UNIT # 12 (PART - I)

Transcription

1 JEE-Pysics od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 MODER PHYSICS (tomic ad ucla pysics) EXERCISE I c 6V c. V c. P(D) t /. T, T B ; T +B 6. so, fist alf livs (by ) xt alf livs (by B) xt tus alf livs (by +B) 8 ( Total igt alf livs) dp (P si ) F F t F psi [ umb of poto] () si 7. I poto lctic ffct t maximum vlocity of will cospodig to KE max & ot a lss ta it. 5. KE max 6. Fo tsold fqucy, KE max ( ) Isatuatio w I K 7. K max V s max K.5 K.5.5 V volts.5 98 Å V S. E k. K.E. max. fqucy of ligt dpds o poptis of catod UIT # (PRT - I) I 6. itsity bcoms t v v 5 v 8 ms 6 M 7. M M t t M t 8. () T / t t 6. days c mv ; () () T / c mv mv mv mv mv v v 9. (a) P c. K K (b) c c. (c) i c c K < K. Gat wok fuctio gat itcpt t. D bogli wavs a idp of sap & siz of t objct.. D bogli wavs a pobability wavs ad a applicabl fo all t objcts. Wav atu is obsvd fo t small paticls lik lctos.. K.E. qv p m K p ; q q q & V is sam m K m m

2 JEE-Pysics 5. (so sam) p 6. ; mk K kt 5.5 Å mkt T m kt 7. Maximum poto gy.6 V (mittd) So K max V Hc stoppig pottial is 9.6 V So V ca stop 8. R(Z ) Fo K li,, R( ) R...(i) ad R(9 ) R 8...(ii) 9 9 Dividig q. (i) by (ii), w gt 8. o. of lcto tat ca accommodat i t sll Total umb of lmts () + () + () + () 6.6V 9. E. V. E E Z E E Z E E Z 7 Z 9 6 Z Z 6 6. E max fo to 9. R(Z ) Fo wavlgt of K, to 875 R R (Z )...(i) 675 R ad R[Z B ]...(ii) By solvig q. (i) & (ii) w gt Z 6 ad Z B [Fou lmts li btw ts two]. mi V so 6. mi.6 Å. Caactistic X ays cospods to t tasitio of lctos fom o sll to aot.. x ( ). Q 7(5.6) + [(7.6)] Q 7. MV 7. Wav umb.97 ow i sis limit cospods to to Wav umb fo sis limit E.6 +.6() 79. V. C 5 C 5. () c V m 6. E 59 kv.m 7. Hig atomic o. ad ig mltig poit. 5. H p BE [( ).5] 9.5 MV 6. Duto H Q BE of poduct BE of actat [8 MV (. MV)] [8.].6 MV 7. K Q 8. p 8 5 t t 9. [ ] 5. 9 days alf livs, lft i...5% 8 Disitgatd % od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 9

3 JEE-Pysics 5. t t () () t t T / t days 5. 6% o aly / m 5. R M w. () L EXERCISE II (B) E c Z (C) v (D) K 7. R,. (a) o c c c.6z U c c c c.6.6z K max.v ;.7 V E V to..vå 7. Stoppig pottial fqucy wav lgt Satuatio cut at of potolcto missio. lso, K.E. max, P 8. () mt () B () T B T.5 V () B mke mt 9. K max V.5V K max.7v at catod K max (.7 + ) V at aod If polaity is vd, o ac at collcto.. t T / log T / T ma. ssumig to b + 69 E D C B B od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65. K.6. V U 7..V L k U k mv 5. U ; F mv k ; m v m (costat), lso V U m k m, K.E. mv 6 m 6 U, m t total gy T.E. U K.E. m m t t : t tim t : t Dcayd i tim t ( ) ( t ) Pobability tat a adioactiv ucli dos ot dcay i t to t : t t. dd quatio H H + p + () Q[ [m ( H )+m(p)+m()]+m( H )] 9 MV (B) 6 W Q t. is balacd bot i mass umb & atomic o. ( ) 5. + V s ; V s ; V s H fqucy of ici ligt ad poptis of mitt c 6. E Fo scod xcitd stat to fist xcitd stat E c c 5 9 6

4 JEE-Pysics Fo fist xcitd stat to goud xcitd stat c c E E 5 E c 7 () E 7 (B) E c 5 (C) P P 5 P 7 7. P.E. (K.E.) T.E. (P.E.) + (K.E.) T.E. (K.E.) + (K.E.) T.E. (K.E.) T.E. K.E. K.E.. V 6.6 m.6z 8.. Z; 9.8. So a lcto of KE 9.8V ca tasf its gy to tis atom. 9. Room tmpatu Upo absoptio xcitatios tak plac to may ig stats wic upo d-xcitatio mit all U.V., ifad ad visibl ligt.. Room tmpatu so lyma sis 6. mi V if V t ( mi ) 7. o. of collisio p lcto icas t itsity icass Z BE/ 8..7, t ( t ) Dcayd amout 9. P (.7) (.6) (.6) log T / ya c, P b c b 6% if P P b Sic > b > b b 7.V.6V. U C k.6v E C E.6V m i ts qustios C + 7. V. W av, ducd mass Kq mv mv ; mv. K >. V fo ilastic collisio. dcay : H, so bot Z & dcass. dcay : +, so will ot cag but Z will cag (dcass) dcay :, so will ot cag but Z will cag (icass) dcay : o cag i & Z. 5. V V mi volt. volt kv. (a) P c (b) i (c) % %. W av wok is do by oly lctic fild. Tus if E v, v dcass, & tus momtum of lcto dcass & vic vsa, wil i magtic fild v mais costat.. Fo lcto db 5 Å 5. I poto lctic ffct oly o to o Itactio.. t, ' t t 5. V 9 c, 9 t c V, V if V V + V amoic pogssio od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 9

