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1 E ngrg Pysics:PHY S JB Institut Tcnology D EPARTMENT OF PHYSICS S olutions Qustion Bnk UNIT-I M ODERN PHYSICS J un/july 9. ( 4 Mrks i An lctron n pron r cclrt troug sm potntil. rtio - B rogli wvlngt A B m/ mp C m p / m D ( mp/ m A n s: D ( mp/m i i Wv function ssocit wit mtril prticl A sgl vlu B fit C contuous D All bov A ns: D All bov iii In blckboy rition spctrum, mximum nrgy pks sift wrs s ortr wvlngt si wit crs tmprtur. T confirms A Stfn s lw B Win s lw C Rylig-J ns lw D Plnck s lw A n s: B Win s lw iv group vlocity prticl x m /s, wos ps vlocity 6 A 6.6 x m/s B x m/s C nm/s D.5 x m /s A n s: B x m /s b. Dscrib Dvson n Grmr xprimnt for confirmtion - Brogli ypos. D von G rmr s Exprimnt. ( 8 Mrks F - T ungstn filmnt t by pssg currnt wic mits lctron. G - E lctron gun wic cclrts lctron by ppli potntil iffrnc btwn f ilmnt n iprgms. N - A lrg sgl crystl nickl mount on support, wic cn b rott bout n x t roug O n prpniculr circulr pt S. C - I t n ioniztion cmbr wic snsitiv glvnomtr connct. cmbr cn b rott bout circulr pt S, vg circulr grut scl, cntr wic c ocis wit O. 6 D prtmnt Pysics, SJBIT, Bnglor-6 Pg

2 E ngrg Pysics:PHY M tllic Diprgm A collimt n cclrt bm lctrons from lctron gun r m cint on nickl crystl N. lctrons scttr t n ngl r rciv by cmbr C wic proucs currnt n gt tct by glvnomtr. lctrons wic ntr i n cmbr r clrt by rtrg potntil btwn two wlls. T civ lctrons wit ig vlocity r bl ntr nr cmbr. Kpg cclrtg potntil constnt t G, ioniztion currnt ws rcor for v rious scttrg ngls. Polr grps r rwn for iffrnt potntils by rptg xprimnt. I oniztion currnt for ngl φ. T grps r s sown figur. It obsrv t potntil V=44V tct mximum w s obsrv. It crss mor n mor up V=54V. Curv n ftrwrs cl n f wy. Dvsion n Grmr trprt ioniztion currnt bcomg mximum for V=54V n φ=5 s u scttrg lctrons s toug bm monocromtic wvs bg scttr. T follows - Brogli s ypos mttr wvs. s scttr lctrons r s wvs wvlngt λ givn by λ=.6-9 / V = / 54 =.66 m ( Tus Dvson n Grmr suggst tt s X- rys unrgos iffrction crystl so lso wvs ssocit wit lctrons unrgos iffrction Nickl crystl obyg Brgg s lw. Accorg Brgg s lw iffrct wvs unrgo constructiv trfrnc s tfyg qution nλ = s θ wr θ glncg ngl or Brgg s ngl n trplnr tnc. Tkg o - orr iffrction n=, θ =65 n =.9A =.9x m. - - λ =.9x s 65 =.65 X m ( F rom qn s ( n ( it follow tt mttr wvs ssocit wit lctrons unrgo constructiv trfrnc t = 5 for V=54V. In Dvson n Grmr xprimnt wit D prtmnt Pysics, SJBIT, Bnglor-6 Pg

3 E ngrg Pysics:PHY Brgg s ngl θ =65, mximum currnt mns mximum numbr lctrons, trn tkn s lrg mplitu u constructiv trfrnc. For or ngls currnt lss, mns lss numbr lctrons, trn tkn s smll mplitu u bsnc constructiv i ntrfrnc. c. Expl ps n group vlocity. Clcult Brogli wvlngt bullt m ss 5 grms movg wit vlocity km/. ( 8 Mrks Ps vlocity (vp s : T ps vlocity vlocity iviul wvs. vlocity wit wic c ps wv movs cll ps vlocity or ps v locity rprsnts vlocity wit wic prticulr ps wv movs. Group Vlocity v (v P s = k g roup : Wn group two or mor wvs iffrnt wvlngts n iffrnt vlocitis r suprimpos on c or mplitu rsultnt wv vri, wic forms w v group or wv pckts. vlocity wit wic nvlop nclosg wv p ckts trnsport cll group vlocity. I n or wors vlocity wit wic nrgy wv group trnsmitt c ll group vlocity. w G roup Vlocity rprsnt by V g roup = k G ivn: M =55gm=55 - k, V =km/r = 5.55m/ s λ = mv λ = λ = m D c 9/Jn. i Win s lw uc from Plnck s rition formul unr conition ( 4 mrks A Vry smll wvlngt n tmprtur B Lrg wvlngt n tmprtur C Smll wvlngt n tmprtur D Lrg wvlngt n smll tmprtur A ns A Vry smll wvlngt n tmprtur ii Compn wvlngt givn b y A Ans m c C B C m c m c m c D m o c i ii Wic followg rltions cn b us trm Brogli wv l ngt ssocit wit prticl? A B C D ll s m mv mv A ns D ll s D prtmnt Pysics, SJBIT, Bnglor-6 Pg

4 E ngrg Pysics:PHY iv if group vlocity prticl x m /s, its ps vlocity 6 8 A m/s B x m/s c x m/s D x m /s Ans D x m /s 6 b.wt Plnck s rition lw? Sow ow Win s lw n Rylig- jns lw cn b riv from it. ( 6mrks P lnck ssum tt wlls xprimntl blckboy consts lrgr numbr lctricl oscillrs. Ec oscillr vibrts wit its own frquncy. i Ec oscillr s n nrgy givn by tgrl multipl υ wr Plnck s c onstnt & υ frquncy vibrtion. E = nυ wr n =,,... tc. i i An oscillr my los or g nrgy by mittg or bsorbg rspctivly rition frquncy υ wr υ=δe/, ΔE iffrnc nrgis oscillr bfor n ftr msion or bsorption tk plc. P lnck riv lw w ic ols goo for ntir spctrum blckboy rition s 8c U λ λ = kt ( sc υ = c/λ ( 5 / T Plnck s Rition Lw. R uction Plnck s lw W s lw n Rylig Jns lw: F or s ortr wvlngts, υ = c/λ lrg. υ/kt Wn υ lrg, i s vry lrg... υ/kt. > >.. υ/kt υ/kt c/λkt. ( - = S ubstitutg qn : C 8c 5 T U λ λ = 5 c/ kt = C W r C = 8πc n C = c/ k T W s lw rition. F or longr wvlngts υ = c/λ smll. W n υ smll υ/kt vry smll. υ/kt Expng s powr sris: υ/kt = + υ/kt + (υ/kt υ /kt. I f υ/kt smll, its igr powrs r nglct. υ/kt c - = kt kt S ubstitutg qn : 8c U λ λ = c 5 kt 8kT = 4 T Rylig Jns Lw Rition. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

5 E ngrg Pysics:PHY C D f group vlocity. Driv rltion btwn group vlocity n ps vlocity. (6mrks Group Vlocity (vg roup : Wn group two or mor wvs iffrnt wvlngts n iffrnt vlocitis r suprimpos on c or mplitu rsultnt wv vri, wic forms w v group or wv pckts. vlocity wit wic nvlop nclosg wv p ckts trnsport cll group vlocity. In or wors vlocity wit wic nrgy wv group trnsmitt c ll group vlocity. w G roup Vlocity rprsnt by V g roup = k R ltion btwn group vlocity n ps vlocity: T qutions for group vlocity n ps vlocity r: vg roup = ( & vp s = ( k k W r ω ngulr frquncy wv n k wv numbr. Ω = k v p s v g roup = = ( k v k ps k v ps vgroup= vps + k k v vg roup = vp s + k ps ( k W v k = (π/λ k Diffrntitg or k k k U sg t qn ( v ps vg roup = vp s λ T rltion btwn group vlocity n ps vlocity.. fst movg nutron foun v ssocit brogli wvlngt Å,f its k tic nrgy n group vlocity Brogli wvs. ( 4mrks g ivn: λ = Å K.E =?, v = E = E = p = m mλ, g roup? (6. 6 x 4 X. 675X 7 (X - E=.X J V g= mλ 6. 6 x V 4 g = X X. 675X 7 V g =.98km/ s D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

6 ngrg Pysics:PHY E Pysics, prtmnt D Bnglor JBIT, S - 6 g P 6 y/jun M. for only pplicbl tribution lw W s rition spctrum, blck boy In i wvlngt Longr b wvlngt ortr s wvlngt Entir c s non B ns A wvlngt sortr m n mss wvlngt ssocit wit n lctron Brogli i i cclrt by V otntil p Vm b mv c Vm Vm D ns A Vm cn b y bcus wv s Elctron bvs ii i fil mgntic by flct b crystl by iffrct gs ioniz fil lctric by flct c nsa A crystl by iffrct Br group vlocity If v i 4x wv ogli 8 vlocity ps its /s, m x 8 b.5x m/s 8 x c5. m/s 8 x. m/s 8 /s m B ns A / m.5x8 s wvs mttr Expl ulity. b trfrnc, pnomnon xibits igt L polctric polriztion, iffrction, ffct. Compn n ffct only xpl b coul polriztion n iffrction trfrnc, pnomnon pnomnon Or ntur. wv xibit ligt Tus ligt. ory wv bs on po ik l quntum troug xpl b only Coul tc. ffct Compn ffct, lctric vg c pckts smll consts ligt bm wic Accorg ligt. ory prticls. lik proprtis v wic pons cll r pckts s ν. nrgy o pot Tus w Hnc ntur. prticl possss ligt tt ict ffct Compn n ffct lctric ntur. ul xibits ligt tt onclu c som t ritions ligt lik ntur ul xibits lso mttr tt suggst Brogli D In stnts. r o wv xibits lso prons n lctrons lik mttr prticls wors or wvs wit ssocit prticl movg ypos, Brogli Accorg proprtis. wv mttr s known r lctrons lik mtr prticls wit ssocit vs w or s by givn T wvs. Brogli = mv P

7 E ngrg Pysics:PHY bov qution known s Brogli wv qution. w vlngt pns upon mss rticl n its vlocity. Hnc Brogli c. Df ps vlocity n group vlocity. Sow tt group vlocity qul prticl v locity. Ps vlocity (vp s : ps vlocity vlocity iviul wvs. vlocity wit wic c ps wv movs cll ps vlocity or ps vlocity rprsnts t vlocity wit wic prti culr ps wv movs. v = k P s Group Vlocity (vg roup : Wn group two or mor wvs iffrnt wvlngts n iffrnt vlocitis r suprimpos on c or mplitu rsultnt wv vri, wic forms wv group or wv pckts. vlocity wit wic nvlop nclosg wv p ckts trnsport cll group vlocity. In or wors vlocity wit wic nrgy wv group tr nsmitt c ll group vlocity. w G roup Vlocity rprsnt by V g roup = k R ltion btwn group vlocity n prticl vlocity: V g roup = ( k B ut ω=πυ = π(e/ ( E ( W v k = π/λ = π (p/ (4 k P (5 D ivig qn ( by (5 w v E (6 k P But w v E = P /(m, Wr P momntum prticl. E P P P m m U sg bov qn (6 P k m But p = mvprticl, Wr vp rticl vlocity prticl. mv prticl v (7 prticl k m F rom qn ( & (7, w v V group = Vp rticl (8... Brogli s wv group ssocit wit prticl trvls wit vlocity qul v locity prticl itslf. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

8 E ngrg Pysics:PHY. Clcult momntum prticl n Brogli wvlngt ssocit wit n lctron wit ktic nrgy.5 V. - 9 J Givn, E=.5 V =.5x.6x p 9 Em =.x -9 m D c /Jn. i Grn ligt cint on surfc rlss polctrons from surfc. If now B lu ligt cint on sm surfc, vlocity lctrons A Incrss B Dcrss C rms sm D Bcoms zro A ns A Incrss i i Ry Lig J n s ory ritions gr wit xprimntl rsults for A All wvlngts B sortr wv lngts only C Longr wvlngts only D mil orr wvlngts only A ns C Longr wvlngts only iii - Brogli wvlngt n lctron cclrt potntil iffrnc volts A. Å B Å C Å D Å A ns A. Å i v Wv ntur ssocit wit lctrons motion ws vrifi by A Polctric ffct B Compn ffct C Diffrction by crystls D Rmn ffct A ns C Diffrction by crystls b. Stt n xpl -B rogli s ypos. (4 mrks D Brogli s concpt mttr wvs Ligt xibits pnomnon trfrnc, iffrction, polriztion, polctric ffct n Compn ffct. pnomnon trfrnc, iffrction n polriztion coul b xpl only on bs wv ory ligt. Tus ligt xibit wv ntur. Or pnomnon l ik polctric ffct, Compn ffct tc. Coul only b xpl troug quntum ory ligt. Accorg wic bm ligt consts smll pckts c vg nrgy ν. s pckts r cll pons wic v proprtis lik prticls. Tus po lctric ffct n Compn ffct ict tt ligt possss prticl ntur. Hnc w c onclu tt ligt xibits ul ntur. D Brogli suggst tt mttr lso xibits ul ntur lik ligt ritions t som o r stnts. In or wors prticls mttr lik lctrons n prons lso xibits wv proprtis. Accorg Brogli ypos, movg prticl ssocit wit wvs wvs ssocit wit prticls mtr lik lctrons r known s mttr wvs or Brogli wvs. T givn by = P mv bov qution known s Brogli wv qution. Hnc Brogli w vlngt pns upon mss rticl n its vlocity. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

