z^JA[^D [HN@S\ 6[hn oleht nanrey br`d jay s`urgn ls jowjys ja latnerjo duotlpon `b j sdjoonr nanrey vjoun gjoonk qujatud boleht.hnagn nanrey Z 4 AN,whnrn N 4 h jak A (audcnr b ph t`as) 4 :,3,7,....Hnrn nanrey ls qujatlznk. hls thn qujatud `b nanrey, lt ls j pjgmnt `b nanrey gjoonk jsph`t`a.

N 4 h 4

hg

jak hg 4 :3;99 nR

>. NLAW[NLAW YH@[@A [HN@S\La : Nlastnla djkn j rndjrmjcon jssudptl`a jc`ut thn ajturn `b oleht= ajdnoy, thjt, uaknr s`dn glrgud-stjagns, lt cnhjvns js lb lts nanrey ls g`agnatrjtnk lat` o gjolznk cuakons, ojtnr gjoonk ph`t`as. [hn nanreyN `b j slaeon ph`t`a ls elvna cy

N 4 h,Lb wn jppoy Nlastnlas ph`t`a g`agnpt t` thn ph`t`nongtrlg nbbngt, wn gja wrltn

h4 U + Mdjx

, (nanreyg`asnrvjtl`a)

Nqujtl`a sjys thjt j slaeon ph`t`a gjrrlns ja nanrey hlat` thn surbjgn whnrn lt ls jcs`rcnk cy j slaeonnongtr`a. Yjrt `b thls nanreyU (gjoonk thn w rm buagtl a `b thn ndlttlae surbjgn) ls usnk la gjuslae thn nongtr`at` nsgjpn br`d thn dntjo surbjgn. [hn nxgnss nanrey (h U ) cng`dns thn nongtr`as mlantlg nanrey= lb thnnongtr`a k`ns a`t o`sn nanrey cy latnrajo g`oolsl`as js lt nsgjpns br`d thn dntjo, lt wloo stloo hjvn thls dughmlantlg nanrey jbtnr lt ndnrens. [hus M

djxrnprnsnats thn djxldud mlantlg nanrey thjt thn ph`t nongtr a gja

hjvn `utslkn thn surbjgn. [hnrn ls g`dpontn jernndnat `b thn ph`t a thn ry wlth nxpnrldnat.

A`w J 4 Ah A 4 hJ 4 a . `b ph`t`as laglknat pnr ualt tldn `a ja jrnj J whna oleht `b

latnaslty ls laglknat a`rdjooy.

Lb wn k`ucon thn oleht latnaslty, wn k`ucon thn audcnr `b ph`t`as jak thus k`ucon thn ph`t`nongtrlg gurrnat=wn k` a`t ghjaen thn nanrey `b thn laklvlkujo ph t`as `r thn ajturn`b thn laklvlkujo ph`t`nongtrlg pr gnssns.

[hn sng`ak `cfngtl`a (thn brnqunagy pr`cond) ls dnt lb Mdjx

nqujos znr , wn hjvnh

th4 U,

Uhlgh jssnrts thjt thn ph`t a hjs fust na`ueh nanrey t` nfngt thn ph`t`nongtr`as jak a`an nxtrj t` jppnjrjs mlantlg nanrey. Lbls rnkugnk cno`w

th, hwloo cn sdjoonr thja U jak thn laklvlkujo ph`t`as, a` djttnr

h`w djay `b thnd thnrn jrn (thjt ls, a` djttnr h`w latnasn thn looudlajtl`a), wloo a t hjvn na`ueh nanrey t`nfngt ph`t`nongtr`as.

[hn thlrk `cfngtl`a (thn tldn knojy pr`cond) b oo`ws br d thn ph`t`a thn`ry cngjusn thn rnqulrnk nanrey lssuppolnk la j g`agnatrjtnk cuakon. Lt ls a`t sprnjk ualb`rdoy `vnr thn cnjd gr`ss sngtl`a js la thn wjvnthn`ry.

7/21/2019 Modern Physics - 1 Theory_E

5/34

YH\WLGW

"djalshmudjrphyslgs.la" >

Hnagn Nlastnlas nqujtl a b`r ph`t`nongtrlg nbbngt ls elvna cy

h4 hth

+ Mdjx

Mdjx

4

hg

th

hg

Nx. : La ja nxpnrldnat `a ph t` nongtrlg ndlssl a, b`oo`wlae `csnrvjtl as wnrn djkn=(l) Ujvnonaeth `b thn laglknat oleht 4 :. v ot.Blak 6 (j) Mlantlg nanrey `b ph t`nongtr`as wlth djxldud spnnk.

(c) U`rm buagtl a jak(g) [hrnsh ok brnqunagy=W`o. (j) Wlagn v

s4 3.> R, M

djx4 nR

s s`, M

djx4 3.> nR

(c) Nanrey`b laglknat ph`t a

N 4 nR::97

Ud3

. [hn cnjd bjoos a rdjooy `a ja jrnj :9;

d3

`b j gonja dntjoolg surbjgn `b w rm buagtl a :.8 nR N

74

2999

:3;994 3.92 nR

jak N;4

5999

:3;994 :.55 nR

[hnrnb rn, oleht `b wjvnonaeths ;999 , ;899 jak 2999 gja `aoy ndlt ph`t`nongtr as. Audcnr `b ph t`nongtr`as ndlttnk pnr sng`ak 4 A`. `b ph t`as laglknat pnr sng`ak)

4:

::

N

J+

3

33

N

J+

7

77

N

J4J

73: N

:

N

:

N

:

4 :.:(

92.3

:

>8.3

:

:.7

:

4 :.:3 :9:3 Jas.

Nx. 7 J sdjoo p`tjsslud b`lo ls pojgnk (pnrpnaklguojr t` thn klrnglt`a `b laglknagn `b oleht) j klstjagn r (4 9.> d)br`d j p`lat oleht s`urgn wh`sn `utput p`wnr Y

9ls :.9U. Jssudlae wjvn ajturn `b oleht h`w o`ae w`uok lt

tjmn b`r thn b`lo t` s`jm upna`uehnanrey (4 :.8 nR) br`d thn cnjd t` nfngt ja nongtr`a0 Jssudn thjt thnnfngtnk ph t`nongtr a g`oongtnk lts nanreybr`d j glrguojr jrnj `b thn b`lo wh`sn rjklus nqujos thn rjklus `b jp`tjsslud jt`d (:.7 :9:9 d).

W`o. Lb thn s`urgn rjkljtns ualb`rdoy la joo klrngtl`as, thn latnaslty`b thn oleht jt j klstjagn r ls elvna cy

4 39

r;Y

4 3)d>.9(;U9.:

4 9.73 U/d3.

[hn tjrent jrnj J ls(:.7 :9:9 d)3 `r >.7 :939 d3, s` thjt thn rjtn jt whlgh nanrey bjoos `a thn tjrent lselvna cy

Y 4J 4 (9.73 U /d3) (>.7 :939 d3)

4 :.5 :939 F/s.Lb joo thls lag`dlae nanrey ls jcs`rcnk, thn tldn rnqulrnk t` jgguduojtn na`ueh nanrey b`r thn nongtr`a t`nsgjpn ls

t 4

s/F:95.:

nR8.:39

nR:

F:92.: :999, a` ph`t`nongtr`as jrn ndlttnk br`d thn surbjgn. Ulth ja uama`wa wjvnonaeth, st`pplae p`tnatljo ls 7 R.Blak thn uama`wa wjvnonaeth.