5 JEE-Pysics od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p V V V V S 6V V V S V 7. J ( ) So J ( ) 8. E E.6 (Z ).6.6 Z () Z E E.6 Z Z.6.6 Z Z E E.6 Z.6 Z E E.6 (.) (E )(E ) (.6) Z Z (.) (E E ) (E E ) (E )(E ) (.6) Z (E )(E ) Z 9. C 5; t 5 obits a ivolvd upo comig to scod xcitd stat so t xcitd stat is 6 t [ d, d, t, 5 t, 6 t ]. O comig fom gy is gat ta, lss ta o qual to gy cospodig to. V V V a 6 a 8. T f Ti T 7 m m. o of spctal lis ( ) 5; E ; c E 95m c. (a) E.6 mv 5 (b) mv 5. Excitatio upto is quid so tat visibl lgt is mittd upo d-xcitatio. 6. So quid gy.6 9.V T T 8 7. t xcitd stat ( ) C 8. Z L ;.5 ; f Z (f L) Z Costat fo all obits. 9. K K & K, K a typ of atom. 5. Egy lasd (BE) poduct (BE) actat t 5. t, (t t ) T t t 5. Radioactivity law is valid fo lag sampls T 5. T ; R ; R ( ) T log log ; T ( ) (R R )T (log ) ( ) (R R )T 5. Fial poduct stat (R R ) d 5 5. t t 9

6 JEE-Pysics Matc t colum EXERCISE III. v,ke, J, v but ad v. Fo giv atomic umb, gy ad c fqucy of K sis is mo ta L sis. I o sis also li as mo gy o fqucy compad to tat of li.. Cosid two quatios V s mv max v...(i) o. of potolctos jctd/sc Itsity...(ii) () s fqucy is icasd kpig itsity costat. V s will icass, m(v ) will icas. max (B) s fqucy is icasd ad itsity is dcasd. V s will icas, m(v ) will icas ad max satuatio cut will dcas. (C) Its wok fuctio is icasd poto missio may stop. (D) If itsity is icasd ad fqucy is dcasd. Satuatio cut will icas.. () I alf lif activ sampl duc R Compsi o. Fo Balm sis, (low) ;, (ig) I tasitio (VI), Poto of Balm sis is absobd.. I tasitio II : E. V, E.85 V E.55 V; E c c 87 m. E. Wavlgt of adiatio m Å E Å.V So diffc of gy sould b. V (appox) Hc ad (.6)V (.5)V Tasitio is V.. Fo logst wavlgt, gy diffc sould b miimum.so i visibl potio of ydog atom, miimum gy is i tasitio VI & IV. Compsi o. i qf. M u v v v. v v v v M t M u M d M d 6 6. t magtic momt i tat cas will b zo. Compsi o. Q CV d V Dcay umb of ucli is (B) t w dcay costat, t/ t/ (C) R () t / t / T () / / Equivalt sistac. V R 6V 6 I 8 6 c P w umb of potos ici p uit tim. lso I Ic P 6 8 ( )(6.6 )( ) 6 9 ( )(.6 ) od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 9

7 JEE-Pysics m Å 687 Å.6.6 Wic cam i t ag of oag ligt.. Stoppig pottial V S 8V ad KE V S KE 8V Compsi o. Rat of poductio of B dpds o t dcayig d at () : B is dcayig simultaously wit two ats d B B d B B umb of ucli of 'B' is. B will icas w > ( + ) as iitially > +., as bot will dcay compltly : tfo B is icoct EXERCISE IV(). umb of potos fallig/s [fo poit souc].(i) Fo mtal tsold wavlgt is (ii) (iii). m o 5 m 5Å Fo mtal tsold wavlgt is.5 m o m Å c o : : 5 Mtal bcaus lis i visibl wavlgt ag. c. W av V, V Fom gap, V V lso slops of t gap J / sc 5 5. Maximum kitic gy of poto lctos K max mv max c ow lt Å t 6Å c v max 9 c v max 8 7c V od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 So fo w distac ' 9 Is 8m Is m 9 9 lso satuatd cut V d is idp of. 8. (i) V S.6V (ii) I s.6. E.7575V m E 5.66V Lt wok fuctio b V (.7575 ), V (5.66 ) V.87 V 6. KE max, lso E poto/tim c (i) W itsity of ligt is dcasd umb of potos dcass but KE max mais sam (ii) W mittig sufac is cagd, cags. So KE max cags. If mitt is cagd t +v o. of potolctos bcoms zo. (iii) Icasig, c 7. Egy ici / aa of sp / sc Egy ici o atom. Egy of o poto c J.55V 95

8 JEE-Pysics o. of poto stikig atom/sc o. of potos/ aa c c E w E' E,' c E E So w wavlgt Sic % 8. d bogli v u + at 8 mk mv E d t m Et Et 9. Fom t figu it is cla tat (P+). /.5 Å / (.5.)Å.5 Å o Å m. d Bogli wavlgt is giv by p Km K kitic gy of lcto (6.6 ) m (9. )( ) 7 K.5 J V 5.8 V.(i) Kitic gy of lcto i t obits of ydog ad ydog lik atoms Total gy Kitic gy. V (ii) T d Bogli wavlgt is giv by P Km K kitic gy of lcto Substitutig t valus, w av. Fom t giv coditios :. ad E E (.+7)V7.V E E ( ) V. V Equatio () () givs E E 7. V o Z (.6) 9 7. Z (.6) (5/6) 7. Z 9 Z Fom quatio () Z (.6) 7. () (.6) 7.. / R R B B 7R R 9 6 p 7 : 6 ; B p 5. ssumig Bo's modl to b applicabl to t H atom too; Egy of lcto.6 V 5. V iitial gy of lcto Egy of poto mittd 5 V c.8mm E (6.6 J s) 9 (..6 J)(9. kg) 6.6 m o 6.6 Å. (i) Magtic momt I m Poducd is t obit (ii) fo ydog Magtic momt M B m B si B 8m m (i)opatig voltag kv,.5% gy fo x ay 99.5 V (ii) Vlocity of ici mv V v V.6 m m/s 9 od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