9 E ngrg Pysics:PHY c. Df ps vlocity n group vlocity. Obt rltion btwn group vlocity n prticl vlocity. Obt xprssion for - Brogli wvlngt usg group v locity. ( 8 mrks P s vlocity: ps vlocity vlocity iviul wvs. vlocity wit wic c ps wv movs cll ps vlocity or ps vlocity r prsnts vlocity wit wic prticulr ps wv movs. v = k P s Group Vlocity (vg roup : Wn group two or mor wvs iffrnt wvlngts n iffrnt vlocitis r suprimpos on c or mplitu rsultnt wv vri, wic forms w v group or wv pckts. vlocity wit wic nvlop nclosg wv p ckts trnsport cll group vlocity. In or wors vlocity wit wic nrgy wv group trnsmitt c ll group vlocity. w G roup Vlocity rprsnt by V g roup = k R ltion btwn group vlocity n prticl vlocity: T qution for group vlocity vg roup = ( k B ut ω=πυ = π(e/ ( E ( W v k = π/λ = π (p/ (4 k P (5 D ivig qn ( by (5 w v E (6 k P But w v E = P /(m, Wr P momntum prticl. E P P P m m U sg bov qn (6 P k m But p = mvprticl, Wr vp rticl vlocity prticl. mv prticl v (7 prticl k m F rom qn ( & (7, w v v group = vp rticl (8... Brogli s wv group ssocit wit prticl trvls wit vlocity qul v locity prticl itslf. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

10 E ngrg Pysics:PHY Exprssion for -B rogli s w vlngt usg Group Vlocity: Accorg Brogli concpt mttr wvs, c movg prticl ssocit wit systm wvs, supr position wic givs r wv pckt. wv p ckt movs wit sm vlocity s prticl. rfor group vlocity qul p rticl vlocity. W v vg roup = k = v = v K = k V g roup = v v v Sc v v group g roup = v v v - ( Consirg prticl mss m movg wit vlocity v. p otntil nrgy. n Lt E b its nrgy n v its E = ½ mv + v ( Lt v frquncy B rogli wv n its nrgy E = v ( C omprg ( ν = ½ mv L t & ( + V ( 4 prticl movg fil constnt potntil n V = constnt. N ow iffrntitg qution (4 w gt. v = ½ m v v. = mvv ( 5 S ubstitut (5 ( D prtmnt Pysics, SJBIT, Bnglor-6 Pg

11 E ngrg Pysics:PHY ( O n mvv Intgrtg bov qution mv = b ut P = mv momntum prticl. P = = p mv Brogli qution.. F ktic nrgy n group vlocity n lctron wit - brogli wv lngt o f.nm. ( 4mrks g ivn: =.nm, vg =?, E =? = p mv V= E = mλ mv =.6x 6 m /s = 7.68v J un/july.. Coos your nswrs for followg : (4 Mrks i In Compn Effct, wvlngt X- r ys scttr t n ngl θ>. A Incrss A ns A Incrss B Dosn t cng C Dcrss D Non s ii K, Kp n Kα r rspctiv ktic nrgy n, pron n prticl sm - B rogli wvlngt, n A K > K p > Kα B K > K p < Kα C K < K p < Kα D K = K p = Kα Ans A K > K p K > α iii vir prticls s smllst - B rogli wvlngt wn bot m. A mov wit sm sp B mov wit sm vlocity C mov wit sm ktic nrgy Dnon s A ns C mov wit sm ktic nrgy iv Mttr wvs r no t lctromgntic wvs bcus A y mov wit vribl vlocity B pn on crg C mov wit constnt vlocity D non s A ns A y mov wit vribl vlocity - D prtmnt Pysics, SJBIT, Bnglor-6 Pg

12 E ngrg Pysics:PHY b. Wt r bsic postults quntum ory rition? Expl ow Plnck ovrcom rwbcks Win s lw n Rylig- j ns lw. ( 6 Mrks. P lnck ssum tt wlls xprimntl blckboy consts lrgr numbr lctricl oscillrs. Ec oscillr vibrts wit its own frquncy. i Ec oscillr s n nrgy givn by tgrl multipl υ wr Plnck s c onstnt & υ frquncy vibrtion. E = nυ wr n =,,... tc. i i A n oscillr my los or g nrgy by mittg or bsorbg rspctivly rition frquncy υ wr υ=δe/, ΔE iffrnc nrgis oscillr bfor n ftr msion or bsorption tk plc. Plnck riv lw wic ols goo 8c U λ λ = kt ( sc υ = c/λ / T Plnck s Rition Lw. 5 for ntir spctrum blckboy rition s c. Df group n ps vlocity. Driv xprssion for - Brogli wvlngt u sg group vlocity concpt. ( 6 Mrks P s vlocity: T ps vlocity vlocity iviul wvs. vlocity wit wic c ps wv movs cll ps vlocity or ps vlocity r prsnts vlocity wit wic prticulr ps wv movs. v = k P s Group Vlocity (vg roup : W n group two or mor wvs iffrnt wvlngts n iffrnt vlocitis r suprimpos on c or mplitu rsultnt wv vri, wic forms wv group or wv pckts. vlocity wit wic nvlop nclosg wv p c kts trnsport cll group vlocity. In or wors vlocity wit wic nrgy wv group trnsmitt c ll group vlocity. w G roup Vlocity rprsnt by V g roup = k Exprssion for -Brogli s w vlngt usg Group Vlocity: Accorg Brogli concpt mttr wvs, c movg prticl ssocit wit systm wvs, supr position wic givs r wv pckt. wv pckt movs wit sm vlocity s p rticl. rfor group vlocity qul p rticl vlocity. W v vg roup = k = v = v K = k V g roup = v v D prtmnt Pysics, SJBIT, Bnglor-6 Pg

13 E ngrg Pysics:PHY v v group Sc v g roup = v v v ( Consirg prticl mss m movg wit vlocity v. p otntil nrgy. n Lt E b its nrgy n v its E = ½ mv + v ( Lt v frquncy Brogli wv n its n rgy E = v ( C omprg ( ν = ½ mv L t & ( + V ( 4 prticl movg fil constnt potntil n V = constnt. N ow iffrntitg qution (4 w gt. v = ½ m v v. = mvv ( 5 S ubstitut (5 ( ( mvv O n Intgrtg bov qution mv = b ut P = mv momntum prticl. P = = p mv Brogli qution. D prtmnt Pysics, SJBIT, Bnglor-6 Pg

14 E ngrg Pysics:PHY. Comput - Brogli wvlngt for nutron movg wit on tnt prt v locity ligt. ( 4 Mrks -7 Givn: Mss nutron,m=.674x k g 8 Vlocity ligt, c=x m /sc. Vlocity ligt, v= c = X 7 m /sc. T o f D- B rogli wvlngt,λ=? S olution - b rogli wvlngt for nutron givn by, λ = mv = 6.6X 4 (. 74X 7 X( X 7-4 λ=.4x m. D-Brogli wvlngt nutron.4x - 4 m. UNIT-I I Q UANTUM MECHANICS J un/july 9 i Accorg Mx born pproximtion, r prsnts crg nsity b prticl nsity c nrgy nsity probbility Ans: D probbility nsity nsity ii An lctron s sp m/s, ccurt.5 %. uncrtty its p osition. m b.5 m c.4 m.4 m Ans B.5 m iii An lctron movg box lngt. If wv function t x=/4 wit n= n t x= for n=, n / i s / b (/ c A ns C i v lowst quntiz nrgy prticl mss m box lngt L g ivn by zro b c ml ml ml A ns B ml b. Expl Hnbrg s uncrtty prcipl. Giv its pysicl significnc. S ttmnt: ( 6 Mrks It impossibl trm prcly n simultnously vlus bot cnoniclly c onjugt mmbrs pir pysicl vribls. Prouct rnt uncrttis msurmnt suc pirs will b qul or grtr tn 4 D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

15 E ngrg Pysics:PHY In gnrl if x rprsnts rror msurmnt position prticl long X- x n p rprsnts rror m surmnt momntum. n X. p x 4 X p x 4 S imilrly E. t / 4π L. θ /4π pysicl significnc t prcipl on cn not trm simultnously n ccurtly bot position n momnt um movg prticl. Hnc on s consir probbility fg prticl t crt position or probbl vlu for m omntum prticl. c. St up tim- pnnt on- imnsionl Scrogr wv qution. ( 6 Mrks A wv function rprsnt by (x,t tt scribs prticl ntirly unknown position movg positiv X irction. Usg Brogli concpt mttr wvs Scrögr vlop ory for wv propgtion Consir prticl mss m movg wit vlocity v. -B rogli wvlngt λ λ = mv P ( W r T mv momntum prticl. wv qn givn by i( kx t A ( W r A constnt n ω ngulr frquncy wv. D iffrntitg qution ( wit rspct t twic t i( kxt A ( T qution trvllg wv imnsion cn b writtn s y y x v t W r y t plcmnt n v vlocity. Similrly for -B rogli wv ssocit wit prticl x v t (4 w r ψ plcmnt t tim t. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

16 E ngrg Pysics:PHY F rom qns ( & (4 x v But ω = πυ n v =υ λ wr υ frquncy n λ wvlngt. U sg Totl 4 x o r (5 4 x m v P K. E mv (6 m m qn (5 (7 m K. E (8 m 4 x 8 m x Enrgy E = K.E + E P. E V 8 m x E V 8 m x T x 8 m 8 m x E V E V tim pnnt Scrogr wv qution.. A quntum prticl conf on imnsionl box wit its first xcit s tt. Wt probbility fg prticl t trvl / mrk s ymmtriclly t cntr box. (4 Mrks G ivn :n = n s n x D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

17 E ngrg Pysics:PHY p / 4 / 4 n x p / 4 / 4 s xx p / 4 / 4 cos( / x x p / 4 / 4 x / 4 / 4 4 cos xx p.5 D EC 9/JAN. i normliztion wv function lwys possibl, if ( 4mrks + A ΨΨ + = i nfit B ΨΨ + = fit C ΨΨ = D ll s A ns B + ΨΨ = f it i i scrogr s tim pnnt qution pplicbl for prticls w it A constn t nrgy B vribl nrgy C Only constnt potntil nrgy DAll s Ans A c onstnt nrgy i ii groun stt nrgy n lctron n lctron n fit wll i s 5.6mv. if wit wll oubl, groun stt nrgy A 9.9x J B 4.48x J C.4x J D non s Ans C.4x - J i v wv function cc ptbl wv function if it A Fit vrywr B contuous vrywr C Sgl vlu vrywr D All s A ns D All s D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

18 E ngrg Pysics:PHY b. Stt Hnbrg s uncrtty prcipl n cuss its pysicl S ignificnc. ( 6mrks S ttmnt: I t impossibl trm prcly n simultnously vlus bot cnoniclly conjugt mmbrs pir pysicl vribls. rnt uncrtty msurmnt suc pir will b qul or grtr tn 4 In gnrl if x rprsnts rror msurmnt position prticl long X- x n p rprsnts rror i n msurmnt momntum. n X. p x 4 X p x 4 ot r forms uncrttis r ( Enrgy n tim uncrtty: If E n t r uncrttis trmg nrg y n tim rspctivly n. E. t 4 ( Angulr momntum n ngulr plcmnt: If L n θ r uncrttis trmg Angulr momntum n ngulr i splcmnt rsp ctivly, n L. θ 4 pysicl significnc t prcipl on cnnot trm simultnously n ccurtly bot position n momnt um movg prticl. Hnc on s consir t probbility fg prticl t crt position or probbl vlu for m omntum prticl. c Solv Scrogr s wv qution for llow nrgy vlus cs i n potntil box ( mrks prticl V= V V = V= P rticl x = x x = C onsir prticl mss m movg si box long X irction. prticl fr mov btwn wlls box t x = o n x =. potntil nrgy p rticl consir b zro si box n fity t ll pots outsi box. i. V = F or < X < V = F or x n x D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

19 E ngrg Pysics:PHY prticl lwys si box n rfor probbility fg prticl outsi box zro. rfor wv function zro for x n x. Scrogr s qut ion for prticl givn by 8 m ( E V x S c V = si box 8 m E ( x 8 me Lt = k + k = x gnr solution o f t qution = A s kx + B cos kx ( Wr A n B r constnts. vlus s constnts cn b (clcult vlut by pplyg followg bounry conitions. ( i = t x = ( = A s + B cos = + B B = = A s kx ( ( ii = t x = ( = A s k s k = k = n k = n ( 4 ( n = A s n x ( 5 W v k 8 me = ( 6 S ubstitutg vlu k from (4 ( 6 n 8 me L n E n = ( 7 8m wn n =,,, E =, E =, E = 8m 8m 8m D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

20 E ngrg Pysics:PHY For c vlu n r n nrgy lvl s obt from qution (7 n corrspong wv function givn by qution (5. E, E, E tc r cll Eign vlus n corrspong wv function n i s cll Eign function. T nrgy corrspong n = cll groun stt nrgy or zro pot nrgy. N ormliztion wv function: nx W v n = A s T constnt A t qution cn b obt by pplyg normliztion conition. i. o r O x = i. A nx Cos O x = O nx A s x = or or A A A x O s nx n O [ ( ] = = = A = A = normliz wv function prticl n = M y/jun s nx. i If fr lctron xts nuclus, its nrgy vlu must v mimum nrgy bout A 4 MV B MV C kv D kv Ans B MV iiaccorg Mx born pproximtion, r prsnts A Crg nsity B prticl nsity C nrgy nsity D probbility nsitya ns D p robbility nsity iii If E nrgy lowst stt on imnsionl potntil box lngt n E i s nrgy lowst stt wn lngt box lv, n A E = E B E= E C E = E / D E= 4 E Ans D E 4 E = D prtmnt Pysics, SJBIT, Bnglor-6 Pg

