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8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
1/33
_| lv S`f| 5
@ ojcht ^bvsfos
Oi`|c`|s ^hec
H. \bc @ ojcht H|im Mhss @ mdct h`l H|imfo @ mdct Fsi|i~cs Hj~b h Lcohv Dc| h Lcohv Ehmmh Lcohv @ ojcht Cx h|fi`s H|imfo Mhss S`f| " & Cf`s|cf`%s Mhss-C`ctev Cx h|fi`Df`lf`e C`ctev h`l Mhss Lcaco|
X cs|fi`s ait ^tho|foc @-W O tqc Df`lf`e C`ctev ~ct @ ojci` O tqc @ ojcht Afssfi` @ ojcht A sfi` T |bctaitl%s Hj~bh-^ht|fojc Lcajco|fi` Cr~ctfmc`|
861
D. Thlfiho|fqc Lcohv Cr~i`c`|fhj Lcohv Bhja-Jfac* \8
4
Lcohv Oi`s|h`| j \bc Dcox ctcj "Dx&Dhoketi `l Thlfh|fi`Thlfh|fi` Flc`|fafoh|fi` Lcajco|fi` ia Hj~bh* Dc|h h`l Ehmmh Thlfh|fi`s dv Mhe`c|fo Afcjls Lcajco|fi` dv Cjco|tfo Afcjls Oji l Obhmdct Thlfifsi|i~c Sscs
Thlfiho|fqc Cr~ctfmc`| _hac|v
4>1
F )
Tcqfsfi` h`l Crhmf`h|fi` ^tho|foc X cs|fi`s 481
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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861 @ ojcht ^bvsfos
H. \BC @SOJCHT H\IM
Mhss @ mdct h`l H|imfo @ mdct
@ ojci` mdct "mhss ` mdct& H fs |bc ` mdct ia ` ojcht ~ht|fojcs "f.c. `c |ti`s + ~ti|i`s& f` |bc ` ojc s.
^ti|i` ` mdct "h|imfo ` mdct& W fs |bc ` mdct ia ~ti|i`s f` |bc ` ojc s. Ait h`c |thj h|im* |bc ` mdct ia ~ti|i`s ufjj cx hj |bc ` mdct ia cjco|ti`s.
Uc utf|c |bcsc ` mdcts hs aijjius7
@ ojci` mdct R
^ti|i` ` mdct
ubctc R fs |bc obcmfohj svmdij ia |bc cjcmc`|; c.e.
84
o 1
Crhm~jc
Efqc |bc oim~isf|fi` f` |ctms ia |bc ` mdcts ia `c |ti`s* ~ti|i`s h`l cjco|ti`s aitchob ia |bc aijjiuf`e `c |thj h|ims7
4?3
"h& S. 674
4?<
"d& \b. 6>
< "o& Bc.
74
8 "l& B.
8
H`suct
"h& 64 ~ti|i`s 4?3 - 64 = 8
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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+
@ ojcht ^bvsfos 865
Crhm~jc
Objitf`c bhs h` h|imfo mdct ia 85 h`l h` h|imfo ucfeb| ia ?3.
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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Ubc` h ` ojc s cmf|s h` hj~bh7
F|s ` ojci` ` mdct lcotchscs dv <
F|s ~ti|i` ` mdct lcotchscs dv 4
Dc|h Lcohv |h ~ht|fojcs htc cjco|ti`s |thqcjjf`e h| bfeb s~ccls. \bcv htc ~til ocl dv h obh`ef`e f`|i h ~ti|i`h`l "ja 8.cjco|ti`. \bc ~ti|i` fs tc|hf`cl dv |bc ` ojc s
h`l |bc cjco|ti` fs cmf||cl atim |bc ` ojc s hs h dc|h ~ht|fojc.
> > Dc|h ~ht|fojcs htc utf||c` f` cx h|fi`s hs g? it c.
-8 -8
862 @ ojcht ^bvsfos
Ubc` h ` ojc s cmf|s h dc|h ~htjfojc7 F|s
` ojci` ` mdct s|hvs |bc shmc F|s
~ti|i` ` mdct f`otchscs dv i`c
Ehmmh Lcohv
Ehmmh thvs htc cjco|timhe`c|fo thlfh|fi` cmf||cl atim `s|hdjc ojcf. \bcv c`hdjc`s|hdjc ` ojcf |i jisc crocss c`ctev.
Ubc` h ` ojc s efqcs i | ehmmh thvs |bctc fs `i obh`ec f` cf|bct |bc ~ti|i` it` ojci` ` mdcts.
@ ojcht Cx h|fi`s
\ui fm~it|h`| ~if`|s7
\bc s m ia |bc ` ojci` ` mdcts i` di|b sflcs ia |bc cx h|fi` m s| dc cx hj.
\bc s m ia |bc ~ti|i` ` mdcts i` di|b sflcs m s| hjsi dc cx hj* c.e7
Crhm~jc
441
Th------- 22 %.
444 T`
21
Af`l |bc ~ti|i` h`l ` ojci` ` mdct f` (Ybc aijjiuf`e tcho|fi`s. Ssf`e |bcsc mdcts*s eecs| ubh| chob ~ht|fojc mfeb| dc.
8< "h& @
5
< 85 f + Bc -------- > + R
4 *2 8.
"d& ? ?
B Bc + R 8 4
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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4< <
"o& @h + Bc 88 4
45
Me + R 84
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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H`suct
8 "h& R = h ~ti|i` ~
8
%.* .
@ ojcht ^bvsfos 866
>
"d& R = c it gG f.c. h dc|h ~htjflc -8
"o& R = h ~ti|i` | Z 88%*Z& H|imfo Mhss S`f| " &
I`c h|imfo mhss `f| "8 hm & fs |bc mhss ia 8| j 4|b ia h ohtdi`-84 h|im.
84 I`c h|im ia ohtdi`-84 bhs mhss " Y . 1 >4 R 8>4?&e
Bc`oc 8 = 8
-R 84 84
"1.>4 R 8 >4?&e
= 8 .11 * R 8 >- 45 ke
Cf`s|cf`%s Mhss-C`ctev Cx h|fi`
H mhss* m ke* fs cx fqhjc`| |i h` hmi `| ia c`ctev* C gi jcs* efqc` dv |bc cx h|fi`
C = mo;j *
ubctc o fs |bc qcjiof|v ia jfeb|* f.c. ?.> r 8>2 ms -8
Bc`oc 8 S 77778.11 R 8>;-45 R "? R 8>2&4 = 8.-8> G
Hjsi 8 = 8.-8>
Cjco|ti`fo obhtec
8.-8> = 8.1> R 8>-86
= 6 . ?8 R 8>2 cQ
Bc`oc 8 = 6?8 McQ
Df`lf`e C`ctev h`l Mhss Lcaco|
\bc mhss ia h ` ojc s fs hjuhvs jcss |bh` |bc mhsscs ia f|s oi`s|f| c`| ~ht|fojcs* h`l |bclfaactc`oc f` |bc mhsscs fs ohjjcl |bc mhss lcaco|.
Mhss Lcaco| = Mhss ia oi`s|f| c`| ~ht|fojcs~ti|i`s & Mhss ia ` ojc s "`c |ti`s h`l
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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\bc hdiqc cx h|fi` mhv dc scl fa |bc mhsscs ia |bc cjco|ti`s mhv dc `cejco|cl. Ait mitchoo th|c uitk f| fs `cocsshtv |i |hkc |bcm f`|i hooi `|* h`l |bc cx h|fi` |bc` dcoimcs7
4>> @ ojcht ^bvsfos
Mhss Lcaco| = Mhss ia oi`s|f| c`| ~ht|fojcs - Mhss ia h|im "cjco|ti`s* `c |ti`sh`l ~ti|i`s&
\bfs tcl o|fi` f` mhss fs cx fqhjc`| |i h` hmi `| ia c`ctev ohjjcl |bc df`lf`e c`ctevubfob fs |bc c`ctev tcjchscl ubc` h ` ojc s fs aitmcl atim f|s oi`s|f| c`| ~ht|fojcs. F`itlct |i s~jf| ~ |bc ` ojc s f`|i f|soi`s|f| c`| ~ht|fojcs* |bc df`lf`e c`ctev ui jl`ccl |i dc s ~~jfcl.