9 JEE-Pysics 7. Giv K 7 pm 7 Å E K E L c V Å 7Å K 7. 6 kv Tus E L E K 7 6 kv kv 7 6 kv 5 86 kv 8. Total mass aiilatd m MV c Total gy poducdmc MV c c Egy of poto.5 MV 9. H H H Q c..pm E.5 MV Q [ 7.] MV.6 MV. mi c V Å V t kv : mi. Å Wavlgt of K is idp of applid pottial. Fo K X ay : c.6 Z E K. ow at t/ tim, activ factio ( t ) / (.6)½.8 So dcayd factio i t/ tim is o % U T H m ( ) u E mc.76 MV If it mits poto spotaously, t quatio is ot balacd i tms of atoms & mass umb. U Pa H m ( )u.65 u m is gativ, so actio is ot spotaous. 5. Lt at t, capacito stats discagig t at tim t, activity of adioactiv sampl R R t cag o capacito Q Q t/rc ow R Q R Q t t RC R Q It is idp of tim if R C t avg C t Rc 6 RC j od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 K 6 Z Å b K mi g ad giv tat 6 bz g. Z 6 8 Z 6 Z 7.9. t ad t t t t t t, fo. ctivity of x ctivity of y o x x y y L M. 69 x ( T ) x y / x ( T ) ( T ) O Q P y x y L M. 69 ( T ) / y O QP 7 9. ft t tim activ factio 6 6 t ] 97. f/ EXERCISE IV(B) f/ Pottial at wic lcto stop comig out f f f fom sp, V f f f fom sp, V ft coctio (i) V + V V + V (V fial commo pottial) V f f (ii) Fo sp : 7f V kq f 7f f R Q fr o. of lctos flows k

10 JEE-Pysics. Pow of souc J/sc Egy of poto c.67v 6 o. of potos mittd /sc o. of potos stikig o sp of.6 m / m o. of potos passig toug aptu potos o. of potos ici / aa o sc (assumig aptu to act as a scoday poit souc) 6. poto flux 5..6 potos / m sc o. of potos ici o cto /sc.6.5 Poto cut.6 W t ls of f.6 m is usd, v.m v u f v. Tus imag will b at. m fom t ls i t dictio opposit to t sc. Distac btw sc & imag 5.7 m o. of potos stikig ls o. of potos stikig t aptu.5 6 potos. Potos tasmittd toug t ls poto/s Tis w situatio, poit souc mittig.8 6 potos/ sc of 6Å is kpt at 5.7 m away fom t sc. Tus potos stikig / aa of sc poto/sc.57 Elctos mittd.9.57 Cut.8 E p.67 V ; V K.E. max.67 V; V S.67 V.5 c. Egy of poto wit Å.V c Egy of poto wit 65Å 7.5V 98. Pow of souc 5 W fo W Cut % Cut. lso v max 65 V max 5 KE KE max 65 max 5 (. ) (7.5 ) c.v t 6Å E c V.V c V.8V 5 c V.6V 6 Ligt avig wavlgt 6 Å will ot b abl to jct lctos. Poto cut ( ) w o. of potos of ligt ici avig wavlgt Å o. of potos of ligt ici avig wavlgt 5Å. H c c c I a itcptd cm m Poto cut ( ) ( )(5 ) Momtum of paticls & Sic paticls a iical, mass of bot paticls a sam. od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

11 JEE-Pysics mv & mv ; v v v ˆ ˆ COM i j v v v i j v v v v COM ˆ ˆ COM COM mv m v v mv mv 6. (i) E 7..6 Z 9 Z 5 (iii) 8.(i) (ii) k k.v. 9 J E max.5 V E mi.7 V mv mv E total 8 de P (loss of gy p sc) d P 8 t d 8 P 8 d P od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 (ii) E V 6.5 V 9 6 (iii) E.6 Z V c V.6 5V 6.Å (iv) (KE) st obit mv 9. (. 5) 9.6 (PE) st obit KE 688V 6 L ().5 (v) Radius (R ) z 5 V.6 m 7. Lt o. of lvl of xcitd stat C 6 (spctal lis) (d xcitd stats) o. of xcitd stat lvl +.7V (Lvl B) (Lvl ) (i) Picipal quatum o. of iitially xcitd lvl B (ii).7 k 6 6 k.7.v Ioisatio gy (iii) 9.(i) 6P ( )t c t Fo, (to collaps ad fall ito uclus) c t / t 8 sc c 9 8 mv mv ad m m Z m (iii) E t.6 E.6 8V. Lt t ag of Eat b t ya ad iitially bot w pst as ; u 8 t / t / t /.5 u 5 8 t /. u8 u 5 9 t.8 t yas. X B o. of uclus disitgatd xt t x 99