21 E ngrg Pysics:PHY iv wv function for motion prticl on imnsionl potntil box l ngt givn by As(nπx/ wr A normliztion constnt. vlu A A B C D Ans C b. Stt n xpl Hnbrg s uncrtty prcipl n prov tt nucli o not c ont lctron. S ttmnt: It impossibl trm prcly n simultnously vlus bot cnoniclly conjugt mmbrs pir pysicl vribls. Prouct rnt uncrttis msurmnt suc pirs will b qul or grtr tn 4 In gnrl if x rprsnts rror msurmnt position prticl long X- x n p rprsnts rror i n msurmnt momntum. n X. p x 4 X p x 4 T or forms uncrttis r ( Enrgy n tim uncrtty: If E n t r uncrttis nrgy n tim rspc tivly n. E. t 4 ( Angulr momntum n ngulr plcmnt: If L n θ r trmg Angulr momntum n ngulr i splcmnt rspctivly T n L. θ 4 I mpossibility xtnc lctrons mic nuclus: trmg uncrttis Accorg ory rltivity, nrgy E o f prticl : E =mc² = m o c v / c Wr mo rst mss prticl n m mss wn its vlocity v. i.. E m 4 o v / c c = m 6 c o ( c v I f p momntum prticl: i.. p = mv = m o v v / c D prtmnt Pysics, SJBIT, Bnglor-6 Pg

22 E ngrg Pysics:PHY M ultiply m p² = o v c c v by c² p²c² = m 4 v c o ( c v S ubtrctg ( E² - ²c² = by ( w v 4 m p o c ( c c v E² = p²c² + mo c 4 ( H nbrg s uncrtty prcipl stts tt x. P (4 x 4 v -4 imtr nuclus orr m. If n lctron xt si nuclus, -4 t uncrtty its position x must not xc m. T i.. x - 4 m mimum uncrtty momntum P x m x 4 mx k g. m/s (5 B y consirg C onsir If mimum uncrtty momntum lctron i.., P x m.5 qn ( - E² = p²c² + mo c 4 = c ( p²+ mo ² c² Wr mo= 9. lctron - k g k g.m/s = p (6 xts nuclus its nrgy must b E² ( 8 - [(.5 + (9. - ( 8 ] i.. E² ( 8 [ ] Nglctg scon trm s it smllr by mor tn orrs mgnitu c ompr fi rst trm. D prtmnt Pysics, SJBIT, Bnglor-6 Pg

23 E ngrg Pysics:PHY T kg squr E.5 roots on bot sis n simplifyg J 9 v 9.4 Mv If n lctron xts nuclus its nrgy must b grtr tn or qul 9.4Mv. It xprimntlly msur tt bt prticls jct from nuclus urg bt cy v nrgis bout 4 MV. T sows tt lctrons cnnot xt nuclus. c. Dcuss wv functions n probbility nsity for prticl n fit potntil wll, for fi rst two stts nx Wv function prticl n =. S ( Wr n n tgr, m mss prticl wit potntil wll or b ox. Cs I n= I t groun stt n t prticl normlly prsnt t stt. T Eign function ψ = S x f rom qn (7 ψ = for x = n x = But ψ mximum wn x = /. x= / x= x= / x= plots ψ vrsus x n ψ v rss x r sown bov figur. ψ = for x = n x = n it mximum for x = /. i.. groun stt prticl c nnot b foun t wlls, but probbility fg it mximum mil. nrgy prticl t groun stt E = 8m = E Cs II n= I n first xcit stt Eign function t stt D prtmnt Pysics, SJBIT, Bnglor-6 Pg

24 E ngrg Pysics:PHY ψ = S x ψ = for vlus x =, /,. Also ψ mximum for vlus x = /4 n /4. T s r rprsnt grps. ψ = t x =, /,, i.. prticl cnnot b foun ir t wlls or t cntr. mximum for x, x 4 4 ψ x= /4 /4 / x= ψ /4 / 4 x= / x= T nrgy prticl first xcit stt E =. 4E. An lctron boun on imnsionl potntil wll wit.8nm. F nrgy vlu V scon xcit stt. Dt: x=.8 nm = x p 4 x p = =.9x kg ms Wr p u ncrtty momntum lctron = p E = p m 5.9 = = 9. = 4.7 x - J =.9 V D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

25 E ngrg Pysics:PHY. D c /Jn i uncrtty trmtion position n lctron t uncrtity trmtion its momntum A B C Ans: A 4,. n i i probbility loctg prticl mximum A t cntr wv wv pckt B t nos wv pckt C cnnot b trm D non s. A ns A t cntr wv wv pckt D i ii In Dvion n grmr xprimnt, wn 54 p ronounc scttrg irction ws foun b t A 9 B C 5 A ns C 5 volts ws D ppli Non s. lctrons, i v groun stt nrgy n lctron n on imnsionl fit potntil wll o f wit Å.6V. its nrgy tir xcit stt A v B64V C 44V D 56V A ns D 56V b Stt n xpl Hnbrg s uncrtty prcipl. ( 4mrks S ttmnt: It impossibl trm prcly n simultnously vlus bot c noniclly conjugt mmbrs pir pysicl vribls. Prouct rnt uncrttis msurmnt suc pirs will b qul or grtr tn 4 In gnrl if x rprsnts rror msurmnt position prticl long X- x n p rprsnts rror t msurmnt momntum. n X. p x 4 X p x 4 T or forms uncrttis r ( Enrgy n tim uncrtty: If E n t r uncrttis trmg nrgy n tim rspctivly n. E. t 4 ( Angulr momntum n ngulr plcmnt: If L n θ r uncrttis trmg Angulr momntum n ngulr plcmnt r spctivly n. L. θ 4 c F Eign vlu n Eign functions for n lctron on imnsionl p otntil wll fit igt. (8mrks D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

26 E ngrg Pysics:PHY Y-A x V= V V = V= P rticl x = x x = X-A x C onsir prticl mss m movg si box long X irction. prticl fr mov btwn wlls box t x = o n x =. potntil nrgy p rticl consir b zro si box n fity t ll poi nts outsi box. i. V = F or < X < V = F or x n x prticl lwys si box n rfor probbility fg prticl outsi box zro. rfor wv function zro for x n x. T Scrogr s qution for prticl givn by 8 m ( E V x S c V = si box 8 m E x ( 8 me Lt = k x + k = gnr solution t qution = A s kx + B cos kx ( Wr A n B r constnts. vlus s constnts cn b (clcult vlut by pplyg followg bounry conitions. ( i = t x = ( = A s + B cos = + B B = D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

27 E ngrg Pysics:PHY = A s kx ( ( ii = t x = ( = A s k s k = k = n k = n ( 4 ( n = A s n x ( 5 W v k 8 me = ( 6 S ubstitutg vlu k from (4 ( 6 n 8 me L n E n = ( 7 8m wn n =,,, E =, E =, E = 8m 8m 8m For c vlu n r n nrgy lvl s obt from qution (7 n corrspong wv function givn by qution (5. E, E, E tc r cll Eign vlus n corrspong wv function n i s cll Eign function. T nrgy corrspong n = cll groun stt nrgy or zro pot nrgy. N ormliztion wv function: nx W v n = A s T constnt A t qution cn b obt by pplyg normliztion conition. i. o r O x = i. A nx Cos O x = O nx A s x = or or A A x O s nx n O [ ( ] = = D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

28 E ngrg Pysics:PHY A = A = A = normliz wv function prticl n = s nx. Estimt tim spnt by n m xcit stt urg xcittion n - -4 xcittion procss, wn spctrl l wv lngt 546nm n wit m mitt. ( 4mrks Δ E. Δ T > Δ 4 Δ T = = λ 4 Δ E 4 ( cδλ o r =.8 nno scons J un/july.. Coos your nswrs for followg : ( 4 Mrks i An lctron movg box lngt ; if ψ, wv function t x= w it n = n ψ t x = for n =, n A A ns C B ψ ψ i s C D ii For prticl n fit potntil wll its xcit stt, probbility f g prticl t cntr box A B.5 C.5 D. A ns A iii To bcom nuclr constitunt, K.E m ust b orr A MV B MV C V D Zro A MV A ns B MV iv An lctron s sp m/s ccurt.5%. uncrtty its position i s A.m B.5m C.4m D.4m A ns B.5m b. Wt wvfunction? Expl proprtis wvfunction. (4 Mrks A pysicl sitution quntum mcnics rprsnt by function cll wv function. I t not by ψ. It ccounts for wv lik proprtis prticls. p roprtis wvfunction ψ sgl vlu vrywr: Consir function f( x wic vris wit position s rprsnt grp. function f(x s tr vlus f, f n f t x = p. Sc f f f it stt tt if f( x wr b wv function. probbility fg p rticl s tr iffrnt vlus t sm loction wic not tru. Tus wv f unction not ccptbl. - st 4 D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

29 E ngrg Pysics:PHY ψ fit vrywr: Consir function f( x wic vris wit position s rprsnt grp. function f( x not fit t x = R but f( x =. Tus it icts lrg probbility fg prticl t loction. It violts uncrtty prcipl. T us wv function not ccptbl. ψ n its first rivti vs wit rspct its vribls r contuous vrywr: Consir function f( x wic vris wit position s rprsnt grp. function f( x trunct t x = Q btwn pots A & B, stt systm not f. To obt wv function ssocit wit systm, w v solv Scrogr wv qution. Sc it scon orr iffrntil wv qution, wv f unction n its first rivtiv must b contuous t x=q. As it contuous wv f unction, wv function not ccptbl. 4 For boun stts ψ must vn t potntil bounry n outsi. If ψ* complx f unction, n ψ* ψ must lso vn t p otntil b ounry n outsi. c. Driv xprssion for nrgy ign vlu for n - i n potntil wll fit pt ( 6 Mrks V= V = V= V P rticl x = x x = D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

30 E ngrg Pysics:PHY C onsir prticl mss m movg i nsi box long X irction. prticl fr mov btwn wlls box t x = o n x =. potntil nrgy p rticl consir b zro si box n fity t ll pots outsi box. i. V = F or < X < V = F or x n x prticl lwys si box n rfor probbility fg prticl outsi box zro. rfor wv function zro for x n x. Scrogr s qution for 8 m ( E V x S c V = si box prticl givn by 8 m E x ( 8 me Lt = k x T + k = gnr solution t qution = A s kx + B cos kx ( Wr A n B r constnts. vlus s constnts cn b (clcult vlut by pplyg followg bounry conitions. ( i = t x = ( = A s + B cos = + B B = = A s kx ( ( ii = t x = ( = A s k s k = k = n k = n ( 4 D prtmnt Pysics, SJBIT, Bnglor-6 Pg

31 E ngrg Pysics:PHY ( n = A s n x ( 5 W v k 8 me = ( 6 S ubstitutg vlu k from (4 ( 6 n 8 me L n E n = ( 7 8m wn n =,,, E =, E =, E = 8m 8m 8m For c vlu n r n nrgy lvl s obt from qution (7 n corrspong wv function givn by qution (5. E, E, E tc r cll Eign vlus n corrspong wv function n i s cll Eign function. T nrgy corrspong n = cll groun stt nrgy or zro pot nrgy.. A quntum prticl conf on imnsionl box wit its first xcit stt. Wt probbility fg prticl t trvl / mrk s ymmtriclly t cntr box. ( 6 Mrks G ivn :n = n s n x p / 4 / 4 n x p / 4 / 4 s xx p / 4 / 4 cos( / x x p / 4 / 4 x / 4 / 4 4 cos xx p.5 D prtmnt Pysics, SJBIT, Bnglor-6 Pg

32 E ngrg Pysics:PHY U NIT - I I I E LECTRICAL CONDUCTIVITY IN METALS J un/july 9. - i If mobility lctron 7x m wn cclrt by fil V/cm, n v i s givn by - A 7x m /s B.7 m/s - C 7x m /s D.7 m/ s A ns B.7 m/s i i tmprtur pnnc for lctricl rstivity mtl A α / T B α / T C α T D α T A ns D α T i ii Frmi fcr for E=E f t T> K i s A B / C D A ns B / i v Accorg quntum fr lctron ory, nrgy lvl mtl A Contuous B crt C ovrlppg D non A ns Contuous b. Expl nsity stts for conuction lctrons for unit volum mtl. ns i ty stts. ( 8 Mrks r r lrg numbrs llow nrgy lvls for lctrons soli mtrils. A group nrgy lvls clos c or cll s nrgy bn. Ec nrgy bn spr ovr f w lctron - volt nrgy rngs. In m m volum mtril, r will b mor tn t ousn billion prmitt nrgy lvls n nrgy rng fw lctron - volts. Bcus t, nrgy vlus ppr b virtully contuous ovr bn spr. To rprsnt it t cniclly it stt s nsity nrgy lvls. pnnc nsity nrgy lvls o n nrgy not by g(e. grp sows vrition g(e vrsus E. It cll nsity stts function. It numbr llow nrgy lvls pr unit nrgy trvl bn ssocit wit mtril unit volum. In n nrgy bn s E c ngs g(e lso cngs. D prtmnt Pysics, S JBIT, Bnglor - 6 P g

33 E ngrg Pysics:PHY Consir n nrgy bn spr n nrgy trvl btwn E n E. Blow E n bov E r r nrgy gps. g(e rprsnts nsity stts t E. As E smll, it ssum tt g(e constnt btwn E n E+E. nsity stts rng E n ( E+E not by g (EE. i.. g(ee = 8 E m E It clr g(e proportionl E i n trvl E c. Dcuss vrious rwbcks clssicl fr lctron ory mtls. Wt r ssumptions m quntum ory ovrcom s? ( 8 Mrks D rwbcks clssicl fr lctron ory. E lctricl n rml conuctivitis cn b xpl from clssicl fr lctron ory. It fils ccount fcts suc s spcific t, tmprtur pnnc c onuctivity n pnnc lctricl conuctivity on lctron concntrtion. S pcific t: molr spcific t gs t constnt volum Cv = R As pr clssicl fr lctron ory, fr lctrons mtl r xpct t o bv just s gs molculs. Tus bov qution ols goo qully wll for fr lctrons lso. But xprimntlly it ws foun tt, contribution spcific t mtl by its conuction lctrons ws CV= -4 RT wic for lowr tn xpct vlu. A lso ccorg ory spcific t pnnt tmprtur wrs xprimntlly spcific t proportionl tmprtur. T mprtur pnnc lctricl conuctivity: E xprimntlly, lctricl conuctivity σ vrsly proportionl tmprtur T. i.. σ xp α /T A ccorg ( ssumptions clssicl fr lctron ory D prtmnt Pysics, SJBIT, Bnglor-6 Pg