W`o. ^slae nqujtl a `b ph t`nongtrlg nbbngtM

djx4 N U (M

djx4 nR

s)

7 nR 4

:3;99

>999

:3;994

:3;99

3.;8 nR

`r 4 3323 Nx. > Looudlajtlae thn surbjgn `b j gnrtjla dntjo jotnrajtnoy wlth oleht `b wjvnonaeths

: 4 9.7> d jak

3

4 9.>; d, lt wjs b`uak thjt thn g`rrnsp`aklae djxldud vno gltlns `b ph t` nongtr as hjvn j rjtl` 4 3.Blak thn w`rm buagtl`a `b thjt dntjo.

W`o. ^slae nqujtl`a b`r tw` wjvnonaeths

Uhg

dv3

:

:

3:

....(l)

Uhg

dv3

:

3

33

....(ll)

Klvlklae Nq. (l) wlth Nq. (ll), wlth v:4 3v

3, wn hjvn ; 4

Uhg

Uhg

3

:

7U 4 ;

3

hg

:

hg4

>;99

:3;99;

7>99

:3;994 >.2; nR

U 47

2;.>nR 4:.88 nR Jas.

Nx. 2 J ph`t`gnoo ls `pnrjtlae la sjturjtl`a d`kn wlth j ph`t`gurrnat ;.8J whna j d`a`ghr`djtlg rjkljtl`a `bwjvnonaeth 7999 jak p`wnr : dU ls laglknat. Uhna ja`thnr d`a`ghr`djtlg rjkljtl a `b wjvnonaeth :2>9 jak p`wnr > dU ls laglknat, lt ls `csnrvnk thjt djxldud vno`glty`b ph`t`nongtr`a lagrnjsns t` tw` tldns.Jssudlae nbblglnagy `b ph`t`nongtr`a enanrjtl`a pnr laglknat t` cn sjdn b`r c`th thn gjsns, gjoguojtn,(j) thrnsh`ok wjvnonaeth b r thn gnoo(c) nbblglnagy `b ph`t`nongtr`a enanrjtl a. ](A . `b ph`t`nongtr`as ndlttnk pnr laglknat ph`t`a) :99T(g) sjturjtl a gurrnat la sng`ak gjsn

W`o. (j) M:4

7999

:3;99 U 4 ;.:7 U ...(l)

M34

:2>9

:3;99 U 4 5.>: U ....(ll)

Wlagn v3 4 3v: s`, M34 ;M: ...(llll)W ovlae jc`vn nqujtl`as, wn entU 4 7 nR

[hrnsh`ok wjvnoneth 94

7

:3;994 ;:77 Jas.

(c) Nanrey `b j ph`t a la blrst gjsn 47999

:3;994 ;.:7 nR

`r N:4 2.2 :9:< F

Sjtn `b laglknat ph t`as (audcnr `b ph t`as pnr sng`ak)

4 :

:

N

Y

4 : :9:>

pnr sng`ak

Audcnr`b nongtr`as nfngtnk 4 :

:7

:9>.:

:99.7

:99 4 3% Jas.

(g) Nanrey `b ph`t a la sng`ak gjsn

N34 :2>9

:3;99

4 5.>: nR 4 :3 :9

: pnr sng`ak

Audcnr `b nongtr`as ndlttnk pnr sng`ak 4:99

3 ;.5 :9:>

4

s:

) t + sla (8 :9:>

s:

)tT bjoos `a jdntjo surbjgnhjvlae w`rm buagtl`a 3.9 nR. Gjoguojtn thn djxldud mlantlg nanrey `b thn ph`t`nongtr as.W`o. [hn oleht g`atjlas tw` klbbnrnat brnqunaglns. [hn `an wlth ojrenr brnqunagy wloo gjusn ph`t`nongtr`as wlth

ojrenst mlantlg nanrey. [hls ojrenr brnqunagy ls

3

s:98

3

::>

[hn djxldud mlantlg nanrey `b thn ph`t`nongtr as lsM

djx4 h U

4 (;.:; :9:> nR-s)

:

:>

s3

:98 3.9 nR

4 >.35 nR 3.9 nR 4 7.35 nR.

2 B@SGN K^N [@ SJKLJ[L@A YH@[@ANjgh ph`t`a hjs j knblaltn nanrey jak j knblaltn olanjr d`dnatud. Joo ph`t`as `b oleht `b j pjrtlguojrwjvnonaeth hjvn thn sjdn nanrey N 4 hg/ jak thn sjdn djealtukn `bd`dnatud p 4 h/.

Uhna oleht `b latnaslty bjoos a j surbjgn, lt nxnrts b rgn a thjt surbjgn. Jssudn jcs`rptl`a jak rnbongtl`ag`nbblglnat `b surbjgn cn j jak r jak jssudlae a` trjasdlssl a.Jssudn oleht cnjd bjoos `a surbjgn `b surbjgn jrnj J pnrpnaklguojroy js sh`wala bleurn.

B`r gjoguojtlae thn b`rgn nxnrtnk cy cnjd `a surbjgn, wn g`aslknr b`oo`wlae gjsns.

Gjsn 6 (L)j 4 :, r 4 9

laltljo d`dnatud `b thn ph`t`a 4h

blajo d`dnatud b ph`t a 4 9

ghjaen la d`dnatud `b ph t`a 4h

(upwjrk)

Y 4h

nanrey laglknat pnr ualt tldn 4J

a . `b ph`t`as laglknat pnr ualt tldn 4

hJ 4

hgJ

t`tjo ghjaen la d`dnatud pnr ualt tldn 4 aY

7/21/2019 Modern Physics - 1 Theory_E

8/34

YH\WLGW

"djalshmudjrphyslgs.la" 8

4

h

hg

J

4g

J(upwjrk)

b`rgn `a ph`t`as 4 t`tjo ghjaen la d`dnatud pnr ualt tldn

4g

J(upwjrk)

b`rgn `a pojtn kun t` ph`t`as(B) 4 gJ

(k`wawjrk)

prnssurn 4J

B4

gJ

J4

g

Gjsn 6 (LL)whna r 4 :, j 4 9

latljo d`dnatud `b thn ph`t`a 4

h(k`wawjrk)

blajo d`dnatud b ph`t`a 4

h(upwjrk)

ghjaen la d`dnatud 4

h+

h4

h3

nanrey laglknat pnr ualt tldn 4 J

a`. `b ph`t`as laglknat pnr ualt tldn 4hg

J

t tjo ghjaen la d`dnatud pnr ualt tldn 4 a .Y

4hg

J.

h34

G

J3

b`rgn 4 t`tjo ghjaen la d`dnatud pnr ualt tldn

B 4g

J3(upwjrk `a ph t`as jak k`wawjrk `a thn pojtn)

prnssurn Y 4JB 4

gJJ3 4

g3

Gjsn 6 (LLL)Uhna ` ? r ? : j + r 4 :

ghjaen la d`dnatud `b ph`t`a whna lt ls rnbongtnk 4h3

(upwjrk)

ghjaen la d`dnatud `b ph`t`a whna lt ls jcs`rcnk 4h

(upwjrk)

a . `b ph`t`as laglknat pnr ualt tldn 4hg

J

A . `b ph`t as rnbongtnk pnr ualt tldn 4hg

J. r

A . `b ph`t a jcs rcnkpnr ualt tldn 4hg

J(: r)

b`rgn kun t` jcs rcnk ph`t`a (Bj) 4

hg

J(: r) .

h

4g

J(: r) (k wawjrk)

B`rgn kun t` rnbongtnk ph`t`a (Br) 4

hg

J.r

h3

4g

J3 (k`wawjrk)

t`tjo b`rgn 4 Bj+ Br (k`wawjrk)

4g

J(: r) +

g

Jr3

7/21/2019 Modern Physics - 1 Theory_E

9/34

YH\WLGW

"djalshmudjrphyslgs.la" 9)la( ....(v)

5.3 kn-Cr`eoln wjvnonaeth `b j ejs d onguon 6

Ont us g`aslknr j ejs d`onguon jt jcs`outn tndpnrjturn [. Mlantlg nanrey `b ejs d`onguon ls elvna cy

M.N. 43

7m[ = m 4 C`otzdja g`astjat

ejs d`onguon

4dm[7

h

Nx. :: Ja nongtr`a ls jggnonrjtnk cy j p`tnatljo klbbnrnagn `b >9 v ot. Blak thn kn-Cr eoln wjvnonaeth jss`gljtnk wlthlt.