12 JEE-Pysics Fo t x x Disitgatio Egy lasd E x Egy utilizd fo mltig Mass of ic mltd E x L F E x.5. D T + P Mass dfct M M Poduct M Ractat m. amu ad amu 9.5 E mc. MV T D H m(mass dfct) M poduct M Ractat [ ] [.69+.] [ ] m.888 E m(9.5) 7.58 MV E duto E total T otal E gy T otal M ass 7.MV m m D (.).8%. (Tak a sampl of Cm atoms) dcay 96 Cm 8 96 Pu + H H m ( ) u.557 u E mc MV Egy lasd i t dcay of o atom E E fissio + E MV Total gy lasd fom t dcay of all atoms.75 MV.6 8 J Pow output Total gy lasd ma lif watts. Lt t amout of R b x 7.6 ucli lft aft 7.6 day Dcay costat.69 t.8 6 /. 6 sc /sc ctivity o. of paticls o. of utos poducd ucli.5 6 g 5. M t Tus momtum of tis mass Mv, v vlcity of mass at tim t M t v Lt at tim, dfct mass is jctd wit lativ vlocity v v jct/gam v + v Lia momtum of M at tim (t+) (M dm) (v+dv) + dm(v v ) Sic f xt (M dm) (v+dv) + dm (v v ) Mv (M dm) dv dmv v dm dv dm v v dv M dm M dm M M v v M t But M t M t ; M v v v t t M 6. Poductio of adioactiv ucli /sc Disitgatio d t ay tim t t d t t ucli disitgatd t t Egy usd i wat atig Total gy poducd E t t t.e t ms T.E t / T ms t od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

13 JEE-Pysics EXERCISE V() TOMIC STRUCTURE & X- RY. Egy quid to ioiz a atom fom t obit is.6 + V.6 E V.V. Egy quid to mov a lcto fom a obit.6 Z is + V. So, to mov t lcto fom t fist xcitd stat of Li + is.6 E V. Ioizatio pottial will b lowst fo t atom i wic t lctos a t fatst fom t uclus. So, t atom wit t lagst siz will av t lcto t fatst fom t ucli, c to mov t lcto fom tis atom will b asist. So, t atom wit last ioizatio pottial is 55 Cs.. T wavlgts ivolvd i t spctum of dutium D a sligtly difft fom tat of ydog spctum; bcaus masss of two ucli a difft. 6. T gy of mittd poto is dictly popotioal to t diffc of t two gy lvls.tis diffcs is maximum btw lvl () ad lvl () c poto fo maximum gy will b libatd fo tis tasitio oly.. Rquid gy.6 (Z) V.6 () 8.8 V. umb of lis C C ()() (). Egy L ( ) I ( ) w µ ducd mass so gy (m m ) mm. Egy of adiatio mittd E E Z. Wok fuctio a Cu m m m m 6 E Z E Z ( ) ( ) PHOTOELECTRIC EFFECT W W.5 W. Cu a c W a Cu f WCu a 5. Covalt bodig lcto cloud ovlappig gio lcto pobability dsity wav atu of lcto 7. Wv a atom gts d-xcitd fom ig to t low obit, it mits adiatio of a giv fqucy 6. f mv, f mv m v v f f od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 8. E f f E T potos of igst fqucy will b mittd, fo t tasitio i wic E is maximum, i.., fom to. k mv mv k (idp o ) mv ad idp of. T mv is 7. Total cag i momtum fom a flcti g sufac P P P T momtum of ici adiatio Hc, momtum tasfd E c E P c

14 JEE-Pysics 8. ccodig to Eisti's quatio of potolctic ffct fw +K max K max ()f W K max 7. d cos i d cos i 8. d cos i db mv V 5 volt q t W T slop of K vs f gap is wic is a fudamtal costat ad sam fo all mtals at all itsifis. c 9. W V, max? ; W V m V max max c m-v max m. 9. E k c.68 By solvig it. V. o. of potos mittig p scod fom a souc of pow P is (5 ) P wavlgt mittig c o P 5 P 5 d tis wavlgt coms i X ay gio. 9.5 m 5Å. Potocut Itsity Itsity du to poit souc at m is I s distac is ducd to alf, t potocut du to poit souc will icas by a facto of.. T d-bogli wavlgts ad kitic gy of a f lcto a latd as 5. Radioactivity ucla Pysics w a is umb of alf-livs. If T / 5 yas t i 5 yas, 8 8 K mk K. ccodig to Eisti's toy of potolctic ffct Egy of ici poto W + V W 6. V; V 5 V Egy of ici poto. V T wavlgt cospodig to tis gy is m wic falls i t ultaviolt gio.. T potolctic pomo is a istataous pomo, c t tim tak by a lcto to com out of mtal is appoximatly sc (foud xpimtally).. Wit t icas i wavlgt gy of t poto dcass. Tfo t KE of t lcto comig out fom t catod also dcass. Du to wic t will b a small dcas i plat cut ad oc bcoms mo ta tsold wavlgt lcto will ot com out fom t catod ad c cut will bcom zo. 5. T latio btw gy (E) of a poto ad momtum (P) associatd wit t poto is E pc T cospodig momtum E v p c c 6. Toug t compoud ca mit all t fou paticls amly lctos, potos, H + ad utos. But t paticl uto ca't b dflctd i t magtic fild, sic it is a utal paticl. Hc, t dflctabl paticls a potos, lctos ad H U U H Lt coil spd b V t by COLM u V u V 9. Rat of disitgatio at ay istat is dictly popotioal to t umb of udcayd ucli at tat istat, i.., d W dcay costat W a giv tat at t d disitgatio 5 miut at t 5 miut d disitgatio - 5 miut t od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