34 E ngrg Pysics:PHY KT m v t v t KT m i.., v t T T mn collion tim τ vrsly proportionl rml vlocity. i.. v t or τ α T B ut σ = σ α τ n m o r σ α T ( F rom qutions ( & ( it clr tt xprimntl vlu not grg wit t ory. D pnnc A ccorg lctricl conuctivity on lctron concntrtion: ory σ = n ; wr n lctron concntrtio n, rfor σ α n m Consir zc n cmium wic r ivlnt mtls. ir lctricl conuctivitis r.9 7 / Ωm n.5x 7 / Ωm. s r muc lssr tn tt monovlnt mtls coppr n silvr. vlus wic r 5.88x 7 / Ωm n 6.x 7 / Ωm rspctivly. 8 lctron concntrtions for zc n cmium r. 8 / m n 9.8 / m wic r 8 muc igr tn tt for coppr n silvr, vlus wic r 8.45 / m n / m r spctivly. Hnc clssicl fr lctron ory fils xpl pnnc σ on lctron concntrtion. A ssumptions Quntum Fr Elctron ory:. nrgy lvls fr lctrons r quntiz.. fr lctrons oby Puli s xclusion prcipl.. tr ibution lctrons vrious nrgy lvls obys Frmi Dirc quntum s tttics. 4. conuction lctrons r ssntilly fr prticls conf pysicl bounry t mtl D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

35 E ngrg Pysics:PHY 5. lctron lctron trction n long rng lctron ngligibl. Only wn n lctron vry clos st trctions mk lctron motion qui t rnom ponon trction r ion, scttrg lik D c 9/Jn. i for orry mtls, rstivity vrsus tmprtur curv t T=, ( 4mrks A Hs positiv trcpt B s ngtiv trcpt C Gos troug orig D non s A ns A Hs positiv trcpt i i Wic on followg rltion corrct for c urrnt nsity? na A J = nav B J = C J = nv D J = i ii i v Ans C J = nv V nv T vlu Frmi nrgy tribution function t bsolut zro ( T=K, unr conition A E=EF B E>E F C E>>E F D E<E F A ns D E<E F If Frmi nrgy silvr 5.5v, Frmi vlocity conuction Elctron s 6 A.98X m/s 6 B.9X m/s 5 C.46X m /s Dnon s 6 Ans B.9X m /s b Dscription t bsolut ow quntum fr lctron ory s bn succssful o vrcomg filurs clssicl fr lctron ory. ( 6mrks M rits Quntum Fr Elctron ory: Spcific Ht: A ccorg clssicl fr lctron ory, ll fr lctrons mtl bsorb r nrgy wn mtl t. It rsults lrg vlu spcific t. But s pr quntum fr lctron ory only fw lctrons tt r occupyg nrgy lvls clos Frmi nrgy lvl ( EF bsorb t nrgy gt xcit igr nrgy lvls. Hnc t vlu smll. K B Accorg quntum ory Cv = RT E F An E K B 4 F i., Cv = -4 R T Wic i s xctly wt ws obsrv.. E lctricl Conuctivity n Elctron concntrtion: Accorg clssicl ory, lctricl conuctivity pns only on n, lctron concntrtion. Wic ls c ontriction lik cmium vn ftr vg ig lctron concntrtion n coppr; s D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

36 E ngrg Pysics:PHY low lctricl conuctivity. but lso on n VF. But ccorg quntum fr - ory not only pns n n i. m V F If w compr css coppr n lumium, vlu n for lumium : tim igr tn tt Cu. But vlu for Cu bout.7 tims igr V F t n Al. Tus lctricl conuctivity coppr xcs tt Al.. Tmprtur pnnc lctricl conuctivity: Clssicl ory pricts b pnnt on T s tt. T cn b xpl s follows. T T. But obsrvtions tlls A ccorg quntum fr lctron ory, lctricl conuctivity givn by. n m V F Frmi nrgy EF n nc Frmi vlocity VF r pnnt tmprtur. But mn fr pt pns on tmprtur s follows. Mn fr pt i s vrsly proportionl t o cross sctionl r scttrg. i. wr r mplitu vibrtions. Sc vibrtions crss s r tmprtur crs r T. i. T n. T C. Wt Frmi nrgy? Dcuss vrition Frmi fcr wit nrgy n t mprtur. (6mrks T uppr most nrgy lvl fill t OK cll Frmi Lvl n nrgy corrspong t o t nrgy lvl cll Frmi Enrgy. B viour Frmi Fcr ovr Tmprturs: D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

37 E ngrg Pysics:PHY C s (i: At T = K n E > EF. f ( E n E E F = + v E E K T B F EEf K BT lrg quntity + lrg quntity. f E lrg quntity f (E = t K n E E F C s (ii: At T = K n E < E E EF E E F = - v K T f ( E i., f (E = t OK n E < EF. C s (iii: A t T > OK EE F K BT E = EF f ( E F B E EF b E > EF K T B + v vlu n +v > f ( E, for ll E > EF. E EF c E < EF K T B - v n -v < f ( E, n s E. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

38 E ngrg Pysics:PHY A bov clcultions r plott blow figur. Clos obsrvtions rvl followg p ots. F (E f (E T = OK T = OK T = K ½ T E F E E F E F i f (E prcly on lf t E = EF for T > OK. T givs n ltrnt fition EF tt Frmi Enrgy tt nrgy t wic occuption probbility xctly lf. Not tt t fition not lk wit tmprtur. ii At room tmprtur r sligt wit trnsition from fill unfill stt. But t only bout.5 v wic vry smll compr EF. Frmi cut- f rfor r ms srp.. Clcult probbility n lctron occupyg n nrgy lvl.v bov F rmi lvl t k, mtril. ( 4mrks E-E f =.v, T=k n k=.8x f ( E f (E=.4 EEf K BT - M y/jun. i collion tim n root mn squr vlocity n lctron t room tmprtur -4 5 r x s n x m/s rspctivly. clssicl vlu mn fr pt lctron -9 A x nm B Å C nm D 7.nm Ans C nm i i Mobility lctron A Rciprocl conuctivity B Flow lctrons pr unit C Rciprocl rstivity D Avrg lctron rifts vlocity pr unit lctric f il Ans D Avrg lctron rifts vlocity pr unit lctric fil D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

39 E ngrg Pysics:PHY i ii T quntum mcnicl xprssion for lctricl conuctivity i s m VF A B n n m VF C m V F n Ans B n m V F D m n i v If Frmi nrgy mtl t K 5 V, f(e for A.5 B C.75 D A ns A.5 Frmi nrgy t T > K i s b. Df rlxtion tim n cuss pnnc lctricl rstivity mtls w it t mprtur n impurity. R lxtion Tim ( τ r : tim rquir for vrg vlocity ruc (/ tims it s v lu just wn fil turn f, known s rlxtion tim τ r. t t tl rstivity mtl sum rstivity u t o ponon scttrg ρ p, wic tmprtur pnnt n rstivity u scttrg by impuritis wic tmprtur i npnnt i. i.. ρ = ρ ρ p + i T grp sows vrition rstivity wit tmprtur low tmprtur rgion for soium. T vrition pplis for ll mtls xcpt for suprconucrs, vrition rstivity wit tmprtur wn t=k, ρ not qul zro. As tmprtur i ncrss ρ crss slowly bgng n ltr fstr n lr. T lrity vrition xts till mtl mlts. Rstivity mtl u scttrg conuction lctrons. Scttrg tks plc two ks wic giv r two componnts rstivity Rstivity ρ p u scttrg l ctrons by lttic vibrtions (ponons wic crss wit tmprtur. It rstivity by pur spcimn tt fr from ll fcts. I t il rstivity. b Rstivity ρ i u scttrg conuction lctrons by prsnc imp u ritis n imprfctions suc s loction vcncis n gr bounris. T rstivity i npnnt tmprtur n prsnt t T= Klv. ρ i i s cll rsiul rstivity. D prtmnt Pysics, S JBIT, Bnglor - 6 P g 9

40 E ngrg Pysics:PHY Sc ρ = σ & σ = n m If τ ρ p= I i ρ= m n p i s mn collion tim ssumg tt r no scttrg by impuritis. m n p f 'τ ' mn collion tim ssumg tt r no scttrg by p onon. ρ i = m n i ρ = m n p m n i At lowr tmprturs, mplitu vibrtions bcoms smll n nc scttrg lctrons by lttic ions lso bcom l ss. τp bcoms lrgr ρp tns zro t vry low tmprturs. It mns ρ=ρi t lowr tmprturs. In grp it sn tt rstivity s rsiul vlu ρi t T=K. A s tmprtur crss mplitu lttic vibrtions crs n scttrg lctrons lso crs. rstivity bcoms lr pnnt on tmprtur. At sufficintly ig tmprtur scttrg u ponons mor tn scttrg u impuritis. At tmprturs nr room tmprturs t rstivi ty curv lr. c. Expl ow quntum fr lctron ory succs ovrcomg rwbcks c lssicl fr lctron ory. M rits Quntum Fr Elctron ory: Spcific Ht: Accorg clssicl fr lctron ory, ll fr lctrons mtl bsorb r nrgy wn mtl t. It rsults lrg vlu spcific t. But s pr quntum fr lctron ory only fw lctrons tt r occupyg nrgy lvls clos Frmi nrgy lvl (EF bsorb t nrgy gt xcit igr nrgy lvls. Hnc t vlu smll. K B Accorg quntum ory Cv = RT E F An E K B 4 F i., Cv = -4 R T W ic us xctly wt ws o bsrv. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

41 E ngrg Pysics:PHY. Elctricl Conuctivity n Elctron concntrtion: Accorg clssicl ory, lctricl conuctivity pns only on n, lctron concntrtion. Wic ls c ontriction lik cmium vn ftr vg ig lctron concntrtion n coppr; s - low lctricl conuctivity. But ccorg quntum fr ory not only pns n but lso on n VF. i. n m V F If w compr css coppr n lumium, vlu n for lumium : tim igr tn tt Cu. But vlu for Cu bout.7 tims igr V F t n Al. Tus lctricl conuctivity coppr xcs tt Al.. Tmprtur pnnc lctricl conuctivity: Clssicl ory pricts b pnnt on T s tt. T cn b xpl s follows. T T. But obsrvtions tlls A ccorg quntum fr lctron ory, lctricl conuctivity givn by. n m V F Frmi nrgy EF n nc Frmi vlocity VF r pnnt tmprtur. But mn fr pt pns on tmprtur s follows. Mn fr pt i s vrsly proportionl t o cross sctionl r scttrg. i. wr r mplitu vibrtions. Sc vibrtions crss s r tmprtur crs r T. i. T n. T. A uniform silvr wir s rstivity.54 x om- m t room tmprtur for n lctric fil V/m. Clcult rlxtion tim n rift vlocity lctrons, ssumg tt r r 5.8x conuction lctrons pr cm o f mtril. -8 D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

42 E ngrg Pysics:PHY G ivn =.54 x E = V/m, -8 o m - m = / σ n = 5.8x 8 conuction lctrons pr cm = 5.8x 8 conuction lctrons pr m E V =. n.6 = =.9 m/s m τ = n - 4 s τ =.9 7 D c /Jn. i mobility lctrons conucr 4x - m v - s -. n rift vlocity t Elctron prsnc ppli lctric fil strngt vm - i s A 4ms B ms c.4ms D.4ms - Ans c.4ms i i clssicl vlu molr spcific t conucrs A R B R A ns A R i ii Frmi nrgy mtl t bsolut zro tmprtur proportionl A B C D n w r n numbr fr lctrons pr unit volum A ns C i v At 5k probbility fg n lctro t Frmi nrgy ½. probbility f g lctron t sm nrgy lvl t k A A ns D ½ B zro C ¼ D ½ b Obt xprssion for lctricl con uctivity on bs fr lctron ory m tls. (8 mrks C onsir conucr subjct n lctric fil E. If crg, m mss n v i s vlocity n lctron, n forc on n lctron F = E Also from Nwn s lws motion, mv F D prtmnt Pysics, S JBIT, Bnglor - 6 P g 4

43 E ngrg Pysics:PHY mv E o r v = E m t I ntgrtg bot v E t m v = E m t sis I f tim trvrs tkn b collion tim τ n v tkn s vrg vlocity ( v v E m W v σ = J E ; wr J currnt nsity. W r But J = I A I currnt n A r cross sction conucr rfor σ = I AE tnc trvll unit tim v V olum swpt = v A i n unit tim. If crg on lctron n numbr lctron pr unit volum. n quntity o f crg crossg givn pot conucr pr unit r pr unit tim givn by currnt I = n va σ = nva nv AE E i.. σ = σ = n E n τ m E m τ D prtmnt Pysics, SJBIT, Bnglor-6 Pg 4

44 E ngrg Pysics:PHY c. Expl Frmi nrgy n Frmi fcr. ( 4 Mrks F rmi nrgy : In mtl vg N ms, r r N llow nrgy lvls c bn. In nrgy bn nrgy lvls r sprt by nrgy iffrncs. It c rctrtic mtril. Accorg Puli s xclusion prc ipl, c nrgy lvl cn ccommot mximum two lctrons, on wit sp up n or wit sp own. fillg up nrgy lvls occurs from lowst lvl. nxt pir lctrons o ccupis nxt nrgy lvl n so on till ll t lctrons mtl r ccommot. Still numbr llow nrgy lvls, r lft vcnt. T pictur wn r no xtrnl nrgy supply for lctrons. nrgy igst occupi lvl t bsolut z ro tmprtur (K cll Frmi nrgy n nrgy lvl cll Frmi lvl. It i s not by 'E f' F rmi fcr : lctrons nrgy lvls for blow Frmi lvl cnnot bsorb t nrgy bov bsolut zro tmprtur. At orry tmprtur bcus t r r no vcnt nrgy lvls bov Frmi lvl wic lctrons coul gt ftr bsorbg rml nrgy. Toug xcittions r rnom, tributions lctrons vrious nrgy lvls will b systmticlly govrn by stti s ticl function t sty stt. probbility f(e tt givn nrgy stt wit nrgy E occupi t sty t mprtur T givn by f ( E ( E E F kt f (E i s cll frmi fcr. Frmi fcr probbility occuption givn nrgy stt for mtril rml quilibrium. T pnnc Frmi fcr on tmprtur n nrgy s sown figur. D prtmnt Pysics, S JBIT, Bnglor - 6 P g 4 4