W`o. B`r ja nongtr`a, kn-Cr`eoln wjvnonaeth ls elvna cy,

4

R

:>94

>9

:>94 7

4 :.57 Jas.

Nx. :3 Blak thn rjtl` `b Kn-Cr`eoln wjvnonaeth `b d`onguons `b hykr`enajak hnolud whlgh jrn jt tndpnrjturns 35Gjak :35G rnspngtlvnoy.

W`o. kn-Cr`eoln wjvnonaeth ls elvna cy

Hn

H3

4

33 HH

HnHn

[d

[d4

)35735(

)357:35(.

3

;

47

8

8. [H@DW@AW J[@DLG D@KNO 6F.F. [h`ds`a sueenstnk thjt jt`ds jrn fust p`sltlvnoy ghjren oudps `b djttnr wlth nongtr as ndcnkknk la

thnd olmn rjlslas la j brult gjmn. [h`ds`as d`kno gjoonk thn poud pukklae d`kno ls looustrjtnk la bleurn.

Nongtr`a

Y`sltlvnoy ghjrenk djttnr

[h`ds`a pojynk ja ldp`rtjat r`on la klsg`vnrlae thn nongtr`a, thr`ueh ejs klsghjren tucn cy klsg`vnrlae

gjth`kn rjys. Hls lknj wjs tjmna snrl`usoy.Cut thn rnjo jt`d turank `ut t` cn qultn klbbnrnat.

7/21/2019 Modern Physics - 1 Theory_E

13/34

YH\WLGW

"djalshmudjrphyslgs.la" :7

7/21/2019 Modern Physics - 1 Theory_E

14/34

YH\WLGW

"djalshmudjrphyslgs.la" :;

Wldlojroy, sucstltutlae vjouns `b n,9jak h wlth a 4 : la Nq. (v), wn ent

v:4 3.:< :92 d/s ....(vlll)

[hls ls thn ernjtnst p`sslcon spnnk `b thn nongtr`a la thn hykr`ena jt`d. Uhlgh ls jppr`xldjtnoynqujo t` g/:75 whnrn g ls thn spnnk `b oleht la vjguud.Nq. (v), la tnrds `b v

:gja cn wrlttna js,

va4

a

v: `r va

a

:

Nanrey onvnos 6 Mlantlg jak p`tnatljo nanrelns Majak ^ala ath `rclt jrn elvna cy

Ma4

3

:dv

a3 4 333

9

;

ha8

dn

jak ^a4

9;

:

a

3

r

n4

3339

;

ha;

dn

(jssudlae lablalty js j znr` p`tnatljo nanrey onvno)

[hn t`tjo nanrey Nals thn sud `b thn mlantlg jak p`tnatljo nanrelns.

s`, Na4 Ma+ ^a4 3339

;

ha8

dn

Wucstltutlae vjouns `b d, n,

9jak h wlth a 4 :, wn ent thn onjst nanrey `b thn jt`d la blrst `rclt, whlgh ls

:7.2 nR. Hnagn,N

:4 :7.2 nR ....(x)

jak Na4

3:

a

N4

3a

2.:7nR ....(xl)

Wucstltutlae a 4 3, 7, ;, ...., ntg., wn ent nanrelns `b jt`d la klbbnrnat `rclts.

N34 7.;9 nR, N

74 :.>: nR, .... N

4 9

:9.: Hykr ena Olmn Jt`ds[hn C`hr d`kno `b hykr`ena gja cn nxtnaknk t` hykr`ena olmn jt`ds, l.n., `an nongtr`a jt`ds, thnaugonjr ghjren ls +zn, whnrn z ls thn jt dlg audcnr, nqujo t` thn audcnr `b pr`t as la thn augonus.[hn nbbngt la thn prnvl us jajoysls ls t` rnpojgn n3 nvnrywhnrn cy zn3. [hus, thn nqujtl as b`r, r

a, v

a

jak Na

jrn jotnrnk js uaknr6

ra4 3

339

adzn

ha4

z

a3j

9 `r r

a

z

a3....(l)

whnrn j94 9.>3< (rjklus `b blrst `rclt ` b H)

va4

ah3

zn

9

3

4 a

zv

: `r v

a

a

z....(ll)

whnrn v:4 3.:< :92 d/s (spnnk `b nongtr a la blrst `rclt `b H)

Na4 333

9

;3

ha8ndz

4 3

3

az N

:`r N

a 3

3

az ....(lll)

whnrn N:4 :7.29 nR (nanrey `b jt`d la blrst `rclt b H)

:9.3 Knblajtl`as vjolk b`r slaeon nongtr a systnd(:) Er`uak stjtn 6O`wnst nanrey stjtn `b jay jt`d `r l`a ls gjoonk er`uak stjtn `b thn jt`d.

Er`uak stjtn nanrey `b H jt`d 4 :7.2 nREr`uak stjtn nanrey `b Hn+ L`a 4 >;.; nREr`uak stjtn nanrey `b Ol++ L`a 4 :33.; nR

(3) Nxgltnk Wtjtn 6Wtjtn `b jt`d `thnr thja thn er`uak stjtn jrn gjoonk lts nxgltnk stjtns.a 4 3 blrst nxgltnk stjtna 4 7 sng`ak nxgltnk stjtn

a 4 ; thlrk nxgltnk stjtna 4 a

9+ : a

9th nxgltnk stjtn

7/21/2019 Modern Physics - 1 Theory_E

15/34

YH\WLGW

"djalshmudjrphyslgs.la" :>

(7) L`alsjtl`ananrey ( N.)6 Dlaldud nanreyrnqulrnk t` d`vn ja nongtr a br`d er`uak stjtn t` a 4 ls gjoonk l`alsjtl a nanrey `b thn jt`d `r l`aL`alsjtl`a nanrey `b H jt`d 4 :7.2 nRL`alsjtl`a nanrey `b Hn+ L`a 4 >;.; nRL`alsjtl`a nanrey `b Ol++ L`a 4 :33.; nR

(;) L`alsjtl a p`tnatljo (L.Y.) 6 Y`tnatljo klbbnrnagn thr`ueh whlgh j brnn nongtr a dust cn jggnonrjtnkbr`d rnst sugh thjt lts mlantlg nanrey cng`dns nqujo t` l`alsjtl`a nanrey `b thn jt`d ls gjoonkl`alsjtl`a p`tnatljo `b thn jt`d.

L.Y `b H jt`d 4 :7.2 RL.Y. `b Hn+ L`a 4 >;.; R

(>) Nxgltjtl ananrey6 Nanrey rnqulrnk t` d`vn ja nongtr a br d er uak stjtn `b thn jt d t` jay `thnrnxltnk stjtn `b thn jt`d ls gjoonk nxgltjtl`a nanrey `b thjt stjtn.Nanrey la er`uak stjtn `b H jt`d 4 :7.2 nRNanrey la blrst nxgltnk stjtn `b H-jt`d 4 7.; nRst nxgltjtl`a nanrey 4 :9.3 nR.