15 JEE-Pysics O multiplyig bot sids by w gt () ( ) t 5 5 t Takig logaitm o bot sids w gt l l (5) l 5 l 5. l. t. 8 av b mittd av b mittd + av b mittd ducs atomic umb by icass atomic umb by + dcass atomic umb by So, Z ff 9 (8 ) + ( ) ( ) Itsity of gamma adiatio w it passs toug x is I 8 I I I x 6...(i) ad I I x...(ii) 8 6 x x 6 ad x mm 7. W kow tat, w, a t adioactiv ucli lft aft -alf livs a t iitial umb of ucli ad is umb of alf-livs, / 8 8. uclus duig dcay mits (H + ), (lctos), o utio; it dos ot mit potos duig dcay. Tfo T / 5 5 mi.. I od to fus two ucli agaist pulsio, t pulsiv pottial gy as to b supplid by kitic gy i.., PEKE 7.7 kt 8. Radius of a ucli (Mass umb) / l / R T 5 5 R 7 X, 9. 7 Li 5 R T R l 6 fmi od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p T T.7 9 k. pplyig cosvatio of momtum, w gt m v m v m v m v / lso, R m m R / m R R : m R R. Giv tat H H H gy Total B.E. of dutium uclus. MV Total B.E. of H uclus 8 MV O cosvatig gy o bot sids w gt (Egy) Duto (Egy) H + Egy lasd. 8 + E E 8..6 MV 5. t t closst poit of appoac Iitial KE Fial PE kq q / m 5. cm X Li H 7 Z O cosvatig atomic umb ad mass umbs o bot sids, w gt (7+) Z (+) 5 Hc, X B Z 5 5. Cag o -paticl Cag o tagt uclus Z W t -paticl is pojctd towads t tagt uclus, t at, t -paticl coms to momtay st. Tis positio fom tagt uclus is kow as distac of closst appoac. pplyig law of cosvatio of gy, w gt K z mv, Z, v m Li P B T paticl tat will b mittd wit Byllium will b Gamma adiatios. 5. T gy spctum of -paticls mittd fom a adioactiv souc is (E) E E

16 JEE-Pysics 5. I a ucla actio t gy mais cosvd p Li H 7 gy of potos + 7(5.6) ( 7.6) gy of poto 7.8 MV 6. Z X ( ) ( Z 6 ) ( + ) Z 8 ( ) Z 8 o. of utos Z o. of potos Z 8 Z 8 5. ucla bidig gy [Expctd mass of uclus-ctual mass of uclus]c 6. t / T t T & t T Expctd mass of uclus 8M p + 9M ctual mass of uclus M ucla bidig gy [8M p +9M M ]c 5 5. Gamma ay is a lctomagtic adiatio, du to t missio of gamma ay, it t mass umb ot t atomic umb cags. Toug t daugt uclus is sam as pat uclus but still t is a diffc i t two, i.., t daugt uclus so obtaid is pst i o of t xcitd stats ad ot i t goud stat Giv tat T T / x av Y.69 Y X.69. R. R Y X Y X X s dcay at of Y is mo ta t lmt X; c Y will dcay fast ta X Total kitic gy of poducts Y ( t t ) T (t t ) T t t T t t mi. 6. 5m M+ m m ' p' p ccodig to Cosvatio of lia momtum P' P. Tfo ' 6 5. Rlasd gy [ ] EXERCISE V-B. T cotiuous X ay spctum is sow i figu. ll wavlgts > mi a foud, w E ( 8 ) J.7 MV Total gy lasd p p m m (mass dfct) c (w m M giv) mi p M M (M m) c m p m c M M v m m c v c M M 6. Bcaus gy is lasig Bidig gy p uclo of poduct > tat of pat E > E. mi 75 Å V(i volt) H, V is t applid voltag (i Å) Å 9 Å W (V). 9. m m. umb of ucli dcass xpitially d t ad Rat of dcay Tfo, dcay pocss lasts upto t. Tfo a giv uclus may dcay at ay tim aft t. od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

17 JEE-Pysics od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65. Sic, t wavlgt () is icasig w ca say tat t galaxy is cdig. Doppl ffct ca b giv by ' c v c v c v 76 c v c + v.6 c.6 v v.6c.6 c v c v 8...(i).6. m / s.6 v. 7 m/s If w tak t appoximatio t quatio (i) ca b v witt as c...(ii) Fom v.c ( 8 ) 656 m/s v. 8 m/s Wic is almost qual to t pvious asw. So, w may us quatio (ii) also. 5. tomic umb of o is. By t missio of two paticls, atomic umb will b ducd by. Tfo, atomic umb of t ukow lmt will b Z 6 Similaly mass umb of t ukow lmt will b Ukow uclus is cabo (, Z6). 6. Fom law of cosvatio of momtum, P P (i opposit dictios) ow d Bogli wavlgt is giv by [ Plak's costat] Sic, momtum (p) of bot t paticls is qual, tfo / 7. Bot t bta ays ad t catod ays a mad up of lctos. So, oly optio (a) is coct. (b) Gamma ays a lctomagtic wavs. (c) lpa paticls a doubly ioizd lium atoms ad (d) Potos ad utos av appoximatly t sam mass. 8. (t / ) x (t ma ) y x y x x < y Rat of dcay Iitially umb of atoms () of bot a qual but sic y > x, tfo, y will dcay at a fast at ta x. y p 9. Radius of a uclus is giv by R R / (w R.5 5 m).5 / 5 m H, is t mass umb ad mass of t uaium uclus will b m m p m p mass of poto (.67 7 kg) Dsity 7 mass m (.67 kg) volum (.5 m) R. 7 kg/m 5. Egy is lasd i a pocss w total bidig gy of t uclus ( bidig gy p uclo umb of uclos) is icasd o w ca say, w total bidig gy of poducts is mo ta t actats. By calculatio w ca s tat oly i cas of optio (c), tis apps. Giv : W Y Bidig gy of actats MV ad bidig gy of poducts (6 8.5) MV > 9 MV. Rc. I ydog atom E. lso E m w m is t mass of t lcto. H, t lcto as b placd by a paticl wos mass is doubl of a lcto. Tfo, fo tis ypottical atom gy i t obit will b Rc giv by E T logst wavlgt max (o miimum gy) poto will cospod to t tasitio of paticl fom to. c E E Rc max. KE (wit positiv sig) Pottial gy U is gativ ad Z U U. [bcaus ] (wit gativ sig) max 8 5R Similaly total gy E (wit gativ sig) Tfo, w a lcto jumps fom som xcitd stat to t goud stat, valu of will dcas. Tfo, kitic gy will icas (wit positiv sig), pottial gy ad total gy will also icas but wit gativ sig. Tus, fially kitic gy will icas, wil pottial ad total gis will dcas. 5