45 E ngrg Pysics:PHY. Clcult probbility n lctron occupyg n nrgy lvl.v bov E- E =.V f i f(e i i t K? f(e t 4k? FE E E kt F FE t K FE E E kt F FE t 4K J un/july. - i If mobility n i n mtl crss rstivity A Dcrss B Incrss C Rms constnt Ans A Dcrss D Non s. i i tmprtur pnnc lctricl rstivity mtl A ρ α /T B ρ α / T C ρ α T D ρ α T A ns A ρ α / T i ii Zro prcntg probbility probbility for - occupy nrgylvl bov Frmi nrgy lvl t T = k A E + EF B E = EF C E > EF D E < EF Ans E = E B F i v If Frmi nrgy mtl.4v, Frmi tmprtur mtl pproximtly A.6 k B. 6 4 k C. 6 5 k D. 6 6 k Ans B. 6 4 k b. Dcuss vrious rwbcks clssicl fr lctron ory mtls. Wt r t ssumptions m quntum ory ovrcom s? (6 Mrks D rwbcks clssicl fr lctron ory. E lctricl n rml conuctivitis cn b xpl from clssicl fr lctron ory. It fils ccount fcts suc s spcific t, tmprtur pnnc c onuctivity n pnnc lctricl conuctivity on lctron concntrtion. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 45

46 E ngrg Pysics:PHY S pcific t: molr spcific t gs t constnt volum Cv = R As pr clssicl fr lctron ory, fr lctrons mtl r xpct bv just s gs molculs. Tus bov qution ols goo qully wll for fr lctrons lso. But xprimntlly it ws foun tt, contribution spcific t mtl by its conuction lctrons ws CV= -4 RT wic for lowr tn xpct vlu. Also ccorg ory spcific t pnnt tmprtur wrs xprimntlly spcific t proportionl tmprtur. T mprtur pnnc lctricl conuctivity: E xprimntlly, lctricl conuctivity σ vrsly proportionl tmprtur T. i.. σ xp α /T A ccorg ssumptions clssicl fr lctron ory ( KT m v t v t KT m i.., v t T T mn collion tim τ vrsly p roportionl rml vlocity. i.. v t or τ α T B ut σ = σ α τ n m o r σ α T ( F rom qutions ( & ( it clr tt xprimntl vlu not grg wit t ory. D pnnc lctricl conuctivity on lctron concntrtion: A ccorg ory σ = n ; wr n lctron c oncntrtion, rfor σ α n m Consir zc n cmium wic r ivlnt mtls. ir lctricl conuctivitis r.9 7 / Ωm n.5x 7 / Ωm. s r muc lssr tn tt monovlnt mtls D prtmnt Pysics, SJBIT, Bnglor-6 Pg 46

47 E ngrg Pysics:PHY coppr n silvr. vlus wic r 5.88x 7 /Ω m n 6.x 7 / Ωm rspctivly. lctron concntrtions for zc n cmium r. 8 / m n / m wic r muc igr tn tt for coppr n silvr, vlus wic r / m n / m rspctivly. Hnc clssicl fr lctron ory fils xpl pnnc σ on lctron concntrtion. A ssumptions Quntum Fr Elctron ory:. nrgy lvls fr lctrons r quntiz.. fr lctrons oby P u li s xclusion prcipl.. tribution lctrons vrious nrgy lvls obys Frmi Dirc quntu m s tttics. 4. conuction lctrons r ssntilly fr prticls conf pysicl bounry t mtl 5. lctron l ctron trction n long rng lctron ponon trction r ngligibl. Only wn n lctron vry clos st ion, scttrg lik i ntrctions mk lctron motion quit rnom c. Expl nsity stts? Driv xprss ion for lctricl conuctivity trms m n collion tim. ( 6 Mrks T r r lrg numbrs llow nrgy lvls for lctrons soli mtrils. A group o f nrgy lvls clos c or cll s nrgy bn. Ec nrgy bn spr ovr f w lctron - volt nrgy rngs. In m m volum mtril, r will b mor tn t ousn billion prmitt nrgy lvls n nrgy r ng fw lctro n - volts. Bcus t, nrgy vlus ppr b virtully contuous ovr bn spr. To rprsnt it tcniclly it stt s nsity nrgy lvls. pnnc nsity nrgy lvls o n nrgy not by g(e. grp s o ws vrition g(e vrsus E. It cll nsity stts function. It numbr llow nrgy lvls pr unit nrgy trvl bn ssocit wit mtril unit volum. In n nrgy bn s E c ngs g(e lso cngs. D prtmnt Pysics, S JBIT, Bnglor - 6 P g 4 7

48 E ngrg Pysics:PHY E xprssion for lctricl conuctivity trms mn collion tim. C onsir n nrgy bn spr n nrgy trvl btwn E n E. Blow E n bov E r r nrgy gps. g(e rprsnts nsity stts t E. As E smll, it i s ssum tt g(e constnt btwn E n E+E. nsity stts rng E n ( E+E not by g(ee. i.. g (EE = 8 E m E I t clr g(e proportionl E i n trvl E Consir conucr subjct n lctric fil E. If crg, m mss n v i s vlocity n lctron, n forc on n lctron i s F = E Also from Nwn s lws motion, mv F v m E o r v = I ntgrtg bot sis v E t m v = I f tim trvrs tkn b collion tim τ n v tkn s vrg vlocity ( v v E m J W v σ = E ; wr J currnt nsity. But J = A Wr I currnt n A r cross sction c onucr D prtmnt Pysics, S JBIT, Bnglor - 6 P g 4 8

49 E ngrg Pysics:PHY T rfor σ = AE tnc trvll unit tim v Volum swpt = v A i n unit tim. If crg on lctron n numbr lctron pr unit volum. n quntity o f crg crossg givn pot conucr pr unit r pr unit tim givn by currnt I = n va σ = nva nv AE E i.. σ = σ = n E n τ m E m τ. Frmi lvl potssium.v. Wt r nrgis for wic p robbilitis occupncy t K r.99 n.5? ( 4 Mrks E =.V =. - 9 J F 6 E =? E =? wn f(e =.99 wn f(e =.5 T = K C s f (E = E E F k T +.99 = E = E E = - E. 6 9 = log( E = J E =.98 V D prtmnt Pysics, SJBIT, Bnglor-6 Pg 49

50 E ngrg Pysics:PHY D ilctric UNIT-I V & Mgntic Proprtis mtrils J un/july i polriztion tt occur frquncy rng H z A ionic B Elctronic C Orinttionl D Spc crg Ans A ionic ii If two lctric crgs q r sprt by tnc L, ipol momnt s ystm A q/l B L/q C ql D q/l A ns C ql i ii Coos corrct rltion A E = Є (Єr P B P = Є (Єr E C Єr = K- D D = Є Ans B P = Є (Єr E ( Єr i v If tnc btwn plts cpcir crs oubl, cpcitnc A oubl B Incrs four tims C Hlv D constnt Ans C Hlv b. Driv qution for trnl fil cs soli or liqui ilctric for on imnsion. (8 M rks I ntrnl or locl fil rsultnt ppli fil n fil u ll surroung ipols on n m soli or liqui ilctric mtril. Consir n rry quivlnt mic ipols rrng prlll irction uniform fil E. Lt b tr- mic tnc n µ b ipol momnt c ipol. E T tl fil E i t x sum ppli E n fil u ll ipols E E i E E ( E T i s foun s follows componnts lctric fil t P u ipol polr form givn by D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

51 E ngrg Pysics:PHY E r cos r n E s 4 r wr μ i s ipol momnt Sc =r & = E r & E = Fil t x u A = E r + E = Similrly Fil t X u A = T nt fil t X u A & E A = = T nt fil t X u B & s E = nt fil t B C i X u C & s E = i tl fil E t X u ll ipols E = E + E + E +... = =... D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

52 E ngrg Pysics:PHY = n n E. = n n.. trnl fil Ei = E + ( 4 E i = E +. E Wr = E, i s lctric polrizbility ipols. T qution for trnl fil tr imnsions givn by E i = E + p, wr p ipol momnt pr unit volum for mtril. i s trnl fil constnt. F or cubic lttic trnl fil cll Lorntz fil. E L orntz = E + p wr c. Driv Clusius-Mossoti qution for - imnsionl cubic s oli ilctric. (8 Mrks Consir ilctric mtril ilctric constnt r. ipol momnt / unit volum= N Wr N numbr ms pr unit volum, ipol momnt c m. If Ei trnl fil n i s lctronic polrizbility ms, n = E i ipol momnt / unit volum = N E i i.., polriztion p= N E i E i = But p = ε (ε r E w r E ppli fil W v E = p ( Nα p ε (ε r E i = E + p ( ε ( wr i s trnl fil constnt From Equtions (, ( n ( p p = Nα ε (ε r + γ p ε = Nα ε (ε r + γ D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

53 E ngrg Pysics:PHY Tkg trnl fil mtril b Lorntz fil γ = T Clusius- M ossotti qution. = Nα ε (ε r + = ε + ε r (ε r ε = ε r + Nα (ε r (ε r (ε r + = Nα ε D EC 9/JAN 4. i wt cngs cpcitnc cpcir occurs if ilctric mtril R mov A Incrss B Dcrss C rms sm D non s A ns B Dcrss i i rltion btwn B, M n H A H=µ ( M+B B M= µ ( H+B C B= µ ( H+M non s ns C B=µ ( H+M A i ii Sulpur n lmntl soli ilctric mic wigt.7 n nsity.7x kg/m. numbr ms pr unit volum for sulpur A.89x /m B.89x / m c 9. x /m D non s 8 Ans A.89x / m i v Wic on followg ncssrily pizolctric mtril? A L B mic C iron D Qurtz A ns D Qurtz b. Wt mnt by polriztion mcnm ilctrics? Dcuss ny tr iffrnt p olriztion mcnms ilctrics n ir frquncy pnnc (8 Mrks Polriztion: Wn n lctric fil ppli ilctric mtril, r plcmnt c rg prticls lg formtion ipols n nc ipol momnt wic cll p olriztion ilctric. TYPES OF POLARIZATION: E lctronic Polriztion, I onic Polriztion O rintl polriztion n 4 S pc crg polriztion. T r r four iffrnt typs polriztion. y r, E lctronic polriztion : r ppli xtrnl lctric fil. T g ts polriz. plcmnt positiv n ngtiv crgs u ls vlopmnt ipol momnt. Tus mtril D prtmnt Pysics, SJBIT, Bnglor-6 Pg 5

54 ngrg Pysics:PHY E Pysics, prtmnt D Bnglor JBIT, S - 6 g P 4 5 polriztion lctronic T N r N r W. volum unit pr ms numbr t : Polriztion onic I l xtrn ppli u ions opposit jcnt plcmnt r plcmnt crs or crs r ions loction on Dpng fil. lctric ls T ions. f o. mtril momnt ipol lopmnt v : polriztion rinttion O orint r ipols fil, xtrnl bsnc In c fil xtrnl prsnc In zro. momnt ipol nt rnomly, so rottion unrgo ipols vlops mtril Tus fil. irction rorint s crs wit crss n pnnt tmprtur It polriztion. lctricl mprtur. t by givn t I kt µ- ipol rmnnt p, omnt m k- T constnt, oltzmnn B -. mprtur T

55 E ngrg Pysics:PHY S pc crg polriztion: It occurs multips ilctric mtrils wr r cng rstivity btwn iffrnt pss. At ig tmprturs wn mtril subjct lctric fil crgs r sttl t trfc u sun rop conuctivity cross bounry. Opposit ntur crgs r sttl t opposit prts low rstivity ps. T us mtril cquirs ipol momnt low rstivity ps. Spc crg p olriztion ngligibl most ilctrics. c. Dscrib r n st mgntic mtrils. (4 Mrks Hr mgntic mtrils v lrg r ystrs curv. y v lrg vlu rmnnt uction wn mgntizg fil rmov. y r wily us p rmnnt mgnts. y v followg proprtis: H ig rmnnt mgntiztio n. H ig corcivty. H ig sturtion flux nsity. 4 L ow itil prmbility. 5 H ig ystrs nrgy loss. 6 H ig prmbility. 7 E y currnt loss low for crmic typ l rg for mtllic typ. n H r mgntic mtrils r wily us mkg prmnnt mgnts. Mgnts r us mgntic sprtion, mgntic tcrs, ntrtmnt lctronic ys, spkrs, uio s ystm, msurg mtrs. E x: Alnico lloy (n lloy Al, Ni, Co, Cu & F Smrium c oblt lloy. Tungstn stl lloy. 4 Pltum coblt lloy. 5 Invr. S t Mgntic Mtrils, ir crctrtic proprtis n pplictions: D prtmnt Pysics, SJBIT, Bnglor-6 Pg 55

56 E ngrg Pysics:PHY S t mgntic mtrils v smll r ystrs curv. y r not us prmnnt m gnts. y v foll owg proprtis: L ow rmnnt mgntiztion. L ow corcivty. L ow ystrs nrgy loss. 4 H ig itil prmbility. 5 H ig prmbility. 6 H ig suscptibility. 7 L ow y currnt loss. S t mgntic mtrils r us cors trnsformrs, cors T rnsformrs n ucrs r us ustris n ntrtmnt lctronics. ucrs. E x: Prmlloy (lloy F & Ni Silicon - I ron lloy. Pur iron 4 Amorpous frrous lloys (lloy o f F, Si & B Iron- N ickl lloys r us for uio frquncy pplictions. Frrits r us for ig frquncy pplictions wr r r low powr rquirmnts. Iron S ilicon lloys r us for low frqunc y n ig powr pplictions. - 4 m. n lmntl soli ilctric mtril s polrbility 7 F.Assumg i ntrnl fil b Lorntz fil, clcult ilctric constnt for mtril, if it s 8 / m. ( 4 Mrks Givn: α = 7 4 Fm, N = 8 / m, ε r =? ε r (ε r + = ε = ε r + Nα (ε r ε r =. 96 ε r =.. 7 ε r M y/jun 4. i For givn ilctric, lctron polriztion, α A Incrss wit tmprtur B crss wit tmprtur C Inpnnt tmprtur D My crs crs wit tmprtur Ans C Inpnnt tmprtur D prtmnt Pysics, SJBIT, Bnglor-6 Pg 56