(2) Nxgltjtl a Y`tnatljo6 Y tnatljo klbbnrnagn thr ueh whlgh ja nongtr`a dust cn jggnonrjtnk br`d rnsts` thjt lts mlantlg nanrey cng`dns nqujo t` nxgltjtl`a nanrey `b jay stjtn ls gjoonk nxgltjtl`ap`tnatljo `b thjt stjtn.st nxgltjtl`a nanrey 4 :9.3 nR.st nxgltjtl`a p`tnatljo 4 :9.3 R.

(5) Claklae nanrey `r Wnpnrjtl a nanrey 6Nanrey rnqulrnk t` d`vn ja nongtr`a br`d jay stjtn t` a4 ls gjoonk claklae nanrey `b thjt stjtn. `r nanrey rnonjsnk kurlae b`rdjtl`a `b ja H-olmn jt d/l`abr`d a 4t` s`dn pjrtlguojr a ls gjoonk claklae nanrey `b thjt stjtn.Claklae nanrey `b er`uak stjtn `b H-jt d 4 :7.2 nR

Nx. :7 Blrst nxgltjtl a p`tnatljo `b j hyp thntlgjo hykr`ena olmn jt`d ls :> v`ot. Blak thlrk nxgltjtl`a p tnatljo `b thnjt`d.

W`o. Ont nanrey `b er`uak stjtn 4 N9

N94 :7.2 V3 nR jak N

a4 3

9

a

N

a 4 3, N3

4;

N9

elvna;

N9 N94 :>

;

N7 9 4 :>

b r a 4 ;, N;4

:2

N9

thlrk nxlgltjtl`a nanrey 4:2

N9 N

9

4 :2

:>N

94

7

:>;

:2

:>

4;

5> nR

thlrk nxgltjtl`a p`tnatljo ls;

5>R

:9.7 Ndlssl a spngtrud `b hykr`ena jt`d 6

H-ejs

Wgrnna

Yrlsd

^aknr a`rdjo g`akltl`as thn slaeon nongtr`a la hykr`ena jt`d stjys la er`uak stjtn (a 4 :). Lt lsnxgltnk t` s`dn hlehnr nanrey stjtn whna lt jgqulrns s`dn nanrey br`d nxtnrajo s`urgn. Cut lthjrkjoy stjys thnrn b`r d`rn thja :98 sng`ak.

7/21/2019 Modern Physics - 1 Theory_E

16/34

YH\WLGW

"djalshmudjrphyslgs.la" :2

J ph`t`a g`rrnsp`aklae t` j pjrtlguojr spngtrud olan ls ndlttnk whna ja jt`d djmns j trjasltl`abr`d j stjtn la ja nxgltnk onvno t` j stjtn la j o`wnr nxgltnk onvno `r thn er`uak onvno.Ont a

lcn thn laltljo jak a

bthn blajo nanrey stjtn, thna knpnaklae `a thn blajo nanrey stjtn b`oo`wlae

snrlns jrn `csnrvnk la thn ndlssl`a spngtrud `b hykr`ena jt`d.@a Wgrnna 6J ph`t`erjph `b spngtrjo olans `b thn Oydna, Cjodnr, Yjsghna snrlns `b jt`dlg hykr`ena.

:

3

7

:

3

7

:3

Oydjasnrlns

Cjodnrsnrlns

Yjsghnasnrlns

Ujvnonaeth(lagrnjslae`rknr)

:, 3, 7..... rnprnsnats thn L, LL & LLL olan `b Oydna, Cjodnr, Yjsghna snrlns.

7/21/2019 Modern Physics - 1 Theory_E

17/34

YH\WLGW

"djalshmudjrphyslgs.la" :5

[hn hykr`ena spngtrud (s`dn snongtnk olans)

al (O`wnr Wtjtn a b(^ppnr Wtjtn) Uj vnonaeth (ad) Nanrey

L : 3 :3:.2 :9.3 nR

LL : 7 :93.2 :3.9< nR

LLL : ; > nR

LLL 3 > ;7;.: 3.82 nR

snrlns oldlt 3 (snrlns oldlt) 72;.2 7.;: nR

L 7 ; :85>.: 9.22 nR

LL 7 > :38:.8 9.;nR9.8>nR

:.>:nR

7.;9nR

:7.2nRa 4:

a 43

a 47

a 4;a 4>a 42a 45

B`r thn Oydna snrlns ab4 :, b`r Cjodnr snrlns a

b4 3 jak s` `a.

:9.; Ujvnonaeth `b Yh t`a Ndlttnk la Kn-nxgltjtl`aJgg`rklae t` C`hr whna ja jt`d djmns j trjasltl`a br`d hlehnr nanrey onvno t` j o`wnr onvno lt ndltsj ph`t`a wlth nanrey nqujo t` thn nanrey klbbnrnagn cntwnna thn laltljo jak blajo onvnos. Lb N

lls thn

laltljo nanrey `b thn jt`d cnb`rn sugh j trjasltl`a, Nbls lts blajo nanrey jbtnr thn trjasltl`a, jak thn

ph`t`as nanrey ls h4

hg , thna g`asnrvjtl`a `b nanrey elvns,

h4

hg4 N

l N

b (nanrey `b ndlttnk ph t`a) ....(l)

Cy :, F`hjaa Cjodnr, j Wwlss tnjghnr b`uak j b`rduoj thjt elvns thn wjvn onaeths `b thnsn olans.[hls ls a`w gjoonk thn Cjodnr snrlns. [hn Cjodnrs b`rduoj ls,

33 a

:

3

:S

:....(ll)

Hnrn, a 4 7, ;, > ...., ntg.

S 4 Sykcnre g`astjat 4 :.9

7/21/2019 Modern Physics - 1 Theory_E

18/34

YH\WLGW

"djalshmudjrphyslgs.la" :8

) `b thls snrlns ls `ctjlank. ^slae thn rnojtl`a, N 4

hgwn gja blak thn ph t`a nanrelns g`rrnsp`ak-

lae t` thn wjvnonaeth `b thn Cjodjr snrlns.

3333 a

Shg

3

Shg

a

:

3

:hgS

hgN

[hls b`rduoj sueensts thjt,

Na4 3

a

Shg, a 4 :, 3, 7..... ....(lll)

[hn wjvnonaeths g`rrnsp`aklae t` `thnr spngtrjo snrlns (Oydna, Yjsghna, (ntg.) gja cn rnprn-snatnk cy b`rduoj sldlojr t` Cjodnrs b rduoj.

Oydna Wnrlns 6

33 a

:

:

:S

:, a 4 3, 7, ;.....

Yjsghna Wnrlns 6

33 a

:

7

:S

:, a 4 ;, >, 2.....

Crjgmntt Wnrlns 6

33 a

:

;

:S

:, a 4 >, 2, 5.....

Ybuak Wnrlns 6

33

a

:

>

:S

:, a 4 2, 5, 8

[hnOydnasnrlns lslathn uotrjvl ont, jakthnYjsghna. Crjgmnttjak Ybuak snrlns jrnla thn labrjrnkrnel a.

Nx. :; Gjoguojtn (j) thn wjvnonaeth jak (c) thn brnqunagy `b thn H olan `b thn Cjodnr snrlns b`r hykr`ena.

W`o. (j) Holan `b Cjodnr snrlns g`rrnsp`aks t` thn trjasltl`a br`d a 4 ; t` a 4 3 onvno. [hn g`rrnsp`aklae

wjvnonaeth b`r H

olan ls,

335

;

:

3

:):992 :95

4 ;.< :95 d Jas.