\bc cx h|fi` ait h ~issfdjc afssfi` tcho |fi`
4?3 8 S + `
64 %% >
63 8?6 Mi + Jh +
> 5 aG -8
Fa |bc mhsscs ia |bc cjco|ti`s mhv dc `cejco|cl* ohjo jh|c* sf`e |bc aijjiuf`e lh|h* |bcc`ctev tcjchscl ~ct h|im ia afssfi` ait |bc hdiqc tcho|fi`7
Mhss ia ` = 8.>>6 X F
8?6 Jh = 8?2.6>1
35 %
4?3 = 4?3.>4 r 8>4? miG-8
H`suct
\bc cx h|fi` fs lfqflcl f`|i |ui ~ht|s h`l |bc |i|hj mhss i` chob sflc ia |bc cx h|fi`fs ai `l7
4?3
64
Tcho|h`|s
4?3.>6
>
8?6
35 Jh 8?2.6>1
8 4 ` 4.>82
>
4?1.>3? 4?3.2?
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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.. . -7;77.
@ ojcht ^bvsfos 4>8
Mhss lca co | == 4?1.>3? - 4?3.2? = >.44? >.4?? R 8.11 R 8>-45 ke = ?.5> R 8>-42 ke
\bfs oittcs~i`ls |i h` c`ctev* C* efqc` dv7
C = mo4 ?.5> R 8>-42 R "? R 8> 2&7( ?.?? %R 8X-88 g
\bc hdiqc c`ctev fs |bc c`ctev tcjchscl ~c*t S h|im.
4?3.>4 r 8>4? h|ims %:
8 e ia S oi`|hf`s 1.>4 R 8>4?
4?3.>48 h|ims
Bc`oc c`ctev tcjc scl dv 8 e = ?.?? r 8>- 88 r 4.31 r 8>48
= 2.3 R 8>8> G
{XSC_\FI@_ AIT ^THO\FOC 0 %
8. \bc fsi|i~c ia irvec` >-85* bhs h mhss ia 85.>>>262 h`l |bc mhss ia h ~ti|i` fs 8.>>28< * ohjo jh|c |bc df`lf`e c`ctev ia|bc irvec` ojc s f` McQ. "8 = 6?8 McQ &
4. Ohjo fh|c |bc df`lf`e c`ctev ~ct ` ojci` f` |bc bcjf m* Bc* ` ojc s efqc` |bcaijjiuf`e lh|h7
Mhss ia ~ti|i` = 8.>>28< Mhss ia `c |ti` = 8.>>262 Mhss ia bcjf m ` ojc s = >83
"8 = 6?8 McQ &
?. H |bitf m h|im ia mhss 4?4.>?2 lcohvs dv |bc cmfssfi` ia i`c hj~bh ~ht|fojc |ih thlf m h|im ia mhss 442.>?8 . Fa |bc hj~bh ~ht|fojc bhs h mhss ia >? * bium ob c`ctev* f` G*fs tcjchscl l tf`e |bfs ~tiocss9
"8 = 8.11 r 8>-45 ke h`l |bc s~ccl ia jfeb|= ? r 8>2m s-%-8&
Ssc |bc aijjiuf`e lh|h ait vi t ohjo jh|fi`7
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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4>4 @ ojcht ^bvsfos
_~ccl ia jfeb| = ?.> r 8>2m s-8
4 Mhss ia B = ?.?-45 ke
8
? B 3.>>2 R 8>-45 ke 8
< Bc= 1.1-45ke
4
8 ` = 8.153 r 8>-45 ke
>
3. L tf`e h a sfi` tcho|fi`* fsi|i~cs ia bvltiec` "lc |ctf m h`l |tf|f m& a sc|iec|bct |i aitm h bcjf m ` ojc s h`l h `c |ti` hooitlf`e |i |bc aijjiuf`ecx h|fi`7
4 ? B + B
< 8 Bc + `
8 8 4 >
Fa |bc c`ctev tcjchscl ~ct h|im l tf`e |bc a sfi` ~tiocss fs 4.22 r 8>-84 G*ohjo jh|c |bc mhss ia |bc bcjf m ` ojc s ~til ocl f` |bc tcho|fi` sf`e |bcaijjiuf`e lh|h7
4 Mhss ia B ` ojc s %((7777?.?-45 ke
8
? Mhss ia B ` ojc s = 3.>>2 r 8>-45 ke
8
8 Mhss ia ` = 8.153 r 8>-45 ke
>
_~ccl ia jfeb| ?.>> r 8>2m s-8
@-W Ostqc
Jiik h| |bc Afe tc 5.8 ubfob fs h ~ji| ia |bc ` mdct ia `c |ti`s hehf`s| |bc ` mdct ia~ti|i`s ait hjj k`iu` fsi|i~cs7
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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@ ojcht ^bvsfos 4>70
@ mdct ia`c |ti`s
81> 8?- cmf||cts 8
@
84.>
8>>
2>
4.>
>--------- -------- ----------J--------- @ t`dctia > 1>
Afe tc 5.8
2> ~ti|i`s W
_|hdjc ojcf aijjiu h o tqc. H| afts|* jfeb| fsi|i~cs bhqf`e jcss |bh` 4> ~ti|i`s aijjiu|bc s|thfeb| jf`c @ = W* si |bcv bhqc |bc shmc ` mdcts ia ~ti|i`s h`l `c |ti`s.
Hs |bc h|imfo mhss f`otchscs* ait |bc ` ojcf |i dc s|hdjc |bcv `ccl |i bhqc h etch|ct` mdct ia `c |ti`s |bh` ~ti|i`s. Hdiqc |bfs htch* ubc` |bc ` ojcf dcoimc jhtec*|bcft f`s|hdfjf|v f`otchscs h`l |bcv lcohv dv `ceh|fqc dc|h cmfssfi`. \bcsc ojcf bhqc h m ob etch|ct ` mdct ia `c |ti`s h`l si oi`qct| simc ia |bcsc f`|i ~ti|i`s uf|b |bc cmfssfi` ia h `ceh|fqc dc|h ~ht|fojc.
\bc ` ojcf bhqf`e |ii mh`v ~ti|i`s oim~htcl |i `c |ti`s oh` ehf` s|hdfjf|v dv h~ti|i` obh`ef`e f`|i h `c |ti`* uf|b |bc cmfssfi` ia h ~isf|fqcjv-obhtecl dc|h ~ht|fojcohjjcl h ~isf|ti`.
`lf`e C`ctev ~ct @sojci` Ostqc
_f`oc h smhjj ojc s bhs i`jv h smhjj df`lf`e c`ctev oim~htcl |i h jhtec ` ojc s* f`itlct |i oim~htc df`lf`e c`ctefcs ait lfaactc`| ` ojflcs f| fs dcs| |i oim~htc |bcdf`lf`e c`ctev ~ct ` ojci`. \i uitk |bfs qhj c i | uc lfqflc |bc |i|hj df`lf`e c`ctevait |bc ` ojc s dv |bc ` mdct ia ` ojci`s.
Ait mis| ` ojflcs |bc df`lf`e c`ctev fs dc|ucc` 5 h`l 6 McQ ~ct ` ojci` d | simc ia|bc jfeb|ct ` ojcf bhqc df`lf`e c`ctefcs smhjjct |bh` |bcsc qhj cs. \bc s|hdjc ` ojcf htc`cht |bc |i~ Ia |bc eth~b sf`oc |bc etch|ct |bc df`lf`e c`ctev |bc etch|ct |bc c`ctevubfob bhs dcc` jis| f` aitmf`e |bc ` ojc s* h`l |bc jiuct |bc c`ctev ia. |bc ` ojc s*ubfob f` | t mhkcs f| mitc s|hdjc. Afe tc 5.4 sbius |bc df`lf`e c`ctev ~ct ` ojci`o tqc7
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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4M @ ojcht ^bvsfos
fI
Df`lf`e c`ctev ~ct ` ojci` 2
"McQ )` ojci`&
1
<
4
> ---- ---- ---- ---- -----J---- @ mdct ia > 2> 84> 81> 4>> 4 ` ojci`s
Afe tc 5.4
@ ojcht Afssfi`
@ ojcht afssfi` .f`qijqcs h bchqv ` ojc s s~jf||f`e f`|i |ui jfeb|ct ` ojcf uf|b |bc tcjchsc ia h jhtec hmi `| ia c`ctev. Ubc` h S- 4?3 ` ojc s fs f`qijqcl f` afssfi`* hdi | 822 McQ ia c`ctev fs tcjchscl. Mis| ia |bfs c`ctev ~tiqflcs |bc kf`c|fo c`ctev ia |bc
afssfi` athemc`|s h`l |bc t s| ia f| fs efqc` i | hs |bctmhj c`ctev.