57 E ngrg Pysics:PHY i i If two pot crgs opposit signs +q n q r sprt by tnc l, lctric ipol momnt A q/l Bq/ l C [(q(-q]/ l D ql Ans D ql iii polriztion tt occurs frquncy rng A Elctronic B Orinttion C Ionic D Spc crg Ans A Elctronic iv For frromgntic substnc, Curi- W s lw givn by A χ = C/T B χ = C/( T- θ C χ = ( T- θ /C D χ = C/(T+ θ Ans b χ = C/(T-θ b. Wt trnl fil? Driv n xprssion for trnl fil cs on- imnsionl rry ms solis or liquis. ( 6 Mrks Intrnl or locl fil rsultnt ppli fil n fil u ll surroung ipols on n m soli or liqui ilctric mtri l. 6 H z Consir n rry quivlnt mic ipols rrng prlll uniform fil E. Lt b tr- mic tnc n µ b ipol. ipol irction momnt c T tl fil E i t x sum ppli E n fil u ll ipols E E i E E ( E T i s foun s follows componnts lctric fil t P u ipol polr form givn by E r cos r s n E 4 r D prtmnt Pysics, SJBIT, Bnglor-6 Pg 57

58 E ngrg Pysics:PHY wr μ i s ipol momnt Sc =r & = E r & E = Fil t x u A = E r + E = Similrly Fil t X u A = T nt fil t X u A & A E= = T T nt fil t X u B & s E = B C i nt fil t X u C & s E = i tl fil E t X u ll ipols E = E + E + E +... = =... = n n E. = n n. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 58

59 E ngrg Pysics:PHY. trnl fil Ei = E + ( 4 E i = E +. E Wr = E, i s lctric polrizbility ipols. T qution for trnl fil tr imnsions givn by E i = E + p, wr p ipol momnt pr unit volum for mtril. i s trnl fil constnt, F or cubic lttic trnl fil cll Lorntz fil. E L orntz = E + p wr c. Wt r st mgntic mtrils? Dcuss ir proprtis. ( 4 Mrks St mgntic mtrils v smll r ystrs curv. y r not us p rmnnt mgnts. y v followg proprtis: L ow rmnnt mgntiztion. L ow c orcivty. L ow ystrs nrgy loss. 4 H ig itil prmbility. 5 H ig prmbility. 6 H ig suscptibility. 7 L ow y currnt loss. St mgntic mtrils r us cors trnsformrs, cors T rnsformrs n ucrs r us ustris n ntrtmnt lctronics. ucrs. E x: Prmlloy (lloy F & Ni Silicon - I ron ll oy. Pur iron 4 Amorpous frrous lloys (lloy F, Si & B Iron- N ickl lloys r us for uio frquncy pplictions. Frrits r us for ig frquncy pplictions wr r r low powr rquirmnts. Iron S ilicon lloys r us for low frquncy n ig powr pplictions.. A soli ilctric mtril s lctronic polrizbillity 7x Fm. If it cubic 8 structur clcult rltiv prmittivity mtril. It s x ms/m. ( 4 Mrks Givn: α = 7 4 Fm, N = 8 / m, ε r =? -4 D prtmnt Pysics, SJBIT, Bnglor-6 Pg 59

60 E ngrg Pysics:PHY ε r (ε r + = ε = ε r + Nα (ε r ε r =. 96 ε r =.. J nury 7 ε r i Cos corrct rltion- A E = ε( ε r -p B D = ε( ε r -E C P = ε( ε r - E D ε r= χ- Ans C P = ε ( r - E ε i i Elctronic polriztion A Dcrss wit crss i n tmprtur B crss wit tmprtur C pnnt t mprtur D my crs or crs wit tmprtur. A ns C pnnt tmprtur i ii Hystrs loss occur wn mg. Mtril subjct A DC voltg B AC voltg C bot AC n DC voltg A ns B AC voltg D non s i v rlti v prmbility for imgntic mtrils A Sligtly grtr tn on B zro C lss tn on t n on. A ns C lss tn on D vry muc grtr b. Obt xprssion for trnl fil solis ( 8 Mrks Intrnl or locl fil rsultnt ppli fil n fil u ll surroung ipols on n m soli or liqui ilctric mtril. C onsir n rry quivlnt mic ipols rrng prlll uniform fil E. Lt b tr- mic tnc n µ b ipol. ipol irction momnt c D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

61 E ngrg Pysics:PHY T tl fil E i t x sum ppli E n fil u ll ipols E E i E E ( E T i s foun s follows componnts lctric fil t P u ipol polr form givn by E r cos r n E s 4 r wr μ i s ipol momnt Sc =r & = E r & E = Fil t x u A = E r + E = Similrly Fil t X u A = T nt fil t X u A & E A = = D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

62 E ngrg Pysics:PHY T T nt fil t X u B & s E = B C i nt fil t X u C & s E = i tl fil E t X u ll ipols E = E + E + E +... = =... = n n E. = n n.. trnl fil Ei = E + ( 4 E i E +. E = Wr = E, i s lctric polrizbility ipols. qution for i ntrnl fil tr imnsions givn by E i = E + p, wr p ipol momnt pr unit volum for mtril. i s trnl fil constnt. F or cubic lttic trnl fil cll Lorntz fil. E L orntz = E + p wr D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

63 E ngrg Pysics:PHY c. Dtgu btwn r n st mgntic mtrils. (5 Mrks Hr mgntic mtrils v lrg r ystrs curv. y v lrg vlu rmnnt uction wn mgntizg fil rmov. y r wily us p rmnnt mgnts. y v followg proprtis: 8 H ig rmnnt mgntiztio n. 9 H ig corcivty. H ig sturtion flux nsity. L ow itil prmbility. H ig ystrs nrgy loss. H ig prmbility. 4 E y currnt loss low for crmic typ l rg for mtllic typ. n H r mgntic mtrils r wily us mkg prmnnt mgnts. Mgnts r us mgntic sprtion, mgntic tcrs, ntrtmnt lctronic ys, spkrs, uio s ystm, msurg mtrs. E x: Alnico lloy (n lloy Al, Ni, Co, Cu & F Smrium c oblt lloy. Tungstn stl lloy. 4 Pltum coblt lloy. 5 Invr. S t Mgntic Mtrils, ir crctrtic proprtis n pplictions: St mgntic mtrils v smll r ystrs curv. y r not us p rmnnt mgnts. y v foll owg proprtis: 8 L ow rmnnt mgntiztion. 9 L ow corcivty. L ow ystrs nrgy loss. H ig itil prmbility. H ig prmbility. H ig suscptibility. 4 L ow y currnt loss. S t mgntic mtrils r us cors trnsformrs, cors T rnsformrs n ucrs r us ustris n ntrtmnt lctronics. ucrs. E x: Prmlloy (lloy F & Ni Silicon - I ron lloy. Pur iron 4 Amorpous frrous lloys (lloy F, Si & B Iron- N ickl lloys r us for uio frquncy pplictions. Frrits r us for ig frquncy pplictions wr r r low powr rquirmnts. Iron S ilicon lloys r us for low fr quncy n ig powr pplictions. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 6

64 E ngrg Pysics:PHY. F polriztion prouc crystl by n lctric fil strngt 5Vm i f it s ilctric constnt 6. ( Mrks givn: E= 5Vm -, ε r= 6, P=? P = ε ( r - E ε P = 8.854x - ( 6-5 P =.x -8 cm - J un/july i For frromgntic substncs, Curi-W lw givn by A ψ = C/T B ψ = C /(T-θ C ψ = ( T- θ/c D C /( T- θ Ans D C /(T- θ ii Clusius-M ossoti qution osn t ol for A gss B liquis A ns A gss C crystll solis D non s iii frromgntic m tril losss spontnous polrtion t A room tmprtur B K C TCK D K ns C T K A C i v In ystrs,polriztion A movs wit lctric fil B lgs b lctric fil C lctric fil D non s A ns D non s b. Expl trm trnl fil? Driv n xprssion for trnl fil cs on- imnsionl rry ms i- lctric solis. (7 Mrks I ntrnl or locl fil rsultnt ppli fil n fil u ll surroung ipols on n m soli or liqui ilctric mtril. - Consir n rry quivlnt mic ipols rrng prlll uniform fil E. Lt b tr- mic tnc n µ b ipol. ipol irction momnt c D prtmnt Pysics, SJBIT, Bnglor-6 Pg 64

65 E ngrg Pysics:PHY T tl fil E i t x sum ppli E n fil u ll ipols E E i E E ( E T i s foun s follows componnts lctric fil t P u ipol polr form givn by E r cos r s n E 4 r wr μ i s ipol momnt Sc =r & = E r & E = Fil t x u A = E r + E = Similrly Fil t X u A = T nt fil t X u A & E A = = T nt fil t X u B & s E = nt f il t B C i X u C & s E = i tl fil E t X u ll ipols E = E + E + E +... D prtmnt Pysics, SJBIT, Bnglor-6 Pg 65

66 E ngrg Pysics:PHY = =... = n n E. = n n.. trnl fil Ei = E + ( 4 E i E +. E = Wr = E, i s lctric polrizbility ipols. T qution for trnl fil tr imnsions givn by E i = E + p, wr p ipol momnt pr unit volum for mtril. i s trnl fil constnt. F or cubic lttic trnl fil cll Lorntz fil. E L orntz = E + p wr c. Driv Clusius- M ossoti qution. ( 4 Mrks Consir ilctric mtril ilctric constnt r. ipol momnt / unit volum= N Wr N numbr ms pr unit volum, ipol momnt c m. If Ei trnl fil n lctronic polrizbility ms, n = E i ipol momnt / unit volum = N E i i.., polriztion p= N E i E i = But p = ε (ε r E w r E ppli fil p ( Nα D prtmnt Pysics, SJBIT, Bnglor-6 Pg 66

67 E ngrg Pysics:PHY W v wr i s trnl fil constnt From Equtions (, ( n ( E = p ε (ε r E i = E + p ( ε p p = Nα ε (ε r + γ p ε = Nα ε (ε r + γ ( Tkg trnl fil mtril b Lorntz fil γ = T Clusius- M ossotti qution. = Nα ε (ε r + = ε + ε r (ε r ε = ε r + Nα (ε r (ε r (ε r + = Nα ε. Sulpur n lmntl soli i-lctric wos i- lctric constnt.4. Clcult lctronic polrizbility if its nsity.7 kg/ m n mic wigt.7. (5 Mrks g ivn: ε o =. 4, D=.7gm/cc=.7x kg/m, Amic wigt=.7, α =? S olution : Sc crystl structur sulpur cubic w cn pply Clusius- M ossotti qution, (ε r (ε r + = Nα. ε α = ε N [(ε r ] ( (ε r + N ow, N numbr ms/unit volum cn b writtn s, N= N AX XD mic wigt N = X. 7X. 7 8 N=. 89X / m. B y substitutg vlus for vrious prmtrs,q( bcoms α = X8. 54 α=.5x 8 X [.4 ]. 89X Fm. Elctronic polrizbility sulpur.5x -4 Fm. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 67

68 E ngrg Pysics:PHY UNIT-V I L ASERS J un/july 9 5. i Pumpg procss us io lsr A opticl pumpg B Forwr b C Elctric crg D Non s A ns B Forwr b i i lif tim n m xcit stt orr A millcon B fw scons C nnoscons D unlimit A ns C nnoscons i ii purpos opticl rsonr lsr A provi covr ctiv mium B provi pt for ms C provi slctivity pons D sn lsr spcifi irction. Ans C provi slctivity pons iv In H-N lsrs, rtio H- N o rr A : B : C : D : Ans C : b. Wit lp nrgy lvl igrm, scrib construction n workg H- N lsr. ( 8 Mrks It consts fus Qurtz tub lngt bout m n imtr.5 cm. tub fil wit mixtur lium t prssur mm mrcury n non t prssur p f. mm mrcury rtio :. Two lctros r provi tub wic r connct ig voltg c supply. ns tub r sl wit trnsprnt mtril qurtz n r curv mirrors M n M r fix t two ns tub. On D prtmnt Pysics, SJBIT, Bnglor-6 Pg 68

69 E ngrg Pysics:PHY m irror prtilly silvr n or fully silvr. lsr bm trnsmitt troug t prtilly silvr mirror. W orkg: Wn crg c voltg ppli cross lctros, fst movg lctros r prouc u crg gs. fst movg lctrons colli wit mor bunnt Hlium gs ms. As rsult lium ms will b xcit mt stbl s stts S n. T procss collion lctrons wit lium ms cll collion o f first k. It cn b rprsnt s H + * + H Wr n r nrgis lctron bfor n ftr collion rspctivly n H* nrgy xcit n lium m mt stbl stt. xcit lium ms collis wit non ms groun stt. As rsult non ms rs its mt stbl nrgy lvls s n s n lium ms coms own its groun stt. T procss cll collion scon k n givn by qution. H* + N N * + H. Tus s n s mt stbl stts non ms r wll popult bcus long rlxtion tim. Hnc popultion vrsion built up btwn its nrgy lvls s n P, s n P, n s n P r spctivly s sown \ fig. rfor tr lsr trnsr tks p lc contuously y r. S r gion P trnsition: Givg lsr ligt wvlngt 9 A o ( four forc. s P trnsition yilg promnt r lsr ligt wv lngt 68 A o n D prtmnt Pysics, SJBIT, Bnglor-6 Pg 69