18 JEE-Pysics. Miimum wavlgt of cotiuous X ay spctum. is giv by mi (i Å) 75 E(i V) H, E gy of ici lctos (i V) gy cospodig to miimum wavlgt mi of X ays E 8 kv 8 V 75 mi (i Å) 8.55 lso t gy of t ici lctos (8 kv) is mo ta t ioizatio gy of t K sll lctos (i kv). Tfo, caactistic X ay spctum will also b obtaid bcaus gy of ici lcto is ig oug to kock out t lcto fom K o L slls. x (t) t (t) t x (Iitially bot av sam umb of ucli say ) t / t 9t, x ad x 9 t t 9 5. Egy of ifad adiatio is lss ta t gy of ultaviolt adiatio. I optios (a), (b) ad (c), gy lasd will b mo, wil i optio (d) oly, gy lasd will b lss... q i t t i t Substitutig i..6 9 C ad t s w gt, 6 R R...(i) H R activity of adioactiv substac aft R alf livs (giv) 6 Substitutig i quatio (i), w gt t ()t / () ( s) s. Duig dcay atomic umb (Z) ad mass umb () dos ot cag. So, t coct optio is (c) bcaus i all ot optios it Z, o bot is/a cagig.. U V V du V F d tis foc will povid t cssay ctiptal foc. mv V Hc, v V...(i) m 6. Wavlgt k is idp of t acclatig voltag (V), wil t miimum wavlgt c is ivsly popotioal to V. Tfo, as V is icasd, k mais ucagd w as c dcass o k c will icas. 7. Duig dcay, a uto is tasfomd ito a poto ad a lcto. Tis is wy atomic umb (Z umb of potos) icass by o ad mass umb ( umb of potos + utos) mais ucagd duig bta dcay. 8. T total umb of atoms ca it mai costat (as i optio a) o ca v icas (as i optios b ad c). Ty will cotiuously dcas wit tim. Tfo, (d) is t appopiat optio. 9. I scod xcitd stat, So, H Li wil E Z ad Z H, Z Li So, E Li 9 E H o E H < E Li Moov, mv...(ii) Dividig quatio (ii) by (i). m W av : m V m. ( m ) z (.5 Å) (.5)Å m z m 5 fo Fm 57 (t outmost sll) ad z (5) 5. ucla dsity is costat c, mass volum m V. 6. Giv tat K + K 5.5 MV...(i) Fom cosvatio of lia momtum, p p K (6m) K (m) as P Km K 5 K...(ii) Solvig quatio (i) ad (ii). W gt K KE of paticl 5. MV od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 6

19 JEE-Pysics 7. Satuatio cut is popotioal to itsity wil stoppig pottial icass wit icas i fqucy. Hc, f a f b wil I a < I b 8. me c E o / E 9. ctivity ducs fom 6 dps to dps i days. It implis tat alf lif of t adioactiv sampl is days. I 8 days (o 5. Momtum of stikig lctos p Kitic gy of stikig lctos K p m m Tis also, maximum gy of X ay potos. Tfo, c m m c od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 two alf livs) activity will mai t of t iitial activity. Hc, t iitial activity of t sampl is 6 dps dps. T fist poto will xcit t ydog atom (i goud stat) i fist xcitd stat (as E E.V). Hc duig d xcitatio a poto of.v will b lasd. T scod poto of gy 5V ca iois t atom. Hc t balac gy i..,(5.6)v. V is taid by t lcto. Tfo, by t scod poto a lcto of gy. V will b lasd.. Z Z (Z ) Z Solvig tis, w gt Z 6. ( H ) 8 O 6 Mass dfct m {(.6) 5.999}. amu Egy lasd p oxyg ucli (.) (9. 8) MV. MV. ft two alf livs / t factio of ucli will mai udcayd. / t factio will dcay. Hc, t pobability tat a uclus dcays i two alf livs is /.. T sis i U V gio is Lym sis. Logst wavlgt cospods to miimum gy wic occus i tasitio fom to. R...(i) T smallst wavlgt i t ifad gio cospods to maximum gy of Pasc sis. R...(ii) Solvig quatio (i) ad (ii), w gt 8.5 m 6. Rst mass of pat uclus sould b gat ta t st mass of daugt ucli. 7. s fo cotiuous X ays mi c so cut off V wavlgt dpds o t acclatig pottial ad is idp of atu of tagt. 8. ctivity & T / So 5 ( ) & ( ) T T T T m ligt caot mit lcto fo mtal of wok fuctio V, so satuat cut dcass fo P to Q to R. lso V sp > V sq > V s. Egy ici Pow(tim) M C Q So momtum E c ( mw) ( s) kg m / sc. Du to mass dfct (wic is fially sposibl fo t bidig gy of t uclus), mass of a uclus is always lss ta t sum of masss of its costitut paticls.. is mad up of potos plus utos. Tfo, mass of uclus, M < (m p + m ) lso, avi t uclus, mo is t mass dfct. Tus, (m + m p ) M > (m p + m ) M (m p + m )>M M M < M + (m p + m ) ow sic M < (m p + m ) M < M. 7