Afssfi` ia th`f m fs dti eb| hdi | dv sjiu |bctmhj `c |ti`s dcf`e hdsitdcl dv |bc` ojc s |i aitm h` `s|hdjc S- 4?6 ` ojc s ubfob s~jf|s f` |ui* uf|b |bc tcjchsc ia |uiit |btcc ahs|-miqf`e c |ti`s.
a ojcht A sfi`
A sfi` f`qijqcs |bc gif`f`e |iec|bct ia |ui jfeb| ` ojcf |i aitm h `cu bchqfct ojc s.Ait crhm~jc* |bc fsi|i~cs ia bvltiec` "lc |ctf m h`l |tf|f m& oh` a sc |iec|bct |iaitm bcjf m hooitlf`e |i |bc aijjiuf`e tcho|fi`7
4 ? B + B
< 8 Bc + `
8 8 4 >
I` |bc ~til o|fi` ia i`c bcjf m h|im f` |bfs uhv* hdi | 85.1 McQ ia c`ctev htctcjchscl. Qctv bfeb |cm~cth| tcs htc `cclcl |i ~til oc a sfi`.
T |bctaitl%s Hj~bh-^ht|fojc Lcajco|fi` Cr~ctfmc`|
Cqflc`oc ait |bc crfs|c`oc ia |bc ` ojc s uhs ~tiqflcl dv T |bctaitl%s cr~ctfmc`|ubfob f`qcs|feh|cl |bc soh||ctf`e ia hj~bh ~ht|fojcs dv |bf` eijl aifj.
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@ ojcht ^bvsfos 4is
Crhm~jc
"h& _|h|c |bc tcs j|s ia cr~ctfmc`|s i` |bc soh||ctf`e ia hj~bh ~ht|fojcs dv h |bf` aifj. Cr~jhf` |bc fm~it|h`oc ia |bcsc tcs j|s.
"d& F` s ob cr~ctfmc`|s cr~jhf`7
"f& Ubv |bc aifj sbi jl dc |bf` h`l ~if`| i | h`v lfaactc`ocs f` |bc tcs j|s aitaifjs ia lfaactc`| mh|ctfhjs
"ff& Ubv |bc hj~bh ~ht|fojcs f`oflc`| i` |bc aifj sbi jl dc f` h `httiu ~hthjjcjdchm
"fff& Biu |bc soh||ctcl hj~bh ~ht|fojcs mfeb| dc lc|co|cl
"o& H` hj~bh ~ht|fojc |thqcjs lftco|jv |iuhtls h ` ojc s ubfob mhv dc hss mcl |itcmhf` s|h|fi`htv. Lcsotfdc f` x hjf|h|fqc |ctms biu* l tf`e |bc mi|fi`* |bckf`c|fo c`ctev h`l |bc ~i|c`|fhj c`ctev ia |bc hj~bh ~ht|fojc mhv qhtv uf|b |bcsc~hth|fi` dc|.;qcc` |bc hj~bh ~ht|fojc h`l |bc ` ojc s.
H`suct
Q$ "h& F` |bc cr~ctfmc`| h |bf` dchm ia hj~bh ~ht|fojcs uhs lftco|cl h| h |bf` ~fcoc ia eijl aifj. \bc h~~hth| s uhs cqho h|cl iuf`e |i |bc aho| |bh| hj~bh ~ht|fojcs i`jv bhqc h th`ec ia 3 cm f` hft. \bc hj~bh ~ht|fojcs* ha|ct f`|ctho|f`e uf|b |bc aifj* uctclc|co|cl hs ajhsbcs ia jfeb| i` h sof`|fjjh|fi` lc|co|it ubfob oi jl dc miqcl hti `l i` h | t`|hdjc. Afe tc 5.? sbius |bc htth`ecmc`|7
I";~ht|flcsi toc
eijl aifj *.-sof`|fjjh|fi`
lc|7co|it
Afe tc 5.?
\bc tcs j|s ia |bc cr~ctfmc`| uctc7
Mis| ia |bc hj~bh ~ht|fojcs uc`| s|thfeb| |bti eb |bc aifj uf|b jf||jc it `ilcqfh|fi`.
_imc ia |bc hj~bh ~ht|fojcs uctc soh||ctcl |bti eb h`ejcs ia dc|ucc` 4> h`l 6>.
H acu "hdi | 8 f` 2>>>& uctc lcajco|cl dv mitc |bh` 6>. \bcv uctc|bctcaitc soh||ctcl dhok |iuhtls |bc f`oflc`| dchm.
\bc fm~it|h`oc ia |bcsc tcs j|s fs |bh| |bcv7
_biucl |bh| mis| ia |bc h|im uhs cm~|v s~hoc.
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8
4>1 @ ojcht ^bvsfos
F`lfoh|cl |bh| |bctc uhs h oi`oc`|th|fi` ia mhss h`l ~isf|fqc obhtec h| |bcoc`|tc ia |bc h|im. \bc jhtec h`ejc soh||ctf`e uhs l c Ji cjco|tis|h|fotc~ jsfi` dc|ucc` |bc ~isf|fqcjv-obhtecl hj~bh ~ht|fojc h`l ` ojc s.
\bc hj~bhs ubfob %di `oc% dhok bhqc mc| |bc ` ojc s %bchl-i`%. \bc aho| |bh| |bfsbh~~c`s qctv thtcjv f`lfoh|cs biu smhjj |bc ` ojc s m s| dc.
"d& "f& Hj~bh~ht|fojcs htc hdsitdcl dv h |bf` sbcc| ia ~h~ct. F| fs `cocsshtv ait |bceijl |i dc |bf` si |bc hj~bhs oh` ~hss |bti eb. Lfaactc`| mh|ctfhjs mhv dc
scl d | |bcv sbi jl bhqc h bfeb h|imfo ` mdct "|i f`otchsc |bc obhtec i`|bc ` ojc s& h`l dc hdjc |i dc dch|c` f`|i |bf` sbcc|s.
"ff& @httiu dchms htc scl si |bc soh||ctf`e h`ejc oh` dc mchs tcl hoo th|cjv.
"fff& Ubc` hj~bh ~ht|fojcs bf| h sotcc` oih|cl uf|b wf`o s j~bflc* h ajhsb ia jfeb|
ohjjcl h sof`|fjjh|fi` fs ~til ocl. \bc sof`|fjjh|.fi` lc|co|it fs mi `|cl i` h | t`|hdjc h`l |bc hj~bhs soh||ctcl h| qhtfi s h`ejcs mhv dc lc|co|cl f` h afrclf`|ctqhj.
Hs |bc hj~bh ~ht|fojc h~~tihobcs |bc ` ojc s* f| jiscs kf`c|fo c`ctev iuf`e |i f|bhqf`e |i li uitk hehf`s| |bc tc~ jsfqc aitocs. Kf`c|fo c`ctev fs jis| h`l cjco|tfo~i|c`|fhj c`ctev fs ehf`cl. Fa |bc hj~bh ~ht|fojc h~~tihobcs h eijl ` ojc s bchli`* |bc` |bc hj~bh ~ht|fojc ufjj s|i~ h| |bc lfs|h`oc ia ojiscs| h~~tihob ubctc f|bhs wcti kf`c|fo c`ctev h`l |bc` miqc dhok f` |bc lftco|fi` f| ohmc* `|fj hjj |bcs|itcl ~i|c`|fhj c`ctev fs obh`ecl f`|i kf`c|fo c`ctev.
D. THLFIHO\FQC LCOHV Cr~i`c`|fhj Lcohv
\bc ` mdct ia ` ojcf ia |bc itfef`hj cjcmc`| lcohv cr~i`c`|fhjjv uf|b |fmc hooitlf`e|i |bc eth~b sbiu` f` Afe tc 5.