70 ngrg Pysics:PHY E Pysics, prtmnt D Bnglor JBIT, S - 6 g P 7 A 5 lngt wv f ligt lsr P trnsition yilg s. o. Out cvity. lsr cll mirrors mium n systm contg ctiv mium, ctiv possibl r wic trnsitions lsr ny m sir bm sr l or wil mirrors two btwn tnc justg by pp b coul Wvlngt rition. tt for cvity rsonnt cll cvity lsr Hnc supprss. r ritions w corrspong ligt csr tir us T A 68 vlngt o rsonnt mplifi H output contuous n vity c - systm. trnsmitt from lsr N Mrks (4 usg lsr. tmospr pollutnts on msurmnt not Writ. c oxis nitrogn, clu wic tmospr pollutnts typs vrious r r convntionl In mttrs. prticult numbr n ioxi sulpur monoxi, crbon c n igts sir t collct r tmospr smpls cniqu, t micl t Wtvr pollutnts. composition out f out crri nlys lsr tcniqu, lsr Wrs t. tim rl not mto t obt rquir scnng by vrition nsity tmospric nss s lctronic n rgion locl t. tim rl wic t, yil procsss t s wy us m lsr pollutnt, msurmnt for lsr ppliction In rfrr tn it Hnc us. systm Rngg n Dtction (Rio ADAR R s prt trnsmittg LIDAR systm, In tcniqu. Rngg n Dtction LIDAR (Ligt n tcr po mirror, concv consts prt rcvg n lsr puls consts procssor. t W plcs t scttrg unrgos bm lsr out, crri r msurmnts n mttr. prticult concntrtion igr u congstion r wr tmospr cong tnc mirror. concv by rciv ligt scttr ck b from stion n msion puls btwn ly tim bs on clcult sttion msurg sttion, roun spc scnng By ligt. scttr bck rcption vrticl iffrnt for mpp b cn pollutnts oncntrtion c tmospr. sction prticls. scttrg ntur rgrg formtion ny provi cnnot mto T scttrg ntur rgrg formtion provi osn t tcniqu t As r tcniqus mor followg two rticls p ollow. f. : bsorption Tcniqu A ollct C tmospr A

71 E ngrg Pysics:PHY lsr bm pss troug smpl collct from tmospr. trnsmitt bm rcor wit tcr. Wil bm psss troug smpl, it unrgos bsorption vrious grs png upon prsnc xct typ cmicl substnc tt prticult compr. Dpng upon crctrtic bsorption pttrn obsrv rcorg, composition tmospric pollutnts coul b trm. R mn Bck Scttrg: Sc lsr igly monocromtic, w xpct s only on l spctrum. But u Rmn scttrg spctrum, svrl ls low tnsity will b sn symmtriclly on ir si cint l. r wvlngt v lus will b clos tt cint ligt. s itionl spctrl ls r cll s si bns. Diffrnt gsss prouc iffrnt si bns. sifts frquncis r trm s Rmn sifts. Tus by obsrvg Rmn spctrum bck scttr ligt t gs smpl on cn ssss composition pollutnts. R mn Bck Scttr Spctrum. In lsr bm wit powr pr puls mw, puls lsts for ns. If numbr 7 p ons mitt pr puls.49 x, clcult wvlngt lsr. (4 Mrks G ivn: P= x - P t = nc λ w, or t = x λ = nc pt -9 s, n=.49 7 λ = λ = m 9/JAN 5. i lif tim n m t orry xcit stt orr A fw mili scon Afw nno scon Afw micro scon DUnlimit A ns Afw nno scon i i A rltion btwn Ests s cofficint A n B 8 λ B 8 γ 8 γ 8 γ C D c c c c A ns C 8 γ c D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

72 E ngrg Pysics:PHY iii numbr mos stng wvs rsonnt cvity lngt m, if H- n 6 6 lsr opr tg t wvlngt 68Å A.4x B.58x C.6x 8 D Non s A ns D Non s iv from brokn ologrm wic % origl, if rconstruction img b g on, n A only % formtion objct cn b obt B complt formtion objct obt C no formtion objct cn b obt D non s A ns B complt formtion objct obt b. Obt n xprssion for nrgy nsity rition unr quilibrium conition t rms Est cofficint. (7 Mrks Wn rition frquncy v cint on n m stt E. Wic stimult m mk ownwr trnsltion n cuss msion stimult pons. rt stimult msion N. Rt stimult msion = BU v N Wr B constnt proportionlity cll Est cofficint stimult msion. An N No, nsity igr nrgy stt E. At rml quilibrium. R t bsorption = (Rt spontnous msion + (Rt stimult ms ion B N U v = AN + B N U v U v ( BN B M = A N U v = ( B AN N B N B A N B N B N N A U v ( B B N B N B y Boltzmnn low w v N N E E KT v KT N N v KT D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

73 E ngrg Pysics:PHY ( 8v C U v = C omprg A U v B B v. B KT ( v KT ( ( from Plnck s lw Eqution ( n (. A = B 8 C v n B B =. Or B = B T mns tt probbility uc bsorption qul probbility stimult msion. Lt A T n = A n B = B. t rml quilibrium qution for nrgy nsity. U v A v B KT c. Dscrib rcorg n rconstruction procss ologrpy, wit lp s uitbl i grm. ( 5 Mrks R corg o f img n objct by wv front ivion tcniqu Expn cornt lsr bm from lsr sourc obt. A portion it m i ncint on mirror n or portion m cint on objct s sown fig. Pogrpic plt plc t suitbl position so tt it rcivs ligt rflct from bot mirror n objct. ligt rflct from mirror form pln wvfront. It D prtmnt Pysics, SJBIT, Bnglor-6 Pg 7

74 E ngrg Pysics:PHY i s cll rfrnc bm. ligt rflct from c pot on objct form spric l wvfront. It cll objct bm. Tus trfrnc ffcts two bms r r cor on pogrpic plt. As spricl wv trsct pln wv circulr zons, trfrnc p ttrn co nsts concntric circulr rgs vg constructiv n structiv trfrnc. I t cll G bor Zon plt. Hologrm consts numbr suc zon plts. cntr c plc from o r. In rcor pttrn n igbour g zons ovrlp c or n bcom pprnt, onc film vlop. It cll ologrm. R corg img n objct by mplitu ivion tcniqu : Expn cornt l sr bm from lsr sourc obt. It m cint on bm splittr. T bm splittr rflcts portion ligt wic cint on mirror. trnsmitt l igt from bm splittr cint on objct. rflct pln w v fron t from t m irror n rflct spricl wvfron ts from iffrnt pots on objct unrgos trfrnc on pogrpic plt kpt t suitbl plc. trfrnc frgs r rcor on pogrpic plt. vlop pogrpic plt bcoms ologrm o f objct. R construction img from ologrm: Origl Lsr bm m cint on ologrm sm irction s rfrnc bm ws cint on it t tim rcorg. bm unrgos rfrction t ologrm. Sconry wvl ts origtg from c constitutg zon plt trfr constructivly n gnrt rl img on trnsmsion si n virtul img on i ncint si. D prtmnt Pysics, S JBIT, Bnglor - 6 P g 7 4

75 E ngrg Pysics:PHY. A ruby lsr mits puls ns urtion wit vrg powr pr puls bg kw. 5 If numbr pons c puls x, clcult wv lngt p ons. ( 4 Mrks 6 5. Givn: P=.x w, t=ns, N=6.98x, N E n E= p c E nc pt λ= 698Å M y/jun 5. i Wic followg not lsr proprty? A Higly monocromtic B Hig irctionlity C Vry nrrow bn wit D igly ivrgnt Ans D igly ivrgnt i i lif tim n m xcit stt orr A millcon B fw C nnoscons D unlimit Ans C n noscons iii Pumpg tcniqu us H- N gs lsr A Forwr b B Opticl pumpg C Elctricl crg D Hig jction currnt Ans D Elctricl crg iv D img n objct c onstruct by ologrm procss Intnsity rcorg b Ps formtion rcorg c Bot ps n tnsity formtion rcorg Trnsmsio n n rflction rcorg A ns c Bot ps n tnsity formtion rcorg b. Dcuss possibl wys troug wic rition n mttr trction tks plc. ( 8 Mrks I nuc bsorption/ Stimult bsorption/bsorption: I nuc bsorption bsorption n cint pon by systm s rsult wic systm lvt from lowr nrgy stt igr stt, wr iffrnc nrgy two stts nrgy pon. C onsir systm vg two nrgy stts E n E, E > E. Wn pon nrgy cint on n m t lvl E, m gos igr nrgy lvl by bsorbg nrgy. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 75

76 E ngrg Pysics:PHY W n n m t groun lvl ( E, if n lctromgntic wv suitbl frquncy i s ppli m, r possibility gttg xcit t o igr lvl ( E. cint p on bsorb. It rprsnt s A m + Pon A m * T frquncy bsorb pon = ( E -E /. S pontnous Emsion: T msion pon by trnsition systm from igr nrgy stt low r nrgy stt witout i n xtrnl nrgy cll spontnous msion. L t E n E b two nrgy lvls mtril, suc tt E > E. E i s groun lvl n E t igr lvl. = E -E i s iffrnc nrgy. m t igr lvl ( E mor u nstbl s compr tt t lowr lvl (E. tim tkn by m rm xcit stt normlly vry sort (orr -8 s n it cll lif tim m. In spontnous msion m mits pon witout i ny xtrnl nrgy. It cll spontnous msion. procss r prsnt s * Am Am + Pon T pons mitt spontnous msion s imilritis. It cornt. E x: Glowg lctric bulbs, Cnl flm tc. my not v sm irction n ps S timult Emsion: Stimult msion msion pon by systm unr flunc pssg p on just rigt nrgy u wic sy stm trnsits from igr nrgy stt l owr nrgy stt. D prtmnt Pysics, S JBIT, Bnglor - 6 P g 7 6

77 E ngrg Pysics:PHY pon tus mitt cll stimult pon n will v sm ps, nrgy n irction movmnt s tt pssg pon cll stimultion pon. I nitilly t m t igr lvl E. cint pon nrgy forcs t m gt - xcit from igr lvl E t o lowr lvl E. i.. = E E cng nrgy. T cint pon stimults xcit m mit pon xctly sm nrgy s tt cint pons. mitt two pons v sm ps, frquncy, irction n polriztion wit cint pon. T k ction rsponsibl for l sg ction. * Am + Pon Am + (Pon + Pon c. D s crib construction n workg smiconucr lsr. (8 Mrks C onstruction: A scmtic igrm smiconucr lsr s sown figur. T io vry smll siz wit sis orr mm. junction lis orizontl p l n. p n botm surfcs r mtliz n Omic contcts r provi for xtrnl connction. front n rr fcs r pol. pol fcs constitut F bry - p rot rsonr. or two fcs r rougn prvnt lsg ction tt irction. ctiv rgion consts bout m ticknss. T mitt pon stimults rcombtion or crrirs. C ross sctionl viw p - n junction io lsr. W orkg: T nrgy bn igrm vily op p n - junction s sown unb conition. At rml quilibrium, Frmi lvl uniform cross junction. Bcus v ry ig opg on n - s i, Frmi lvl pus conuction bn n lct r ons o ccupy portion conuction bn lyg blow Frmi lvl. On P - si, Frmi lvl lis wit vlnc bn n ols occupy portion vlnc bn tt lis D prtmnt Pysics, S JBIT, Bnglor - 6 P g 7 7

78 E ngrg Pysics:PHY bov Frmi lvl. Wn junction forwr b lctrons n ols r jct junction rgion ig concntrtions. At low forwr currnt, lctron- ols rcombtion rsults spontnous msion pons n junction cts s LED. As t forwr currnt crs grully n wn it rcs trsol vlu crrir concntrtion junction rgion r will b lrg concntrtions lctrons wit bn. As rsult conition popultion vrsion tt nrrow rgion. T n rrow zon wic p opultion vrsion occurs cll s n ctiv rgion, t tt stg pon mitt spontnously triggrs stimult msion. T stimult lctron- ol r combtion proucs cornt rition. Enrgy lvl igrm p-n junction io lsr ( B for bg (b Aftr bg. stimult lctron- ol rcombtion cuss msion cornt rition vry nrrow bnwit. At room tmprtur, GAs lsr mits ligt wvlngt 9A n GAsP lsr rits t 65A. J nury 5. i rt uc bsorption pns on A numbr ms lowr nrgy stt C numbr ms igr nrgy stt A ns D bot A n B B nrgy nsity D bot A n B i i In smiconucr lsr mtril us A ny smi conucr B irct bn gp smi conucr C irct bn gp smi conucr D not smi conucr. A ns B i rct bn gp smi conucr i ii rquir conition civ lsr ction systm D prtmnt Pysics, SJBIT, Bnglor-6 Pg 78

79 E ngrg Pysics:PHY A Stt popultion vrsion C rsonnt cvity A ns D ll tr B xtnc mtstbl stt D ll t tr iv In rcorg img on pogrpic plt rfrnc bm n objct bm unr go t pogrpic plt. A Diffrction B rflction C trfrnc D pol riztion A ns C trfrnc b. Expl construction n workg H- Ni lsr. Wit lp suitbl igrms. (8 Mrks It consts fus Qurtz tub lngt bout m n imtr.5 cm. tub fil wit mixtur lium t prssur mm mrcury n non t prssur p f. mm mrcury rtio :. Two lctros r provi tub wic r connct ig voltg c supply. ns tub r sl wit trnsprnt mtril qurtz n r curv mirrors M n M r fix t two ns tub. On m irror prtilly silvr n or fully silvr. lsr bm trnsmitt troug t prtilly silvr mirror. W orkg: D prtmnt Pysics, SJBIT, Bnglor-6 Pg 79