(c) 4

g

4 5

8

:9 Blak thn ojrenst jak sh`rtnst wjvnonaeths la thn Oydna snrlns b`r hykr`ena. La whjt rnel`a `b thn nongtr`-djeantlg spngtrud k`ns njgh snrlns oln0

W`o. [hn trjasltl`a nqujtl`a b`r Oydna snrlns ls elvna cy,

33 a

:

):(

:S

:a 4 3, 7, ......

b`r ojrenst wjvnonaeth, a 4 3

;

:

:

::99; :95 d 4 :3:> Jas.[hn sh`rtnst wjvnonaeth g`rrnsp`aks t` a 4

:

:

::99

7/21/2019 Modern Physics - 1 Theory_E

19/34

YH\WLGW

"djalshmudjrphyslgs.la" : nR

7.98 nR

>.79 nR

:>.2 nR

(c) Blak thn sh rt wjvnonaeth oldlt b thnsnrlns tnrdlajtlae jt a 4 3

(g) Blak thn nxgltjtl a p tnatljo b r thn stjtna 4 7.

(k) Blak wjvn audcnr`b thn ph`t andlttnkb`r thn trjasltl`a a 4 7 t` a 4 :.

(n) Uhjt ls thn dlaldud nanrey thjt janongtr`a wloo hjvn jbtnr latnrjgtlae wlththls jt`d la thn er`uak stjtn lb thn laltljomlantlg nanrey `b thn nongtr`a ls(l) 2 nR (ll) :: nR

7/21/2019 Modern Physics - 1 Theory_E

20/34

YH\WLGW

"djalshmudjrphyslgs.la" 39

W`o. (j) L`alzjtl a p tnatljo 4 :>.2 R

(c) dla

47.>

:3;994 37;9

(g) N7:

4 7.98 ( :>.2) 4 :3.>3 nR[hnrnb`rn, nxgltjtl`a p`tnatljo b`r stjtn a 4 7 ls :3.>3 v`ot.

(k)7:

:

4 :3;99

N7:: 4

:3;99

>3.:3:

:.9: :95 d:

(n) (l) N3 N

:4 :9.7 nR 1 2 nR.

Hnagn nongtr`a gjaa`t nxgltn thn jt`ds. W`, Mdla

4 2 nR.(ll) N

3 N

:4 :9.7 nR ? :: nR.

Hnagn nongtr a gja nxgltn thn jt`ds. W`, Mdla

4 (:: :9.7) 4 9.5 nR.

Nx. 3: J sdjoo pjrtlgon `b djss d d`vns la sugh j wjy thjt thn p tnatljo nanrey ^ 4 jr3 whnrn j ls j g`astjat jakr ls thn klstjagn `b thn pjrtlgon br`d thn `rlela. Jssudlae C`hrs d`kno `b qujatlzjtl a `b jaeuojr d`dnatudjak glrguojr `rclts, blak thn rjklus `b ath joo`wnk rclt.

W`o. [hn b`rgn jt j klstjagn r ls,

B 4 kr

k^4 3jr

Wupp`sn r cn thn rjklus `b ath `rclt. [hn angnssjry gnatrlpntjo b`rgn ls pr`vlknk cy thn jc`vn b`rgn. [hus,

r

dv34 3jr

Burthnr, thn qujatlzjtl`a `b jaeuojr d`dnatud elvns,

dvr 43

ah

W`ovlae Nqs. (l) jak (ll) b`r r, wn ent

;/:

3

33

jd8

har

Jas.

Nx. 33 Ja ldjelajry pjrtlgon hjs j ghjren nqujo t` thjt `b ja nongtr`a jak djss :99 tldns thn djss `b thn nongtr`a.Lt d`vns la j glrguojr `rclt jr`uak j augonus `b ghjren + ;n. [jmn thn djss `b thn augonus t` cn lablaltn.Jssudlae thjt thn C`hrs d`kno ls jppolgjcon t` thn systnd.(j) Knrlvn jak nxprnssl`ab`r thn rjklus b ath C`hr `rclt.(c) Blak thn wjvnonaeth `b thn rjkljtl`a ndlttnk whna thn pjrtlgon fudps br`d b`urth `rclt t` thn sng`ak.

W`o. (j) Un hjvn 3a

3

9a

3p

r

zn

;

:

r

vd

.....(l)

[hn qujatlzjtl`a `b jaeuojr d`dnatud elvns,

dpvr

a4

3

ah......(ll)

W`ovlae Nqs. (l) jak (ll), wn ent

r 4 3p

933

ndz

ha

Wucstltutlae dp4 :99 d

whnrn d 4 djss `b nongtr`a jak z 4 ;

wn ent, r a4 3

933

dn;99

ha

Jas.

(c) Js wn ma`w,Nanrey `b hykr ena jt`d la er`uak stjtn 4 :7.29 nR

jak Na d

a

z3

3

7/21/2019 Modern Physics - 1 Theory_E

21/34

YH\WLGW

"djalshmudjrphyslgs.la" 3:

B r thn elvnapjrtlgon, N;4 3

3

);(

);()29.:7( :99 4 :729 nR

jak N34 3

3

)3(

);()29.:7( :99 4 >;;9 nR

KN 4 N; N

34 ;989 nR

(la ) 4 ;989:3;99

4 7.9 Jas.

Nx. 37 J pjrtlgon ma`wa js -dnjs`a, hjs j ghjren nqujo t` thjt `b ja nongtr a jak djss 398 tldns thn djss `b thnnongtr`a. Lt d`vns la j glrguojr `rclt jr`uak j augonus `b ghjren +7n. [jmn thn djss `b thn augonus t` cnlablaltn.Jssudlae thjt thn C`hrs d`kno ls jppolgjcon t` thls systnd, (j) knrlvn ja nxprnssl`a b`r thn rjklus`b thn ath C`hr `rclt, (c) blak thn vjoun `b a b`r whlgh thn rjklus `b thn `rclt ls jppr`xldjtnoythn sjdn js thjt`b thn blrst C`hr `rclt b`r j hykr`ena jt`d jak (g) blak thn wjvnonaeth `b thn rjkljtl`a ndlttnk whna thndns`a fudps br`d thn thlrk `rclt t` thn blrst `rclt.

W`o. (j) Un hjvn,

39

33

r;

Vn

r

dv

`r,d;

Vnrv

9

33

...(l)

[hn qujatlzjtl`a ruon ls vr 4d3

ah

[hn rjklus ls r 4rv

)vr(3

3

4 39

Vn

d;

4 39

33

dnV

ha

....(ll)

B`r thn elvna systnd, V 4 7 jak d 4 398 dn.

[hus 3n

933

nd23;

har

(c) Br`d (ll), thn rjklus `b thn blrst C`hr `rclt b`r thn hykr`ena jt`d ls

3n

93

hnd

hr

B`r r4 r

h, 3

n

933

nd23;

ha

4 3

n

93

nd

h

`r, a3

4 23;`r, a 4 3>(g) Br`d (l), thn mlantlg nanrey `b thn jt`d ls

3

dv34

r8

Vn

9

3

jak thn p`tnatljo nanrey ls r;

Vn

9

3

[hn t`tjo nanrey ls Na4

r8

Vn

9

3

^slae (ll), Na4 333

9

;3

ha8

dnV

4 333

9

;n

ha8

d398;>;>> pd.

Nx. 3; J ejs `b hykr`ena olmn jt`ds gja jcs`rc rjkljtl`as `b 28 nR. G`asnqunatoy, thn jt`ds ndlt rjkljtl`as `b`aoy thrnn klbbnrnat wjvnonaeth.Joo thn wjvnonaeths jrn nqujo `r sdjoonr thja thjt `b thn jcs`rcnk ph t`a.(j) Kntnrdlan thn laltljo stjtn `b thn ejs jt`ds.(c) Lknatlby thn ejs jt ds.(g) Blak thn dlaldud wjvnonaeth `b thn ndlttnk rjkljtl`as.(k) Blak thn l`alzjtl a nanrey jak thn rnspngtlvn wjvnonaeth b`r thn ejs jt`ds.