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@ ojcht ^bvsfos 4>5
_f`oc |bc ` mdct ia ` ojcf tcmhf`f`e fs ~ti~it|fi`hj |i |bc ho|fqf|v* |bc eth~b f` Afe tc 5.3 mhv dc id|hf`cl7
Ho|fqf|v )o~s. F`f|fhj ho|Gqf|v H >
Bhja ia f`f|fhj ho|fqf|v Hi
--4
jfmc)s
Afe tc 5.3
Q Bhja-Jfac) \.8. 4
\bfs fs |bc hqcthec |fmc ait bhja |bc ` ojcf itfef`hjjv ~tcsc`| |i lcohv.
Crhm~jc
H shm~jc ia h oct|hf` thlfiho|fqc ` ojflc bhs h bhja-jfac ia 2.> s. Ubh| fs |bc |fmc* f`scoi`ls* tcx ftcl ait scqc`-cfeb|bs ia |bc shm~jc |i lcohv9
H`suct
Fa 5)2 bhs lcohvcl* |bctc m s| dc 8)2 ia |bc itfef`hj ` ojflc jca|.
Ha|ct 8 bhja-jfac |bctc ufjj dc 8)4 jca|* ha|ct 4 bhja-jfqcs bhja ia h bhja f.c. 8)< h`l ha|ct ? $- - .. %t
bhja-jfqcs |bctc uffj dc bhja ia h x ht|ct* f.c. 8)2 jca|. ? bhja-Gfqc9 = ?* r 2 = -s
Thlfiho|fqc lcohv fs h th`lim ~tiocss h`l f`qijqcs |bc s~i`|h`ci s cmfssfi` ia~ht|fojcs it thvs atim |bc ` ojc s ia |bc h|im.
\bc th|c ia lcohv ia |bc ` oj7;;- " -l @& * it ho|fqf|v* fs ~ti~it|fi`hj |i |bc ` mdct ia
thlfiho|fqc ` ojcf* @* tcmhf`f`e.
q -l@ Bc`oc -.- h7 @ @i|c |bh| |bc mf` s sfe` fs f`|til ocl dcoh sc |bc ho|fqf|v
%l| lcotchscs uf|b |fmc.
F`|til of`e h oi`s|h`| ia ~ti~it|fi`hjf|v* j* ohjjcl |bc lcohv oi`s|h..FG.J |bc cx h|fi`dcoimcs7 ----- - ...
Q -l@ --=j@
l|
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l@ >
v h
4>2 @ ojcht ^bvsfos
l@ -= -j@
ql|
F`|ceth|f`e |bc hdiqc cx h|fi` efqcs7
Ubctc @ = ` mdct ia ` ojcf tcmhf`f`e ha|ct |fmc | @ > = ` mdct ia ` ojcf itfef`hjjv ~tcsc`|
| = |fmc j = lcohv oi`s|h`|
H sfmfjht cx h|fi` |i |bc i`c hdiqc mhv dc utf||c` f` |ctms ia |bc ho|fqf|fcs hs aijjius7
l@ l@ > *
-= -- c - .. l| l| . ubctc l| = itfef`hj ho|fqf|v "f.c. h| | = >&
l @| = . . ho|tqt| a|ct . |tmc |
F| mhv hjsi dc utf||c` f` |ctms ia |bc mhsscs7
t7-7
777=7 $ 8
j.7.7....... ... ... - -----Yg Ubctc m > = itfef`hj mhss h| | = >
m mhss ha|ct |fmc |
Crhm~jc
H thlfiho|fqc si toc lcohvcl |i 8(842|b ia f|s itfef`hj ho|fqf|v ha|ct 3> lhvs. Ubh| fs f|sbhja-jfac9
H`suct
@%
|-Gi
8 --h`l @ = x c-j| 842 -| c
\b s - 8- = c 842
->.16? R 3> \
\hkf`e jiec ia di|b sflcs efqcs7
- .16? R 3> \8
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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= -7t*-=
@ ojcht ^bvsfos 4|f(G
Bc`oc \ = 5.8 ~e ia |bc fsi|i~c uctc ~tcsc`|._biu |bh| |bc hmi `| ia |bfs fsi|i~c bhs dcc` tcl ocl |i h~~tirfmh|cjv ?.3 ~e.
H`suct
>.16? >.16? Lcohv oi`s|h`| 8
42 4
_f`oc |bc ` mdct ia h|ims fs ~ti~it|fi`hj |i |bc mhss* |i uitk i | |bc mhss |bc lcohvaitm jh fs scl7
@ = @> c -j|* ubctc @ > fs |bc ` mdct ia h|ims itfef`hjjv ~tcsc`| h`l @ fs |bc` mdct ia h|ims ~tcsc`| ha|ct |fmc |.
@ = 3 r c->.16? r 8< ) 42 = ?.3 ~e
Crhm~jc 4
\bc oi `| th|c ia h sij |fi` oi`|hf`f`e 8 e ia ohtdi` cr|tho|cl atim h` h`ofc`|lio mc`| fs 5>> ~ct bi t. Ubc` h sfmfjht sij |fi` oi`|hf`f`e 8 e ia ohtdi` cr|tho|clatim h jfqf`e ~jh`| uhs scl*.|bc oi `| th|c uhs 6>> ~ct bi t. Ubh| fs |bc hec ia |bclio mc`| fa |bc bhja-jfac ia ohtdi` fs 335> vchts9
H`suct
Ssf`e |bc cx h|fi` l @| = l@ > c-j|l|
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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48> @ ojcht ^bvsfos
\bctc fs `i `ccl |i obh`ec |bc oi `| th|cs |i s- F sf`oc |bc shmc `f|s h~~cht i` di|bsflcs si |bc oi`qctsfi` aho|its ui jl oh`ocj i |.
^ ||f`e f` |bc ` mdcts efqcs 5>> = 6>> c- >.16GS335>
>.5552 = c- >.16?|(335>
\hkf`e jiec ia di|b sflcs efqcs ->.483? = - >.16?|(335>
_ijqf`e efqcs hec ia lio mc`|* = 85?> vchts
\bc Dcoxsctcj "Dx&
H dcox ctcj fs |bc _j `f| ia thlfiho|fqf|v. F| fs |bc ho|fqf|v ia h thlfi` ojflc lcohvf`e h|h` hqcthec th|c ia i`c s~i`|h`ci s `% ojcht |th`sf|fi` ~ct scoi`l* si7
8 tDx = 8 s -8 "
Dhoketis`l Thlfh|fi`
Dhoketi `l thlfh|fi` fs `h| thj thlfh|fi` ubfob fs hjj hti `l s h`l f| mhv dc mchs tclsf`e h Ecfect-M jjct | dc uf|b `i si toc ~tcsc`|. Ubc` mchs tf`e |bc thlfh|fi`
atim si tocs f| fs `cocsshtv |i |hkc |bc hqcthec dhoketi `l oi `| iqct h 8 >-mf` |c~ctfil h`l |bc` mhkc |bc `cocsshtv hlg s|mc`| |i |bc si toc tchlf`es.
Dhoketi `l thlfh|fi` itfef`h|cs f` h qhtfc|v ia uhvs; simc fs ~tcsc`| f` tioks f` |bceti `l h`l f` d fjlf`e mh|ctfhjs. M ob ia f| oimcs f` |bc aitm ia oismfo thvs atimi |ct s~hoc.
Thlfh|fi` Flc`|fafoh|fi`
) Crhm~jc q%
"h&. Thlfiho|fqc lcohv fs h th`lim ~tiocss f` ubfob |bc |fmc ia lcohv ia h` f`lfqfl hj ` ojc s oh``i| dc ~tclfo|cl. \bc lcohv ia h thlfiho|fqc s ds|h`oc aijjius h`cr~i`c`|fhj jhu uf|b h ucjj-lcaf`cl lcohv oi`s|h`|. Cr~jhf` biu |bcsc |uis|h|cmc`|s htc oi`sfs|c`|.
"d& Vi htc efqc` h smhjj thlfiho|fqc si toc dcjfcqcl |i cmf| |ui lfaactc`| |v~cs iathlfh|fi`. Lcsotfdc |cs|s vi mfeb| ohttv i | |i flc`|fav |bc thlfh|fi`s ~tcsc`|.