20 JEE-Pysics. Tim piod, T v (i t stat) i.. T But ad Tfo, T Hc,. Fom t latio, V c Giv T 8T c V Tis is quatio of staigt li. Slop is ta c c c c : : : : : :.m.m.m Å 5Å 5 Å Violt colou as wavlgt Å. So violt colou ca jct potolctos fom mtal ad mtal.. ( ) Fo < < 5, o fusio mass umb fo compoud uclus is lss ta Bidig gy p uclo mais sam o gy is lasd ( B ) Fo 5 < <, o fusio mass umb fo compoud uclus is btw & Bidig gy p uclo icass Egy is lasd. ( C ) Fo < <, o fissio, t mass umb of poduct ucli will b btw 5 & Bidig gy p uclo dcass o gy is lasd ( D ) Fo < < 6, o fissio, t mass umb of poduct ucli will b btw & Bidig gy p uclo icass Egy is lasd. 5 gula momtum a 9a lso a Z Z Fo d- xci tati o Rz R Fo to : 9 R 9 R Fo to : 9 R 9 5R Fo to : R R Matc t colum. (i) Egy of capacito is lss / cv tfo p. (ii) wok is do o t gas c gy icass tfo q. (iii) W mass dcass its gy icass. (iv) w cut flows gy of magtic fild is gatd tfo t. (B) wok is do o t gas (C) mass is ducd ad mass dfct is covtd ito gy. (D) mass dcass du to mass dfct. Matcig List Typ. Compltig actio i list II 5 5 () 8 O 7 8 () 9 U () 8 Bi 8 9 () 9 Pu 57 + dcay) T (lpa dcay) Pb (Poto missio) La (Fissio) Compsio Basd Qustio Compsi o#..v H.V.6V.V H +.V 6.V.6V 5.V Fo H atom E. V, Tis gos to xcit H + io fom to od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 8

21 JEE-Pysics. Fo visibl gio E <. V ad i tis cas E. ( 6).6 V c E V Å 8Å.8 7 m.6v. Ratio of kitic gy Sic & Z K Z K Z K fo H, Z fo H + K Compsi o#. Du to t ig tmpatu dvlopd as a sult of collisio & fusio causs t co of fusio acto to plasma. Compsio. E I I / I I 8 I. E E 8 I 8 I I.87 kgm Momt of itia of CO molcul about ct of mass : mm I w m m. KT T Kqq KT Kqq T K T K 6 I I.87 m m 6 5 / m m 6 Paagap 5.. m Po Pb H Q od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65. t > 5 t > 5 t 6 > 5 Compsi o#. E. p m... (i) p... (ii) By quatio (i) ad (ii) E [ m ( ) m(a ) a fo statioay wav o stig fixd at bot d] E a (6.6 ) E m a (. ) (6.6 ) E 8 mv 9. mv v m v m(a) M M M C Total gy lasd Po Pb H [( ) ( )] 9 MV [.588] 9 MV 5.76 MV Kitic gy of paticl 6 Q 5.76 MV MV 59 KV 5.9. Oly i optio (C); sum of masss of poduct is lss t sum of mass of actat M alpa Subjctiv fo actio H H 6 Li. s M Li < M Duto +. (i) Lt at tim t, umb of adioactiv ucli a. t at of fomatio of ucli of d Solvig tis quatio, w gt [ ( ) t ]...(i) d d t 9

22 JEE-Pysics (ii) (i) Substitutig ad t t / quatio (i) w gt, (ii) Substitutig ad t i quatio (i), w gt () i E 5 E 5 E.8 V E 5 E 5 E.5 V > V E E E.6 V E E E. V > V Hc, t gy of mittd potos i t ag of V ad V a. V duig combiatio ad.8 V ad.6 aft combiatio.. Giv wok fuctio W.9 V Wavlgt of ici ligt, m. Lt goud stat gy (i V) b E T, fom t giv coditio E E V Egy of ici ligt, E c (Substitutig t valus of, c ad ).V Tfo, maximum kitic gy of potolcto K max E W (..9). V ow t situatio is as sow blow : E E V E ' V...(i) ad E E.8 V E E.8 V K max.v 5 E 5.V E.8 V...(ii) -paticls + H i fout xcitd stat o 5 (Z) H + Egy of lcto i t xcitd stat of H + (5) will b E 5 (.6) Z E 5.6 V () (5). V Tfo, gy lasd duig t combiatio. (.). V Similaly gis i ot gy stats of H + will () b E.6 () () E.6 () () E.6. V 6. V.6V T possibl tasitios a E 5 E 5 E. V < V Fom quatio (i) ad (ii), 5 5 Fom quatio umb (ii), E (.8) V () (.8) V E 7.6 V E (.6)Z Z E.6 E mi E E E E ( ) E mi.58 V Z.6 7 ( 7.6) V E E 6 7 E 9 od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