W`o. (j) 73

):a(a

a 4 7l.n., jbtnr nxgltjtl`a jt`d fudps t` sng`ak nxgltnk stjtn.Hnagn a

b4 7. W` a

lgja cn : `r 3

Lb al4 : thna nanrey ndlttnk ls nlthnr nqujo t`, ernjtnr thja `r onss thja thn nanrey jcs`rcnk.

Hnagn thn ndlttnk wjvnonaeth ls nlthnr nqujo t , onss thja `r ernjtnr thja thn jcs`rcnk wjvnonaeth.Hnagn a

l :.

Lb al4 3, thna N

nN

j. Hnagn

n

9

(c) N7 N

34 28 nR

(:7.2) (V3)

Ja nongtr`a ls `rcltlae la j glrguojr `rclt `b rjklus r uaknr thn labounagn `b j g`astjat djeantlg blnok `b strnaethC. Jssudlae thjt C`hrs p`stuojtn rnejrklae thn qujatlsjtl`a `b jaeuojr d`dnatud h`oks e``k b`r thlsnongtr`a, blak

(j) thn joo wnk vjouns b thn rjklus r b thn rclt.(c) thn mlantlg nanrey `b thn nongtr`a la rclt(g) [hn p`tnatljo nanrey b latnrjgtl`a cntwnna thn djeantlg d`dnat `b thn `rcltjo gurrnat kun t` thn

nongtr`a d`vlae la lts `rclt jak thn djeantlg blnok C.(k) [hn t tjo nanrey`b thn joo`wnk nanreyonvnos.

W`o. (j) rjklus `b glrguojr pjth

r 4Cn

dv....(l)

dvr 43

ah....(ll)

W`ovlae thnsn tw` nqujtl as, wn ent

r 4Cn3

ah

jak v 4 3d3

ahCn

7/21/2019 Modern Physics - 1 Theory_E

23/34

YH\WLGW

"djalshmudjrphyslgs.la" 37

(c) M 43

:dv3 4

d;

ahCn

Jas.

(g) D 4 l J 4

[

n(r3) 4

3

nvr

43

nCn3

ah

3d3

ahCn

4

d;

ahn

A`w p tnatljo nanrey ^ 4 D . C

4d;

ahnC

(k) N 4 + M 4d3

ahnC

::. NBBNG[ @B A^GON^W D@[L@A @A NANSE\ @B J[@DOnt c`th thn augonus `b djss D, ghjren Vn jak nongtr`a `b djss d, jakghjren n rnv`ovn jc`ut thnlr gnatrn `b djss (GD) wlth sjdn jaeuojrvno glty () cut klbbnrnat olanjr spnnks. Ont r

:

jak r3

cn thn klstjagn `b GDbr`d augonus jak nongtr a.[hnlrjaeuojr vno`glty sh`uok cn sjdn thna`aoy thnlr snpjrjtl`a wloo rndjla uaghjaenk la ja nanrey onvno.

dr3

GD

r:D

Ont r cn thn klstjagn cntwnna thn augonus jak thn nongtr`a. [hnaDr

:4 dr

3

r:+ r

34 r

r:4

dD

dr

jak r

34

dD

Dr

Gnatrlpntjo b`rgn t` thn nongtr`a ls pr`vlknk cy thn nongtr`stjtlg b`rgn. W`,

dr33 4

9;

:

3

3

r

Vn

`r d

dD

Dr3 4

9;

:

. 3

3

r

Vn

`r

dD

Ddr7 3 4

9

3

;

Vn

`r r73 49

3

;

n

whnrndD

Dd

4

D`dnat `b lanrtlj `b jt d jc`ut GD,

4 Dr:

3 + dr3

3 4

dD

Ddr3 4r3

Jgg`rklae t` C`hrs thn`ry,3

ah4

`r r3 43

ah

W ovlae jc vn nqujtl as b`r r, wn ent

r 4

Vn

ha3

339

jak r 4 (9.>3< )

d

V

a3

Burthnr nongtrlgjo p`tnatljo nanrey `b thn systnd,

7/21/2019 Modern Physics - 1 Theory_E

24/34

YH\WLGW

"djalshmudjrphyslgs.la" 3;

^ 4r;

Vn

9

3

^ 4 3339

;3

ha;

nV

jak mlantlg nanrey, M 43

:3 4

3

:r3 3 jak M 4

3

:v3

v-spnnk `b nongtr`a wlth rnspngt t` augonus. (v 4 r)

hnrn 3 4 79

3

r;

Vn

M 4 r8Vn

9

3

4 3339

;3

ha8

nV

[`tjo nanrey `b thn systnd Na4 M + ^

Na4 333

9

;

ha8

n

thls nxprnssl`a gja jos` cn wrlttna js

Na4 (:7.2 nR)

d

a

V3

3

[hn nxprnssl`a b`r Nawlth`ut g`aslknrlae thn d`tl`a `b pr`t`a ls N

a4 333

9

;

ha8

dn

, l.n., d ls rnpojgnk cy

whlon g`aslknrlae thn d`tl a `b augonus.

Nx. 32 J p`sltr`alud jt`d ls j systnd thjt g`aslsts `b j p`sltr`a jak ja nongtr`a thjt `rclt njgh thnr. G`dpjrnthn wjvnonaeth `b thn spngtrjo olans `b p`sltr`alud wlth th`sn `b rklajry hykr`ena.

W`o. Hnrn thn tw` pjrtlgon hjvn thn sjdn djss d, s` thn rnkugnk djss ls

4Dd

dD

4

d3

d34

3

d

whnrn d ls thn nongtr`a djss. Un ma`w thjt Nad

3:

dN

'N

a

a

nanrey `b njgh onvno ls hjovnk. [hnlr klbbnrnagn wloo jos` cn hjovnk.

Hnagn a

4 3a

:3. J[@DLG G@OOLWL@ALa sugh g`oolsl`as jssudn thjt thn o`ss la thn mlantlg nanrey `b systnd ls p`sslcon `aoy lb lt gja nxgltn `rl`alsn.

Nx. 35 H jt`d jt rnstla er`uak stjtnjak brnn t` d`vn

anutr`a

M, v

hnjk `a g`oolsl`a

Uhjt wloo cn thn typn `b g`oolsl`a, lb M 4 :;nR, 39.; nR, 33 nR, 3;.:8 nR(nojstlg/lanojstlg/pnrngtoy lanojstlg)

W`o. O`ss la nanrey(N) kurlae thn g oolsl`a wloo cn usnk t` nxgltn thn jt`d r nongtr`a br`d an onvno t` ja`thnr.Jgg`rklae t` qujatud Dnghjalgs, b`r hykr`ena jt`d.

N 4 {9, :9.3 nR, :3.9< nR, ........., :7.2 nR)Jgg`rklae t` Anwt`al`a dnghjalgs

dlaldud o`ss 4 9. (nojstlg g oosl a)

b`r djxldud o`ss g`oolsl`a wloo cn pnrbngtoy lanojstlg d d vblb anutr`a g`oolkns pnrbngtoy lanojstlgjooythna, Jppoylae d`dnatud g`asnrvjtl`a

d94 3d

b

7/21/2019 Modern Physics - 1 Theory_E

25/34

YH\WLGW

"djalshmudjrphyslgs.la" 3>

3

vv 9b

blajo M.N. 43

: 3d

;

39

4

3

d3

: 39

4

3

M

djxldud o`ss 43

M

Jgg`rklae t` gojsslgjo dnghjalgs (N) 4 ]9,3

MT

(j) Lb M 4 :; nR, Jgg rklae t` qujatud dnghjalgs(N) 4 {9, :9.3nR, :3.9< nR}Jgg`rklae t` gojsslgjo dnghjalgsN 4 ]9, 5 nRTo`ss 4 9, hnagn lt ls nojstlg g`oolsl`a spnnk `b pjrtlgon ghjaens.