"o& \bc fsi|i~c ia dfsm |b ia mhss ` mdct 4>> bhs h bhja-jfac ia 3 r 8>? s. F| cmf|shj~bh ~ht|fojcs uf|b h` c`ctev ia 2.4 r 8>-8? ].
"f& _|h|c |bc mch`f`e ia |bc |ctm bhja-jfac.
Ohjo jh|c ait |bfs fsi|i~c7
"ff& \bc lcohv oi`s|h`|
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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=
@ ojcht ^bvsfos 488
"fff& \bc f`f|fhj ho|fqf|v ia 8.> r 8>- d mijc ia |bc fsi|i~c
"fq& \bc f`f|fhj ~iuct i |~ | ia |bfs x h`|f|v ia |bc fsi|i~c
H`suct
"h& Thlfiho|fqc lcohv fs h 4.t7(4... 4s;;*;;Y *ubfob mch`s f| fs fm~issfdjc |i lc|ctmf`cubc` h ~ht|fo jht ` ojc s ufjj lcohv. Uc oh`* biucqct* cso|fmh|c |bc ~tidhdfjf|v iah ` ojc s lcohvf`e f` h efqc` |fm%c f` |bc shmc uhv |bh| uc oh` cs|fmh|c |bc~tidhdfjf|v ia |btiuf`e h sfr i` h` `dfhscl lfc. \bc ~tidhdfjf|v ia |btiuf`e h sfr"f.c. 8)d|b& i`jv h~~jfcs fa h jhtec shm~jc fs |hkc`. \bc shm~jc ia ` ojcf `itmhjjvdcf`e oi`sflctcl fs jhtec si uc oh` dc ahftjv s tc ia |bc ~tidhdfjf|v.
\bc th|c ia lfsf`|ceth|fi * l@)l|* lc~c`ls i` |bc ` mdct ia `lcohvcl ` ojcf~tcsc`|* @* f.c7
l@ ot7.@
l|
H oi`s|h`|* ohjjcl |bc lcohv oi`s|h`| H.*fs |bc oi`s|h`| ia ~ti~it|fi`hjf|v f` |bfscx h|fi`.
l@ \bc cx h|fi` `iu dcoimcs l| -..j.@
"d& \bc |cs|s mfeb| dc7
\bc dhoketi `l oi `| fs |hkc` uf|b `i si toc ~tcsc`|. \bfs fs s d|tho|clatim s dscx c`| tchlf`es |i id|hf` |bc oittco|cl oi `|s.
\bc si toc fs ~jhocl ojisc |i h E-M | dc h`l |bc oittco|cl oi `| id|hf`cl "Afe tc 5.1&7
:3om
_i toc bijlct Hdsxtic t bijlct
Ecfect- M jjct | dc
Th|c mc tc| it sohjht
Afe tc 5.1
\bf` ohtl fs ~jhocl dc|ucc` |bc si toc h`l E-M | dc. H jhtec tcl o|fi` f`|bc oittco|cl oi `| th|c f`lfoh|cs |bc ~tcsc`oc ia h-~ht|fojcs.
\bc ohtl fs `iu tc~jhocl uf|b hj mf`f m hdi | ? mm |bfok. H jhtec tcl o|fi`f` |bc oi `| th|c f`lfoh|cs |bh| g?uctc cmf||cl.
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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l@
l@
484 @ ojcht ^bvsfos
Fa |bc oi `| th|c fs s|fjj bfebct |bh` |bc itfef`hj dhoketi `l thlfh|fi`* |bc` |bcsi toc m s| dc cmf||f`e v thvs.
"o& "f& Bhja-jfac fs |bc hqcthec |fmc ait |bc ho|fqf|v |i ahjj |i bhja ia f|s itfef`hj qhj c.
>.16? >.16? "ff&. Lcohv oi`s|h`|* j = --=
\8 3 R 8>? 4
= 8.?21 R 8>-< s-8
"fff& Ho|fqf|v0* l| = -j@ ubctc @ fs |bc ` mdct ia thlfiho|fqc h|imsitfef`hjjv ~tcsc`|.
F` 8 mijc |bctc htc 1.>4 r 8>4? h|ims* bc`oc f` 8 r 8>-1 mijcs |bctc htc 1.>4 r 8>4? r 8 r 8>-1 = 1.>4 r 8>85 h|ims.
Bc`oc l| = -7-8.?21 r 8>-< r 1.>4 r 8>85
2.?< r 8>8?s-8
"fq& ^iuct Th|c ia lfsf`|ceth|fi` r C`ctev ia ~ht|fojc tcjchscl
= 2.?< R 8>8? R 2.4 R 8>)
= 12.< uh||s
Lcajco|fi` ia Hj~bh* Dc|h h`l Ehmmh Thlfh|fi`s dv Mhe`c|fo Afcjls
Ajcmf`e%s jca|-bh`l t jc "oiqctcl jh|ct& mhv dc scl |i ~tclfo| |bc lftco|fi`s "Afe tc 5.5&. Tcmcmdct |i sc |bc lftco|fi` ia |bc oi`qc`|fi`hj o ttc`|.
o tv eics |bti eb`lcqfh|cl
Lftco|fi` ia Oi`qcm7fi`cj o ttc`|
afcjl
Aitoc
Ait8oc ) Lf |fi` ia a? Ac|l
Lftco|fi` ia oi`qc`|fi`hj o ttc`|
Afe tc 5.5
Ehmmh thvs* bhqf`e `i obhtec* ~hss |bti eb `lcqfh|cl.
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%. % @ ojcht ^bvsfos 48?
Lcajco|fi` dv Cjco|tfo Afcjls
Hehf`* ehmmh thvs tcmhf` `lcqfh|cl7
a?- ~ht|fojc +
8- % % % i"- ~ht| flc Afe tc 5.2
_ mmhtv ia |bc ^ti~ct|fcs ia Hj~bh* Dc h h`l Ehmmh Thlfh|fi`
h ~ 8%
@h| tc
Obhtec
Mhss
Hdfjf|v |i fi`fscehscs
Hdsit~|fi` "_|i~~cl dv&
Lcajco|fi` f`cjco|tfo afcjls
Lcajco|fi` f`mhe`c|fo afcjls
Oji l Obhmdct
Bc ` ojc s
+4
>> hm
Mclf m
? mm ia HF; 3 m ia hft
\iuhtls + qc
^tclfo|cl dvAjcmf`e%s jca|bh`l t jc ait - qc~ht|fojcs
Cjco|timhe`c|fothlfh|fi`
@i obhtec
@i mhss
Jiu
\bfok jchl
@i lcajco|fi`
@i lcajco|fi`
--- .
\bctc htc |ui |v~cs ia oji l obhmdct d | |bc i`c lcsotfdcl bctc fs |bc LFAAS_FI@\V^C. _cc Afe tc 5.67
8/2/2019 Nuclear Physics Notes For A-Level By Hubbak
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48< @ ojcht ^bvsfos
Acj| tf`e sihkcl f` hoi bif
--------
Djhok dhsc
si toc
3~i`sc |i kcc~ --ltv foc f` oi`|ho|
uf|b dhsc
Afe tc 5.6
F|s i~cth|fi` fs hs aijjius7
Iuf`e |i |bc jiu |cm~cth| tc `cht |bc dhsc* |bc hft f` |bfs tcefi` dcoimcss ~ctsh| th|cl uf|b hjoibij qh~i t.
\bc s ~ctsh| th|cl qh~i t fs hdjc |i oi`lc`sc fa f| oh` af`l simc ~ht|fojcs |ioi`lc`sc i`.
Ubc` |bc thlfh|fi` ~hsscs |bti eb |bc hft* fi`s htc ~til ocl ubfob ~tiqflc sf|csi` ubfob |bc qh~i t oh` oi`lc`sc. \bc |thfj ia fi`s |bctcaitc sbius ~ hs hsctfcs ia smhjj lti~jc|s ia jfx fl.