23 . Egy of ici poto, 5.(i) E i.6 V J J Egy ici p uit aa p uit (itsity) J o. of potos ici o uit aa i uit tim Tfo, umb of potos ici p uit tim o giv aa (. m ) (.8 8 ) (. ).8 But oly.8% of ici potos mit potolctos o. of potolctos mittd p scod ().5 (.8 ) 6.5 K mi ad K max E i wok fuctio K max 5. V (.6 5.6) V 5. V Lt at tim tt, umb of ucli of Y ad Z a Y ad Z. T Rat quatios of t populatio of X,Y ad Z a d X...(i) X X d Y...(ii) X X Y Y (iii) 6.(i) T populatio of X at tis momt, JEE-Pysics X Xt ( ) (.) (6.8) X.9 9 Y X Y X (.9 9 ) [Fom quatio (iv)] (.) ( / ) Z X Y Z. 9 Giv mass of paticl, m. amu ad mass of daugt uclus M.6 amu, d Bogli wavlgt of paticl, m So, momtum of paticl would b p p.5 9 kg m/s kg m/s Fom law of cosvatio of lia momtum, tis sould also b qual to t lia momtum t daugt uclus (i opposit dictio). Lt K ad K b t kitic gis of paticl ad daugt uclus. T total kitic gy i t fial stat is: K K + K p m p M od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65 d Z...(iii) Y Y X (ii) Giv Y (t) Yt Xt X Fo Y to b maximum Y d Y (t) i.. X X Y Y... (iv) (fom quatio (ii)) X Xt Yt X t X ( ) Y [ ] X Y Y t Y t ( X Y )t () X X Y X Y t X ( )t Y X Y X X Y Y Substitutig t valus of X ad Y, w av. t 5() (. / ) / t6.8 s. (ii) p m M p M m Mm amu.67 7 kg Substitutig t valus, w gt 9 (.5 ) M m K M m 7 p (..6)(.67 ) 7 7 (..67 )(.6.67 ) K J MV 6.5 MV.6 K6.5 MV 6.5 Mass dfct, m amu.67 amu 9.7 Tfo, mass of pat uclus mass of paticl + mass of daugt uclus+mass dfct (m) ( )amu 7.6 amu

24 JEE-Pysics 7. T acto poducs MW pow o 9 W pow of 9 J/s of pow. T acto is to fuctio fo y. Tfo, total gy wic t acto will supply i y is E (pow) (tim) ( 9 J/s) ( 65 6 s).56 7 J But sic t fficicy of t acto is oly %, tfo actual gy dd is tims of it o.56 8 J. O uaium atom libats MV of gy o.6 o. J of gy. So, umb of uaium atoms dd a o umb of kg mols of uaium dd a (i) umb of potolctos mittd upto t s a (o. of potos fallig i uit aa i uit tim) (aa tim) 6 6 [()6 (5 ) ()] 5. 7 (ii) t tim ts cag o plat, q +(5. 7 ) (.6 9 ) 8. C ad cag o plat B, q B (.7 8. ) 5.7 C Elctic fild btw t plats E (q q ) B 8.(i) Hc, total mass of uaium quid is m ()M (6.7) (5) kg m 87 kg m.87 kg Total 6 lis a mittd. Tfo ( ) 6 So, tasitio is takig plac btw m t gy stat ad (m + ) t gy stat. E m.85v Z.6 m.85 Z m.5...(i) Similaly E m+.5 V (5.7 8.) E (5 )(8.85 ) C (iii) Egy of potolctos at plat E W (5 ) V V Icas i gy of potolctos (Ed) joul (Ed) V ( ) ( ) V V Egy of potolctos at plat B ( + )V V. E Rc (Z b) Fo K sis, b Rc(Z ) (ii) z z.6.5 (m ) (m ) Solvig quatio (i) ad (ii) fo z ad m. W gt m ad z...(ii) Smallst wavlgt cospods to maximum diffc of gis wic is obviously E m+ E m. E max.5 (.85).6 V mi c 5. m. E.6 max 9. a of plats 5 m distac btw t plats d cm m Substitutig t valus,. 8 (. 7 ) ( 8 )(Z ) (Z ) 697 Z Z. Maximum kitic gy of t potolctos would b K max E W (5 ) V V Tfo, t stoppig pottial is V. Satuatio cut dpds o t itsity of ligt ici. W t itsity is doubld t satuatio cut will also bcom two fold. T cospodig gaps a sow i figu. od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65

25 JEE-Pysics. Wavlgts cospodig to miimum wavlgt ( mi ) o maximum gy will mit potolctos avig maximum kitic gy. ( mi ) blogig to Balm sis ad lyig i t giv ag (5 m to 75 m) cospods to tasitio fom ( to ). H,. Lt b t umb of adioactiv ucli at tim t. umb of ucli dcayd i tim t a giv by ( t ), wic is also qual to t umb of bta paticls mittd duig t sam itval of tim. Fo t giv coditio, ( )...(i) Dividig quatio (ii) by (i), w gt ( +.75) ( )...(ii).6 E ().6.85V E () E E E.55 V K max Egy of poto wok fuctio V.V. Lt b t iitial umb of ucli of 8 U ft tim t, U H umb of alf livs.75...(iii) Lt us tak x T t abov quatio is x.75 x +.75 x.75 (.75) ()(.75) x ad t.5 9 t /.5 ad Pb U 9 U / Fom quatio (iii) it, but is ot accptd bcaus wic mas / U Pb.86 od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65. Hc, () () () () () () () Substitutig t giv valus,.69 (.986).95 s Ma lif t ma 6.97 s 5. (i) Fom t latio / W av / / / () 56 (ii) Z o. of utos 56 6 Rc f ka Rc (Z ) (Z ) Substitutig t giv valus of R, c ad Z. W gt f ka.55 8 Hz

26 JEE-Pysics 6. Fo < x <, PE E Kitic gy K Total gy PE E E E...(i) m(e ) Fo x >, PE 9. V s V S v s Kitic gy K Total gy E m(e )...(ii) Fom quatio (i) ad (ii), w av p mqv m q P d m q P P 8 d t t d t slop ya y.69 t /.86 giv tim is tims of t / slop costat atio. Giv T ½ 86 sc. d Factio t l 8 86 t % valu of p is 8. od-6\e:\data\\kota\jee-dvacd\smp\py\solutio\uit-9 & \5.Mod Pysics.p65