(c) Lb M 4 39.; nRJgg`rklae t` gojsslgjo dnghjalgs

o`ss 4 ]9, :9.3 nRTJgg`rklae t` qujatud dnghjalgs

o`ss 4 {9, :9.3nR, :3.9.(

3

: 39 4 )dv3

:.(

>

: 39 4 >

M

7/21/2019 Modern Physics - 1 Theory_E

26/34

YH\WLGW

"djalshmudjrphyslgs.la" 32

djxldud o`ss 4 M >

M4

>

M;

s` o`ss wloo cn

>

M;,9 ....(3)

B`r lanojstlg g`oolsl`a thnrn sh`uok cn jt onjst `an g`dd`a vjoun `thnr thja znr` la snt (:) jak (3)

>

M;

1 ;9.8 nRM 1 >: nR

dlaldud vjoun `b M 4 >: nR.

Nx. 3< J d`vlae hykr`ena jt`d djmns j hnjk `a g`oolsl`a wlth j stjtl`ajry hykr`ena jt`d. Cnb`rn g`oolsl`a c`thjt`ds jrn la er`uak stjtn jak jbtnr g`oolsl`a thny d`vn t`enthnr. Uhjt ls thn dlaldud vjoun `b thn mlantlgnanrey `b thn d`vlae hykr`ena jt`d, sugh thjt `an `b thn jt`ds rnjghns `an `b thn nxgltjtl`a stjtn.

W`o. Ont M cn thn mlantlg nanrey `b thn d`vlae hykr`ena jt`d jak M, thn mlantlg nanrey `b g`dclank djss jbtnrg`oolsl`a.Br`d g`asnrvjtl`a`b olanjr d`dnatud,

N 4 :9.3 nR

a 4 3

a 4 :

p 4 p `r Md3 4 )d3('M3

r M 4 3M ....(l)Br`d g`asnrvjtl a `b nanrey, M 4 M +N ....(ll)

W`ovlae Nqs. (l) jak (ll), wn ent N 43

M

A`w dlaldud vjoun bN b`r hykr`ena jt`d ls :9.3 nR.`r N :9.3 nR

3

M:9.3

M39.; nR[hnrnb rn, thn dlaldud mlantlg nanrey`b d`vlae hykr`ena ls 39.; nR Jas.

Nx. 79 J anutr`a d`vlae wlth spnnk v djmns j hnjk-`a g oolsl`a wlth j hykr`ena jt d la er`uak stjtn mnpt jt rnst.Blak thn dlaldud mlantlg nanrey`b thn anutr`a b`r whlgh lanojstlg (g`dpontnoy `r pjrtljooy) g`oolsl a djy tjmnpojgn. [hn djss `b anutr`a 4 djss `b hykr`ena 4 :.25 :935 me.

W`o. Wupp`sn thn anutr`a jak thn hykr`ena jt d d`vn jt spnnk v:

jakv3

jbtnr thn g`oolsl`a. [hn g`oolsl`a wloo cnlanojstlg lb j pjrt `b thn mlantlg nanrey ls usnk t` nxgltn thn jt`d. Wupp`sn ja nanrey N ls usnk la thls wjy.^slae g`asnrvjtl`a `b olanjr d`dnatud jak nanrey.

dv4dv:

+ dv3

....(l)

jak3

:dv3 4

3

:dv

:3 +

3

:dv

33 +N ....(ll)

Br`d (l), v3 4 v:

3 + v3

3 + 3v:v

3,

Br`d (ll), v3 4 v:

3 + v3

3 +d

N3

[hus, 3v:v

34

d

N3

Hnagn, (v: v

3)3 ;v

:v

34 v3

d

N;

Js v: v

3dust cn rnjo, v3

d

N;9

`r,3

:dv3 1 3N.

[hn dlaldud nanreythjt gja cn jcs`rcnk cy thn hykr`ena jt d la er uak stjtn t` e` la ja nxgltnk stjtn ls:9.3 nR. [hus, thn dlaldud mlantlg nanrey `b thn anutr`a annknk b`r ja lanojstlg g`oolsl`a ls

nR;.39nR3.:93dv3: 3

dla

7/21/2019 Modern Physics - 1 Theory_E

27/34

YH\WLGW

"djalshmudjrphyslgs.la" 35

Nx. 7: H`w djay hnjk-`a, nojstlg g`oolsl`as dust j anutr a hjvn wlth knutnrlud augonus t` rnkugn lts nanreybr`d: DnR t` 9.93> nR.

W`o. Ont djss b anutr a 4 d jak djss b knutnrlud 4 3dlaltljo mlantlg nanrey `b anutr`a 4 M

9

Ont jbtnr blrst g`oolsl`a mlantlg nanrey `b anutr`a jak knutnrlud cn M:jak M

3.

^slae G.@.O.D. jo`ae klrngtl`a `b d`tl`a

9dM3 4 :dM3 + 3dM;

vno glty `b snpnrjtl`a 4 vno glty `b jppr`jgh

d3

dM; 3 d

dM3 : 4d

dM3 9

W ovlae nqujlt a (l) jak (ll) wn ent

M:4

39 4 :97 nR 4 :97 nR.

[hus, nR:9

h 7

4 nR:9

)s/d:97()snR:9:;.;(

7

8:>

4 ad3;.:

nR:9

adnR:3;3

7

7/21/2019 Modern Physics - 1 Theory_E

30/34

YH\WLGW

"djalshmudjrphyslgs.la" 79

3. GhjrjgtrlstlgX-rjys[hn shjrp pnjms `ctjlank la erjph jrn ma`wa jsghjrjgtnrlstlg x-rjys cngjusn thny jrn ghjrjgtnrlstlg `btjrent djtnrljo.

:,

3,

7,

;, ........ 4 ghjrngtnrlstlg wjvnonaeth `b

djtnrljo hjvlae jt`dlg audcnr V jrn gjoonk ghjrjgtnrls-tlg x-rjys jak thn spngtrud `ctjlank ls gjoonkghjrjgtnrlstlg spngtrud. Lb tjrent `b jt dlg audcnr V ls

usnk thna pnjms jrn shlbtnk.

R, V

: 3

7

; dla

Ghjrjgtnrlstlg x-rjy ndlssl`a `ggurs whna ja nanrentlgnongtr`a g`oolkns wlth tjrent jak rnd`vn ja laanr shnoonongtr a br`d jt`d, thnvjgjagygrnjtnk la thn shnoo ls bloonkwhna ja nongtr`a br`d hlehnr onvno kr`ps lat` lt.Wupp`sn vjgjagy grnjtnk la laanrd`st M-shnoo ls bloonk cyja nongtr`a kr`plae br`d anxt hlehnr onvno O-shnoo thna M

ghjrjgtnrlstlg x-rjyls `ctjlank. Lb vjggjayla M-shnoo ls bloonkcy ja nongtr a br`d D-shnoo, M

olan ls pr`kugnk jak s` `a

sldlojroy O, O

,.....D

, D

olans jrn pr`kugnk.

dla : 3 7 ;

R, V' ? V

R, V

: 3 7 ;

M D D

A

M

M

O O O

a4>a4;

a47

a43

a4:

x-rjys

O

M

DA

@

Nx. 7; Blak whlgh ls Mjak M

o : o 3

:

3

W`o. N 4

hg, 4

N

hg

slagn nanrey klbbnrnagn `b M

ls onss thja M

Nm

?Nm

m

? m

: ls Mjak 3 ls M

Nx. 7>

: 3

:3

Blak whlgh ls Mjak O

W`o NM

1 NO

: ls Mjak 3 ls O

:;. D@WNON\W OJU 6D`snony dnjsurnk thn brnqunaglns `b ghjrjgtnrlstlg x-rjys b`r j ojren audcnr `b nondnats jak po`ttnk thnsqjurn r` t `b brnqunagy jejlast p`sltl a audcnr la pnrl`klg tjcon. Hn klsg`vnrnk thjt po t ls vnry go`snk t`j strjleht olan a`t pjsslae thr`ueh `rlela.