"h& h-^ht|fojc \thoks
_f`oc h-~ht|fojcs htc jhtec |bcv htc eiil fi`fscts h`l jcss jfkcjv |i dc lcqfh|cl.\bcv ~til oc |bfok* s|thfeb| h`l ucjj lcaf`cl |thoks "Afe tc 5.8> &7
i:-si toc
Afe tc 5.8>
"d& a|-^ht|flc \thoks
8?-~ht|fojcs htc cjco|ti`s h`l iuf`e |i |bcft smhjj sfwc |bcv htc ~iit fi`fscts h`lhtc chsfjv lcqfh|cl. \bc |thoks ~til ocl htc |bf` uhqv jf`cs "Afe tc 5.88 &7
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F
@ ojcht ^bvsfos 483
*!si toc F
-+---i Z j Z --
Afe tc 5.88
"o& v-Thv \thoks
S`jfkc h it 8? ~ht|fojcs* v thvs m s| bf| |bc h|im lftco|jv f` itlct |i fi`fsc f|. \bfsfs qctv `jfkcjv si |bc |thoks htc `i| ojchtjv lcaf`cl "Afe tc 5.84 &7
- -
Thlfifsi|i~c Sscs
Afe tc 5.84
"h& F`l s|tfhj h`l Limcs|fo H~~jfoh|fi`s
Crhm~jc
_|h|c h`l cr~jhf` ubfob ia |bc thlfiho|fqc si tocs "hj~bh* dc|h it ehmmh& ui jldc |bc mis| s f|hdjc ait sc f`7
"f& H limcs|fo smikc lc|co|it
"ff& Crhmf`f`e |bc |bfok`css ia h |bfok s|ccj ohsf`e
"fff& Mi`f|itf`e |bc |bfok`css ia hj mf`f m kf|obc` aifj l tf`e ~til o|fi`
H`suct
"f& \bc si toc ui jl `ccl |i ~til oc thlfh|fi` |bh| ui jl chsfjv dc hdsitdcl dv|bc smikc. Bc`oc |bc `ccl ait h` hj~bh si toc.
"ff& Hj~bh h`l dc|h ui jl dc chsfjv s|i~~cl dv |bc |bfok s|ccj ohsf`e; biucqct*ehmmh thlfh|fi` ui jl |thqcj |bti eb. H`v ajhus f` |bc s|ccj ufjj dc sbiu`
~ hs obh`ecs f` f`|c`sf|v f` |bc ehmmh thvs lc|co|cl dcbf`l |bc s|ccj.
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481 @ ojcht ^bvsfos
"fff& Dc|h ~ht|fojcs htc hdsitdcl dv ? mm ia HF. Ait HF |bf``ct |bh` |bfs |bc` mdct ia dc|hs ~hssf`e |bti eb lcotchscs uf|b |bfok`css. \bfs mhv dc scl|i mi`f|it h`l oi`|tij |bc |bfok`css.
"d& Mclfohj Sscs
Fa h s ds|h`oc fs k`iu` |i ~jhv h ~ht| f` h ~tiocss f` |bc dilv* f| mhv dc ~issfdjc|i f`|til oc f`|i |bc svs|cm h thlfiho|fqc qctsfi` ia |bh| s ds|h`oc ubfob ufjjdcbhqc crho|jv jfkc f|s `i`-thlfiho|fqc oi `|ct~ht|. \bfs mc|bil c`hdjcs h lisc iathlfh|fi` |i dc h~~jfcl ait |bcth~c |fo ~ t~iscs. F` hllf|fi`* uf|b |bc hfl ia |bccmf||cl thlfh|fi`* ~ht|s ia |bc dilv mhv dc s| lfcl ait lfhe`is|fo ~ t~iscs.Thlfiho|fqc |thocts oh` dc scl |i tcqchj f`aitmh|fi` hdi | ~ht|s ia |bc dilv s obhs |bc djiil* tf`c it h` iteh` .
Thlfiho|fqc Cr~ctfmc`| _hac|v
\bc fi`fsf`e caaco| ia thlfh|fi` lhmhecs ocjjs f` |bc dilv h`l oh` jchl |i qhtfi s aitmsia oh`oct. \i ~tcq `| |bfs* |bc aijjiuf`e s|c~s sbi jl dc |hkc` ubc` ~ctaitmf`ethlfiho|fqc cr~ctfmc`|s7
Thlfiho|fqc si tocs sbi jl `cqct dc bh`ljcl uf|b |bc af`ects. Hjuhvs bh`ljcsf`e |i`es.
_i tocs sbi jl `i| dc ~if`|cl |iuhtls vi tscja it h`vi`c cjsc .
O |s i` bh`ls m s| dc oiqctcl h`l bh`ls uhsbcl ha|ct sc. Hj|ct`h|fqcjv* sclfs~ishdjc t ddct ejiqcs.
_i tocs sbi jl dc kc~| f` h jchl-jf`cl dir h`l hjuhvs tc~jhocl f` |bc dir ha|ctsc. \bc ubijc dir sbi jl dc jiokcl shacjv huhv.
_bfcjls ia |bfok jchl-ejhss sbi jl dc scl ubc` sf`e bfeb-ho|fqf|v si tocs .
TCQF_FI@ H@L CRHMF@H\FI@ ^THO\FOC XSC_\FI@_
8. Oi`sflct |bc hj~bh ~ht|fojc* cjco|ti` h`l ~ti|i`. \bc aijjiuf`e oittco|jv ~jhocs|bc ~ht|fojcs f` itlct ia f`otchsf`e mhe`f| lc ia |bc obhtec |i mhss th|fi "X)m&7
H Cjco|ti`* ~ti|i`* hj~bh ~ht|fojc
D Cjco|ti`* hj~bh ~ht|fojc* ~ti|i`O Hj~bh ~ht|fojc* ~ti|i`* cjco|ti`L ^ti|i`* hj~bh ~ht|fojc* cjco|ti`C ^ti|i`* cjco|ti`* hj~bh ~ht|fojc
4?2
4. H ` ojc s ia S lcohvs dv cmfssfi` ia i`c hj~bh ~ht|fojc* 64
aijjiucl dv |bc cmfssfi` ia |ui dc|h ~ht|fojcs. \bc tcs j|f`e ` ojc s aijjiuf`e |bcsc lcohvs bhs h|imfo ` mdct W h`l mhss ` mdct H. Ubfob i`c ia |bcaijjiuf`e sbius |bc oittco| qhj cs ia H h`l W9
*.
{
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@ ojcht ^bvsfos 485
H w H 4?2 22 D 4?< 6> o 4?< 64 L 4?< 22 C 4?> 26
?. F` Ecfect h`l Mhtslc`%s cr~ctfmc`|s |i f`qcs|feh|c |bc `h| tc ia |bc h|im* h qctv|bf` eijl aifj uhs dimdhtlcl uf|b hj~bh ~ht|fojcs. F| uhs ai `l |bh|7
H Hjj hj~bh ~ht|fojcs uctc lcajco|cl atim |bcft itfef`hj ~h|b D @i hj~bh ~ht|fojcs uctc lcajco|cl atim |bcft itfef`hj ~h|b O @i hj~bh ~ht|fojcs uctc lcajco|cl |bti eb h`ejcs etch|ct |bh` h tfeb| h`ejc L H acu hj~bh ~ht|fojcs uctc lcajco|cl |bti eb h`ejcs etch|ct |bh` h tfeb| h`ejc C Mis| hj~bh ~ht|fojcs uctc lcajco|cl |bti eb h`ejcs etch|ct |bh` h tfeb| h`ejc
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F
a 482 @ ojcht ^bvsfos
1. Fsi|i~cs ia h` cjcmc`| bhqc |bc shmc7
8 Obcmfohj ~ti~ct|fcs 4 ^ti|i` mdct ? @ ojci` ` mdct
H`suct7
H fa 8* 4 h`l ? htc hjj oittco|D fa 8 h`l 4 i`jv htc oittco|O fa 4 h`l ? i`jv htc oittco|L fa 8 i`jv fs oittco| C fa ? i`jv fs oittco|
5. H` c`ef`cct ufsbcs |i sc h thlfifsi|i~c |i |thoc h othok f` h ~f~c d tfcl hdi | hmc|tc dcjiu |bc eti `l. Ubfob i`c ia |bc aijjiuf`e fsi|i~cs sbi jl dc obisc`9
Cmfssfi` Bhja-jfac H Hj~bh H acu bi ts D o
Dc|h Dc|h
H acu bi ts . _cqcthj vchts
L Ehmmh H acu bi ts C Ehmmh _cqcthj vchts
2. \bc bhja-jfac ia thlf m-441 fs 81>> vchts. Ubfob ia |bc aijjiuf`e s|h|cmc`|s fs)htcoittco|9
8 \bc lcohv oi`s|h`| fs -< vcht -8 4 \bc atho|fi` ubfob tcmhf`s ha|ct 1> vchts fs 8)81 ? \bc atho|fi` ubfob tcmhf`s ha|ct 2>> vchts fs ?)<
H`suct7
H fa 8 h`l 4 i`jv htc oittco|D fa 4 h`l ? i`jv htc oittco|O fa 8 i`jv fs oittco| L fa ? i`jv fs oittco|
6. \bc bhja-jfac ia h oct|hf` thlfiho|fqc fsi|i~c fs 4 lhvs. \bc f`f|fhj oi `| th|c ia hoct|hf` x h`|f|v ia |bfs fsi|i~c uhs mchs tcl hs 84 >>> oi `|s ~ct mf` |c. \bcoi `| th|c* f` oi `|s ~ct mf` |c* ha|ct 2 lhvs ui jl dc7
H ?>>> D %83>> o 53> L ?53
8>. "h& Lcaf`c |bc lcohv oi`s|h`| ia h thlfiho|fqc mh|ctfhj h`l sbiu biu f| fs tcjh|cl|i |bc bhja-jfac ia |bc mh|ctfhj.
"d& H ehmmh thv cmf||ct* ubfob mhv dc oi`sflctcl |i dc h ~if`| si toc thlfh|f`e`faitmjv f` hjj lftco|fi`s* fs sf| h|cl 3> cm huhv atim h ehmmh thv lc|co|it.
ubfob bhs h` caaco|fqc htch ia 1.> om4. \bc tcoitlcl oi `| th|c h| h efqc`|fmc fs ?4> s -8.
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@ ojcht ^bvsfos 486
"f& Cs|fmh|c h qhj c ait |bc ho|fqf|v ia |bc si toc h| |bfs |fmc.
"ff& Ofqc` |bh| |bc bhjj-jfac fs ?> scoi`ls* ohjo jh|c h qhj c ait |bc ` mdct a thlfiho|fqc h|ims ~tcsc`| f` |bc shm~jc 84> scoi`ls dcaitc |bc mchs tcmc`|uhs mhlc .
.88. \bc thlfiho|fqc lcohv th|c l@)l| ait h s~cofmc` ubfob oi`|hf`s @ h|ims ia h thlfiho|fqc fsi|i~c fs cjh|cl |i |bc lcohv oi`s|h`| *jhs aijjius7
l@ = -*|@
l|
\bc lcohv th|c ait h shm~jc ia thli` ehs h| h ~ht|fo jht f`s|h`| fs ai `l |i ic 5.< r 8>? Dx "f.c. 5.< r 8>? lfsf`|ceth|fi`s -~ct scoi`l&. \bc lcohv oi`s|h`| |itthli` fs 84.1 r 8>-? s-8.
"h& Cr~jhf` ubh| vi `lcts|h`l dv |bc lcsotf~|fi` ia thlfiho|fqc lcohv hs hth`lim ~tiocss.
%
"d& Ohjo jh|c h qhj c ait |bc ` mdct ia thli` h|ims ~tcsc`| h| |bc ~ht|fo jhtf`s|h`|.
"o& Ubv fs f| ~issfdjc ait |bc qhj c ia @ ohjo jh|cl f` "d& |i lfaact atim |bc ho| hjqhj c h| |bh| f`s|h`| cqc` uf|bi | cttit f` |bc lh|h9
"l& Lcaf`c |bc |ctm bhja-jfac h`l ohjo jh|c h qhj c ait |bc bhja-jfac ia thli`.
"c& \bc c`ctev tcjchscl f` |bc lcohv ia i`c thli` ` ojc s fs 1.? McQ ubctc 8 McQ cx hjs 8.1 r 8>-8? g. Af`l |bc th|c ia c`ctev tcjchsc ait |bc thli` shm~jc hdiqc.
84. H| |bc s|ht| ia h` cr~ctfmc`| h mfr| tc ia thlfiho|fqc mh|ctfhj oi`|hf`s 4>.> ]je ia hthlfifsi|i~c H*ubfob bhs h bhja-jfac ia 5> s* h`l .> ~e ia thlfifsi|i~c D*ubfobbhs h bhja-jfac ia ?3 s.
"h& Ha|ct ubh| ~ctfil ia |fmc ufjj |bc mfr| tc oi`|hf` cx hj mhsscs ia chobfsi|i~c9 Ubh| fs |bc mhss ia chob fsi|i~c h| |bfs |fmc9
"d& Ohjo jh|c |bc th|c h| ubfob |bc h|ims ia fsi|i~c H htc lcohvf`e ubc` |bcmhsscs htc |bc shmc.
"Mijht mhss ia fsi|i~c H = 4?< e Hqiehlti oi`s|h`| = 1.> r 8>4? mij-8&
8?. "h& "f& Utf|c liu` h` cx h|fi` cr~tcssf`e |bc jhu ia thlfiho|fqc lfsf`|ceth|fi`s*lcaf`f`e hjj svmdijs scl.
"ff& Cr~jhf` biu |bc cr~tcssfi` fs h oi`scx c`oc ia |bc th`lim `h| tc iathlfiho|fqc lcohv.
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..
"d& \bc eth~b f` Afe tc 5.8< sbius |bc oi `| th|c l c |i |bc lfsf`|ceth|fi` ia |bcohtdi`-8< f` 8 e ia ohtdi` |hkc` atim lchl ~jh`| mh|ctfhj ~ji||cl hehf`s| |bc hec ia |bc mh|ctfhj7
83
....F.sC ja G F
ff t.
o7 778 >
.X ...G . a( $o$7%G$% " 77j > ".&
> 4>>> ciii 8>>>> 84.>>> Hec "vchts &
Afe tc 5.8<
"f& Id|hf` h qhj c ait |bc lcohv oi`s|h`| ia |bc fsi|i~c.
"ff& >.4> e ia ohtdi`-8< id|hf`cl atim h` h`ofc`| dih| ehqc h oi `| th|c ia 8.6 oi `|s ~ct mf` |c. Cs|fmh|c |bc hec ia |bc dih|.
84bi ts h`l lcohvs dv |bc cmfssfi` ia h ehmmh thv |i ~til oc h mitc s|hdjcqctsfi` ia |bc shmc fsi|i~c.
F` i`c ohsc |bc ~h|fc`| suhjjius h x h`|f|v ia hjmis| ~ tc \o-66m uf|b h` ho|fqf|via?.5 r 8>Ds-8.
"h& Cr~jhf` biu |bc cmfssfi` ia h ehmmh thv oh` jchl |i |bc ~til o|fi` ia h
mitc s|hdjc fsi|i~c.
"d& Ohjo jh|c |bc lcohv oi`s|h`| ait \o-66m h`l lc|ctmf`c |bc ` mdct ia \o-66mh|ims ~tcsc`| f` |bc mh|ctfhj efqc` |i |bc ~h|fc`|.
"o& Lfso ss |bc hlqh`|hec ia sf`e h ehmmh cmf||ct th|bct |bh` h` hj~bh cmf||ctit h dc|h cmf||ct ait |bfs ~ t~isc.
83. F` i`c thlfiho|fqc sctfcs |bc aijjiuf`e lcohv ~tiocsscs ioo t7
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--*
@ ojcht ^bvsfos 44> @ ojcht ^bvsfos 448
4?2
4?< \b
4?<
^h 64 68
"h& @hmc |bc lcohv ~tiocsscs ioo ttf`e f` "f& th`f m* "ff&|bitf m.
"d& Lfso ss ubc|bct mhss fs oi`sctqcl f` |bcsc ~tiocsscs.
81. Afe tc 5.83 sbius skc|obcs ia oji l obhmdct |thoks ~til ocl ubc` hj~bh ~ht|fojcsia |bc shmc c`ctev |thqcjjf`e atim jca| |i tfeb| htc soh||ctcl dv h|ims ia ehs f` |uioji l obhmdcts R h`l V. \bc soh||ctf`e fs |bc tcs j| ia cjhs|fo oijjfsfi`s. I`cobhmdct fs k`iu` |i oi`|hf` i`jv bcjf m h`l |bc i|bct i`jv `f|tiec`.