7/21/2019 Modern Physics - 1 Theory_E

31/34

YH\WLGW

"djalshmudjrphyslgs.la" 7:

:, : : :', ' ', ' ''

3, 3 3 3', '', '' '

V

V: o : o 3

V3 o :' o 3'

V7 o :" o 3''

V; o :"' o 3'''

Ujvnonaeth `b ghjrjgtrlstlg wjvnonaeths.

D`snonys `csnrvjtl`as gja cn djthndjtlgjooy nxprnssnk js

)cV(j

j jak c jrn p`sltlvn g`astjats b`r `an typn `b x-rjys & b`r joo nondnats (laknpnaknat `b V).D`snonys Ojw gja cn knrlvnk `a thn cjsls `b C`hrs thn`ry `b jt`d, brnqunagy `b x-rjys ls elvna cy

4

33

3: a

:

a

:GS . (V c)

cy uslae thn b`rduoj

:4 S z3

33

3: a

:

a

:wlth d`klblgjtl`a b`r duotl nongtr`a systnd.

c ma`wa js sgrnnalae g`astjat `r shlnoklae nbbngt, jak (V c) ls nbbngtlvn augonjr ghjren.b r M

olan

a: 4 :, a

34 3

4;

SG7(V c)

4 j(V c)

Hnrn j 4;

SG7, ]c 4 : b`r M

olansT

Nx. 72

: 3

M

M

V:

V3

Blak la V:

jak V3

whlgh `an ls ernjtnr.

W`o.

33

3: a

:

a

:gS . (V c)

Lb V ls ernjtnr thnawloo cn ernjtnr,wloo cn onss

:

? 3 V: 1 V3.

Nx. 75 J g`cjot tjrent ls c`dcjrknk wlth nongtr`as jak thn wjvnonaeth `b lts ghjrjgtnrlstlg spngtrud jrn dnjsurnk.J sng`ak, bjlatnr, ghjrjgtnrlstlg spngtrud ls jos` b`uak cngjusn `b ja ldpurlty la thn tjrent. [hn wjvnonaeth`b thn M

olans jrn :58.< pd (g`cjot) jak :;7.> pd (ldpurlty). Uhjt ls thn ldpurlty0

W`o. ^slae D`snonys ojw jak puttlae g/b`r(jak jssudlae c 4 :), wn `ctjla

jjVg

9

9

gg

jak jjVg

x

x

Klvlklae ylnoks

7/21/2019 Modern Physics - 1 Theory_E

32/34

YH\WLGW

"djalshmudjrphyslgs.la" 73

:V

:V

9

9

g

x

x

g

Wucstltutlae elvns us

pd>.:;7

pd pd

W`o. D`snonys nqujtl`a ls

)cV(jv

[hus, )cV(jg

::

....(l)

jak )cV(jg

33

....(ll)

Br`d (l) jak (ll) )VV(j::

g 3:3:

`r, j 4

3:3:

::

)VV(

g

435;3

)s/d:97( 3/:8

3/::33/::3 )d:9>.:58(

:

)d:95:(

:

4 >.9 :95 (Hz):/3

Klvlklae (l) cy (ll),

cV

cV

3

:

:

3

`r, c35

c;3

5:

>.:58

`r, c 4 :.75

Yr`cond :. Blak thn d`dnatud b j :3.9 DnR ph`t`a.

W`outl`a 6 p 4g

N4 :3 DnR/g.

Yr`cond 3. D`a`ghr`djtlg oleht `b wjvnonaeth 7999 ls laglknat a rajooy `a j surbjgn `b jrnj ; gd3. Lb thnlatnaslty `b thn oleht ls :> :93 U/d3, kntnrdlan thn rjtn jt whlgh ph`t`as strlmn thn surbjgn.

W`outl`a 6 Sjtn jt whlgh ph`t`as strlmn thn surbjgn

4

/hg

J

ph`t`a/F:927.2

s/F:92:

4 :9:7 ph`t`a/s.

7/21/2019 Modern Physics - 1 Theory_E

33/34

YH\WLGW

"djalshmudjrphyslgs.la" 77

Yr`cond 7. [hn mlantlg nanrelns `b ph`t nongtr as rjaen br`d znr` t` ;.9 :9:< F whna oleht `b wjvnonaeth 7999 bjoos `a j surbjgn. Uhjt ls thn st`pplae p`tnatljo b`r thls oleht 0

W`outl`a 6 Mdjx

4 ;.9 :9:< F F:92.:

nR:: nR..

[hna, br`d nRs4 M

djx, R

s4 3.> R.

Yr`cond ;. Uhjt ls thn thrnsh`ok wjvnonaeth b`r thn djtnrljo la jc`vn pr`cond 0

W`outl`a 6 3.> nR 4 th

77 .nR:9;.:3

7999

.nR:9;.:3

W`ovlae, th

4 5>. Blak thn kn Cr`eoln wjvnonaeth b j 9.9: me pnoont hjvlae j vno`glty `b :9 d/s.

W`outl`a 6 4 h/p 4s/d:9me9:.9

s.F:927.2 7;

4 2.27 :937 .

Yr`cond 2. Kntnrdlan thn jggnonrjtlae p`tnatljo angnssjry t` elvn ja nongtr a j kn Cr`eoln wjvnonaeth b : ,whlgh ls thn slzn `b thn latnrjt`dlg spjglae `b jt`ds la j grystjo.

W`outl`a 6 R 4 39

3

nd3

h

4 :>: R..

Yr`cond 5. Kntnrdlan thn wjvnonaeth `b thn sng`ak olan `b thn Yjsghna snrlns b`r hykr`ena.

W`outl a .:

4 (:.9

:

7

:`r 4 :3,839 .

Yr`cond 8. H`w djay klbbnrnat ph`t`as gja cn ndlttnk cy hykr`ena jt`ds thjt uaknre` trjasltl`as t` thner`uak stjtn br`d thn a 4 > stjtn 0

W`outl`a 6 A` `b p`sslcon trjasltl`a br`d a 4 > jrn 3>G 4:9

Jas. :9 ph`t`as.

Yr`cond

7/21/2019 Modern Physics - 1 Theory_E

34/34

YH\WLGW

4 2.8 3a

:nR

(l) N:4 2.8 nv

N34 2.8 33

:nR 4 :.59 nR

N74 2.8 37

:nR 4 9.52 nR

(ll) N (73) 4 N7 N

34 9.52 ( :.59) nR

4 9.:.9 nv

>

m;4 >: m 4 27.5> nR

Yr`cond :3. J [R tucn `pnrjtns wlth j 39 mR jggnonrjtlae p tnatljo. Uhjtjrn thn djxldudnanreyXrjys br`dthn [R snt 0

W`outl`a 6 [hn nongtr as la thn [R tucn hjvn ja nanrey`b 39 mnR, jak lb thnsn nongtr as jrn cr ueht t` rnst cy

j g`oolsl`a la whlgh `an Xrjy ph`t`a ls ndlttnk, thn ph`t`a nanrey ls 39 mnR.

Yr`cond :7. La thn D`snony rnojtl`a, )cV(jv whlgh wloo hjvn thn ernjtnr vjoun b`r thn g`astjat j b`r M `r

M

trjasltl`a 0W`outl`a 6 J ls ojrenr b`r thn M

trjasltl`as thja b`r thn M

trjasltl`as.