Y*)
F Oji l obhmdct R Oji l obhmdct V Afe tc 5.83
"h& "f& Ubfob obhmdct oi`|hf`s |bc `f|tiec`9 Cr~jhf` vi t tchsi`f`e.
"ff& Lthu h lfhethm |i sbiu |bc ~h|b ia |bc hj~bh ~ht|fojc hs f| h~~tihobcsh`l fs lcajco|cl dv |bc ` ojc s ia |bc h|im ia `f|tiec`.
"fff& Lthu i` |bc shmc lfhethm |bc ~h|b aijjiucl dv h` hj~bh ~ht|fojc ubfobfs lcajco|cl |bti eb h smhjjct h`ejc.
"d& "f& _|h|c |bc i |oimc ia h bchl-i` oijjfsfi` ia h` hj~bh ~ht|fojc uf|b hbcjf m ` ojc s ubfob fs f`f|fhjjv h| tcs|.
"ff& Ubh| ui jl dc |bc i |oimc ia h bchl-i` oijjfsfi` fa h ~ti|i` uctcf`qijqcl f`s|chl ia |bc hj~bh ~ht|fojc9 "@i ohjo jh|fi` fs tcx ftcl.&
H@_UCT_ \I XSC_\FI@_ AIT ^THO\FOC 8. \bc >-85 ` ojc s oi`|hf`s 2 ~ti|i`s h`l 6 `c |ti`s.
Mhss lcaco| Mhss ia oi`s|f| c`| ~ht|fojcs - Mhss ia h|im
"2 R 8.>>28< + 6 R 8.>>262& - 85.>>.8.8
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4. Mhss lcaco| = Mhss ia oi`s|f| c`| ~ht|fojcs - Mhss ia h|im
= "4 R 8.>>28< + 4 R 8.>>262& - >83>
=
>.>?54<
>.>?45< R 6?8 R 8>1 cQ = ?.>5 cQ
Df`lf`e c`ctev ~ct ` ojci`
Df`lf`e c`ctev ait ` ojc s it h|im = @ mdct ia ` ojci`s
?.>5 =
< = 5.14 R 8>1 cQ = 5.14 McQ
?. \bitf m = Thlf m + Hj~bh ~ht|fojc 4?4.>?2 = 442.>?8 + >?
+ C`ctev + C`ctev
Bc`oc C`ctev = >.>><
= >.>>< R 8.11 R 8>-45 R "? R 8>2&4 G
= 3.62 R 8>-8? G
-45&
= ?.8 R 8>-46 ke
@iu C = mo4 ubctc o fs |bc s~ccl ia jfeb|
= ?.8 R 8>-46 R "? R 8>2&4
= 4.56 R 8>-84 G
3.. _7`oc C == mo4
C = Mhss lcaco| f` ke r o4
4.22 r 8>-84 = Mhss lcaco| f` ke r "? r 8 >2&4
Efqf`e mhss lcaco| f` ke 4.22 R 8>-84
= "? R 8>2&4 = ?.4 R 8X-46 ke
Mhss lcaco| = "?.?-45 + 3.>>2 r 8>-45& - "8.153 r 8>-45 + M&
ubctc M fs |bc mhss ia |bc bcjf m ` ojc s
% Z Cx hjf`e h`l s i jqf` e ef qc s m h ss i a b|jf m ` ojc s7 Z M = 1.1-45 ke
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@ ojcht ^bvsfos 444
>
@ ojcht ^bvsfos 44?
Cx hjf`e h`l sijqf`e efqcs mhss a bcjf m ` ojc s7
M = 1.1-45 ke
H@_UCT_ \I TCQF_FI@ H@L CRHMF@H\FI@ ^THO\FOCXSC_\FI@_
8. H`suct= H
4. H`suct = o
?. H`suct= [&
> = -< vcht-(
. . "8&< 8 1> vchts fs < bhja-jfqcs. Atho|fi` tcmhf`f`e ufjj dc 4 = 81
H`suct= H
6. 2 lhvs fs < bhja-jfqcs* si |bc ho|fqf|v ia |bc si toc ufjj bhjqc ai t |fmcs* f.c.
84 >>> |i 1 >>> |i ? >>> |i 83>>
H`suct= D
8>. "h& _cc |cr|.
"d& "f& Tcact |i Afe tc 5.817
Afe tc 5.81
\bc si toc sc`ls i | thlfh|fi` iqct h s~bctc ia htch
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-*=;--
>.16?
44< @ ojcht ^bvsfos
Htch ia s~bctc < r ` r ">.3&4 = ` mj Htch ia lc|co|it = s omj = 1 r 8>-< t`J
` Bc`oc* htch ia s~bctc fs ----- = 34Gb |f`us FGtect |bh` |bc
"E R 8>- = 8.12 r 8 "&1 s- F
Bc`oc* ho|fqf|v ia si toc = 8.12 r 8>1 s -8
>.16? >.16? "ff& Lcohv oi`s|h`|* j = = ---7?"&= >.>4 8$8 s- F
4
$ _f`oc ho|fqf|v cr7 ` * dct ia ` ojcf* @ uc oh` utf|c7
H = H> c-.j| ub tc H fs |bc ho|fqf|v ubc` mchs tcmc`| uhs mhlch`l H > fs |bc ho|jZ"f|v 84> s dcaitc |bc mchs tcmc`| uhs mhlc.
8.12 R 8>1 = H > c...7.% ->4?8R 84>
Efqf`e Hi = 4.16 R \>5 l@
= -j@ l|
4.16 R 8>5 = ->.>4?8 @
Efqf`e ` mdct ia ` ojcf* @ = 8.81 r 8>6
88. "h& _cc |cr|.
l@ "d&
l|
" = -j@
5.< R 8>? = -84.1 R 8>-? @
Efqf`e mdct ia ` ojcf* @ = 3.25 r 8>3
"o& _cc |cr|.
"l& Lcohv oi`s|h`|* = --7t*- -w
84.1 R 8>-? = >.16?
\8. 4
16?
Efqf`e b hFa -F fa c* \ = -
>
- -Y -
-Y-
= 33s
-r- 84 1 8> ?
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@ ojcht ^bvsfos 443
l@ "c&
l| 5.< r 8 "&? s -8 h`l l tf`e chob lfsf`|ceth|fi`
1.? r 8.1 r 8>- 8? Gia c`ctev htc tcjchscl.Bc`oc th|c ia c`ctev tcjchsc
5.< R 8>? R 1.? R 8.1 R 8>-S
5.-6 U
84. "h& jH --= I.II:G:G s-8 5>
jD = >.16?
= >.>$862s- F ?3
Ssf`e m = m > c-j| ait shm~jc H efqcs
t`H = 4> r 8>-d c->.>>66| h`l* ait shm~jc D*
ms = r 8>-1 c-I.Ij62|
Ha|ct h oct|hf` |fmc |bc mhsscs ufjj dc cx hj h`l t`H = me7
4> r 8>-1 c->.>>66| = r 8>-1 c-I.(tj62|
_ijqf`e dv |hkf`e jiec ia di|b sflcs efqcs7
| =5>s
Mhss ia chob fsi|i~c ha|ct 5> s = 4> r 8>-1 c- i.|G>66 r 5i
= 8> R 8>-d e = 8>~e
"d& l@ -= -j| l|
= ->.>>66 R 8> R 8>-1 R
= -4.3 r 8>8< s-8
1 R 8>4?
4?<
Th|c ia lcohv ia H ubc` mhsscs htc |bc shmc
= 4.3 r 8>8< 3 -8
8?. "h& "f& _cc |cr|.
"ff& _cc |cr|.
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4
>.16? >.16?
4
.
441 @ ojcht ^bvsfos
"d& "f& Atim |bc eth~b* bhja-jfac 3>>> vchts.
>.16? Lcohv oi`s|h`|* .j = = 8.?21 R
\-%$ 8>-< vcht- 8
8.?21 R 8>-<
= "?13 R 4< R 1> R 1>& = -84 s
"ff& >.4 e ia ohtdi` efqcs af`hj oi `| th|c ia 8.6 o~m h`l 8.> e efqcs 6.3 o~m. Bc`oc* atim |bc eth~b |bc h~~tirfmh|c hec = >> vchts.
8