80 E ngrg Pysics:PHY Wn crg c voltg ppli cross lctros, fst movg lctros r prouc u crg gs. fst movg lctrons colli wit mor bunnt Hlium gs ms. As rsult lium ms will b xcit mt stbl s stts S n. T procss collion lctrons wit lium ms cll collion o f first k. It cn b rprsnt s H + * + H Wr n r nrgis lctron bfor n ftr collion rspctivly n H* nrgy xcit n lium m mt stbl stt. T xcit lium ms collis wit non ms groun stt. As rsult non ms rs its mt stbl nrgy lvls s n s n lium ms coms own its groun stt. T procss cll collion scon k n givn by qution. H* + N N * + H. Tus s n s mt stbl stts non ms r wll popult bcus long rlxtion tim. Hnc popultion vrsion built up btwn its nrgy lvls s n P, s n P, n s n P rspctivly s sown \ f ig. rfor tr lsr trnsr tks p lc contuously y r. S r gion P trnsition: Givg lsr ligt wvlngt 9 A o ( four forc. s P trnsition yilg promnt r lsr ligt wv lngt 68 A. s P trnsition yilg lsr ligt f wv lngt 5 A m ny systm contg ctiv mium n mirrors cll lsr cvity. Out lsr trnsitions wic r possibl ctiv mium, lsr bm sir W vlngt coul b pp by justg tnc btwn two mirrors wil or ritions r supprss. Hnc lsr cvity cll rsonnt cvity for tt rition. o Tus tir csr ligt corrspong wvlngt 68A i s mplifi rsonnt cvity n contuous output H- N lsr trnsmitt from systm. c. Mntion pplictions ologrpy. (4 Mrks A pplictions ologrpy: Hologrpy Microscopy: L rg fil viw wit bttr rsolution cn b obt usg ologrpy. In t tcniqu, grtg ivir us prouc objct bm n rfrnc bm. First, objct bm llow illumt n iffrct ligt llow pss troug norml microscop. rflct rfrnc bm trfrs wit objct bm n ologrm obt. It ifficult gt rsolution by microscop. rsolution ologrpic mulsion n cornc rfrnc bm g ivs t pt fil. o. o n D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

81 E ngrg Pysics:PHY Siz Prticl: fog lik prticl os not rm for long tim. It vry ifficult focus m. Hologrpy cn b us for prticl nlys. ologrm p rticls volum m n rconstruction ologrm givs i siz n gomtry prticl. Hologrpic iffrction grtg: ologrpy bs on prcipl trfrnc. I ntrfrnc pttrn givs ltrnt rk n brigt bn. T mto proucs rulgs m or ccurt tn norml mto. 4 Hologrpic Intrfromtry: T tcniqu us msur vibrtion mplitus n mut rtions objcts. ologrm strss objct llow illumt w it monocromtic ligt. Durg rconstruction ologrm, ligt rflct from objct trfrs wit ligt rflct from strss objct. It proucs rk n brigt trfrnc pttrn. By usg t tcniqu, w cn msur ccurt cngs t boy. 5 ROM (R Only Mmory Dvics: Sc lrg mount t cn b sr, ologrms r us ROM vics.. vrg output powr lsr sourc mittg lsr bm wvlngt 6nm i s 5mw f numbr pons mitt pr scon by l sr sourc. (4 Mrks J un/july 5. i Wvlngt lsr bm cn b us s stnr A tim Btmprtur C ngl D lngt A ns D lngt i i Img sr on ologrm form A trfrnc pttrn B iffrction pttrn A ns A trfrnc pttrn C pogrp D non s iii Wic vnt likly tk plc, wn pon nrgy qul iffrnc nrgy btwn two lvls cint s ystm. A bsorption B msion C bsorption n msion D non s A ns C bsorption n msion iv Qurtz plts r fix t ns crg tub H-N lsr so tt A r won t b lkg gs B t tub cn witstn ig lctric voltg C loss ligt cn pss out witout ny loss D mrgnt ligt polr A ns D mrgnt ligt polr b. Expl rquits n conitions lsr systm. ( 5 Mrks. R quits Lsr Systm: T xcittion sourc for pumpg ction. A ctiv mium for popultion vrsion. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

82 E ngrg Pysics:PHY Lsr cvity, n ctiv mium boun by two mirrors. (Rsonr/ Fbry- Prot r sonr. M t Stbl Stt: I t stt wr ms gt xcit n rms xcit s tt for longr tim tn norml stt. T stt plys n importnt rol lsg ction. In mtstbl stt, ms sty orr scon. In xcit stt or tn mtstbl m sty orr s con.. P opultion Invrsion: It stt systm t wic popultion igr nrgy lvl grtr tn tt lowr nrgy lvl. Lt E, E, E b nrgy lvls systm E> E > E. E mtstbl stt systm. Ams gt xcit from stt E E by mns xtrnl sourc n sty r for sort tim. s ms unrgo spontnous trnsitions E n E. ms t stt E sty for longr tim. A stg rc wic numbr ms t stt E mor tn numbr ms t E w ic known s popultion vrsion. 4. P umpg: T procss proucg popultion vrsion cll pumpg. It procss xcitg ms from lowr nrgy lvl igr nrgy lvl. It cn b civ b y iffrnt mtos.. O pticl pumpg: Usg ig tnsity ligt or by oprtg fls tub. Ex:Ruby L sr. b. Elctric Dcrg: B y pplyg vry ig potntil btwn plts crg t ub gs gts crg ls pumpg. Ex: Argon Lsr. c. Am- A m Collion: Excit ms colli wit or typs m n trnsfr its nrgy brg or ms xcit stt. Ex: H- N Lsr.. C micl M to: Exormic cmicl rctions librt nrgy. T librt nrgy us pumpg ms. Ex: Dy Lsr.. U sg Currnt : In smiconucr io lsr tung currnt put brgs c rg crrirs civ popultion vrsion. c. Dscrib prcipl n workg LIDAR us msur pollutnts tmospr. ( 6 Mrks In ppliction lsr for msurmnt pollutnt, lsr m us wy s RADAR (Rio Dtction n Rngg systm us. Hnc it tn rfrr s L IDAR (Ligt Dtction n Rngg tcniqu. In LIDAR systm, trnsmittg prt consts puls lsr n rcvg prt consts concv mirror, po tcr n t procssor. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

83 E ngrg Pysics:PHY Wn msurmnts r crri out, lsr bm unrgos scttrg t plcs tmospr wr r congstion u igr concntrtion prticult mttr. b ck scttr ligt rciv by concv mirror. tnc congstion from msurg sttion clcult on bs tim ly btwn puls msion n rcption bck scttr ligt. By scnng spc roun sttion, c oncntrtion pollutnts cn b mpp for iffrnt vrtic l sction tmospr.. F numbr mos stng wvs n ir frquncy sprtion rsonnt cvity m lngt H- N oprtg t wvlngt 6.8nm. ( 5 Mrks -9 g ivn: L=m, λ=6.8x m, m=? λ= l m m= l λ = X 6.8X 9 m=.655x X 6 m=.655x 9 S upr UNIT-6 conuctivity n Opticl fibrs J un/july 9 6. i Numricl prtur n opticl fibr pns on A imtr fibr B ccptnc ngl C criticl ngl D n A ns B ccptnc ngl i i wit nrgy gp suprconucr mximum t A Tc B K C Tc / D Tc/ Ans A T c c or m tril i ii Wic followg corrct A Clg for provig grtr strngt B C or s igr R.I tn clg C Clg s igr RI tn cor D Non Ans B Cor s igr R.I tn clg D prtmnt Pysics, SJBIT, Bnglor-6 Pg 8

84 E ngrg Pysics:PHY iv Frctionl x cngs opticl fibr for R.I cor n clg r.56 n.498 A.45 B.45 C.4 D.4 Ans B.45 b. Wit nt figur riv n xprssion for N.A n opticl fibr. A ngl Accptnc n Numricl Aprtur: (6 Mrks Consir ligt ry AO cint t n ngl θ ntrs fibr. Lt θ b ngl rfrction for ry OB. rfrct ry OB cint t criticl ngl (9 - θ t B grzs trfc btwn cor n clg long BC. If ngl cinc grtr tn criticl ngl, it unrgos tl trnl rflction. Tus θ cll wvgui ccptnc ngl n sθ i s cll numricl prtur. Lt n, n n n b rfrctiv ics mium, cor n clg r spctivly. F rom Snll s n o lw, s θ = s θ n ( At B ngl cinc (9 - θ F rom Snll s lw, n s(9-θ = ns 9 n F rom qn ( n S n cosθ n = cosθ = n / n ( s = n n o cos θ ( D prtmnt Pysics, SJBIT, Bnglor-6 Pg 84

85 E ngrg Pysics:PHY U sg qn ( i n ( S n n n n T surroung mium ir, n o = = n n (4 n o S Wr sθi i s cll numricl prtur. n n N.A= n n rfor for ny ngl cinc qul θ bl propgt. i qul or lss tn θ, cint ry θ i < θ S i S S n n i s conition for propgtion S i N. A c. Giv brif ccount SQUID (6 Mrks S QUIDS (Supr conuctg Quntum Intrfrnc Dvic: It n ultrsnsitiv - 4 strumnt us msur wk mgntic fils orr Tsl. SQUID m b y jog two Jospson s junction loop suprconuctg mtril. A voltmtr connct cross suprconucr sows zro flction wn currnt flowg troug it. If suprconucr cut two pics n sprt by tnc cm. Now c urrnt will not flow n voltmtr sows voltg qul opn circuit voltg.if tnc btwn pics crss nm voltmtr sows zro flction.t k nown s D.C Jospson s ffct. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 85

86 E ngrg Pysics:PHY W n mgntic fil ppli suprconuctg circuits, it ucs circultg currnt wic proucs opposg mgntic fil s xclu flux from loop. flux rms xclu so long s junction currnt o not xc criticl vlu.tus c ircuit cts s gt llow or xclu flux. prioic vrit ion criticl currnt ( I c wit mgntic fil sown fig. ppli mgntic fil sows trfrnc ffct n quntiztion ffct. y v got mjor rol functiong SQUIDS. SQUIDS r u s tctg frctions flux quntu m. SQUIDS r us tction or posits n xplortion oil. SQUIDS r us msur mgntic fils rt n br.. A Fibr 5m long s n put powr 8.6 mw n output powr 7.5 mw. Wt t loss spcifiction cbl? ( 4 Mrks G ivn: L =5m = 5, p i 8.6mw, p = 7.5mw, =? = o p out log B/km L p log ( B / km D EC 9/JAN 6. i sgl mo fibr, imtr cor nrly qul ( 4mrks A 5µm A ns D µ m b µm c 5µm µm i i numricl prtur n opticl fibr. wn surroun by ir. ccptnc ngl wn fibr wtr rfrctiv x. A 8. B C. n on s A ns B D prtmnt Pysics, S JBIT, Bnglor - 6 P g 8 6

87 E ngrg Pysics:PHY i ii loss powr by opticl signl troug opticl fibr mly u A Rylig scttrg B Rmn scttr g C Win s scttrg D ll s A ns A Rylig scttrg i v W n typ - suprconuctg mtril plc n xtrnl mgntic Fil, i t A Attrcts mgntic fil B n ncs mgntic fil ls C Rpls mgntic fil ls D os not flun c mgntic fil l s A ns C Rpls mgntic fil ls b. Dscrib pot pot communiction systm, wit lp block igrm. ( 5 Mrks Opticl fibr communiction systm consts trnsmittr, formtion cnnl n r civr. Trnsmittr convrts n lctric l signl opticl signl. Informtion cnnl crris signl from trnsmittr rcivr. rcivr convrts opticl signl lctricl f orm. block igrm opticl fibr communiction systm sown fig. M ssg orig: I t convrt s non lctricl mssg n lctricl signl. M oulr: It convrts lctricl mssg propr formt n it lps improv t s ignl on wv wic gnrt by crrir sourc. T r r two typs formt. y r Anlog n igitl. Anlog signl i s contuous n it osn t mk ny cng origl formt. But igitl signl will b ir ON or OFF stt. C rrir sourc: It gnrts wvs on wic t trnsmitt. s crrir wv s r prouc by lctricl oscillr. Ligt mittg ios (LED n lsr ios (LD r iffrnt sourcs. C nnl Couplr: (Input function cnnl couplr provi formtio n t o formtion cnnl. It cn b n ntnn wic trnsf rs ll t. I nformtion cnnl: It pt btwn trnsmittr n rcivr. r r two typs o f formtion cnnl. y r gui n ungui. Atmospr goo xmpl for u ngui formtion cnnl. Co - xil cbl, tw o - w ir l n rctngulr wv gui r xmpl for gui cnnl. D prtmnt Pysics, S JBIT, Bnglor - 6 P g 8 7

88 ngrg Pysics:PHY E Pysics, prtmnt D Bnglor JBIT, S - 6 g P 8 8 (Output Couplr: nnl C o t on fibr from ligt mrg guis couplr output tcr. ligt t tcr: D o pot Hr wv. crrir from formtion sprts tcr T - t cr signl. lctronic signl opticl onvrts c procssor: ignl S unsir frquncis. filtrs n signls mplifis procssor ignl S output: ssg M t s cn prson Eir forms. two b will mssg output r or nformtion i or wv soun convrt b cn signl lctricl formtion. CRO. usg by img ul v Mrks (7 Expl SQUID. conucr. supr BCS ory.dcuss c pnom xpl 957 (BCS Scriffr n Coopr rn, B non It ory. BCS cll It pirs. coopr formtion on bs suprconuctivity concpt. untum mcnicl q cor ion positiv nr com lctrons suprconucr, flow currnt Wn cor ion forc. ttrctiv u ttic, l wic position, from its plc gts lso ll c n rtio ttic l trm cll quntiz r vibrtions lttic.. onons P w No tns T lttic. rt wit trct will plc tt nr coms wic lctron n nrg uc r lctrons two btwn trction quivlnt It lctron. y pirs. coopr formtion ls T lttic. roug t s pir oopr C boun r n sp opposit wit lctrons btwn trction by form lctrons ir p s trt pir coopr quntum mcnics Accorg fil. ponon momnt ovr goo ols T pir. coopr c wit ssocit function A wv ntity. sgl s function wv mplitu. its for vlu fit wit volum rg l pirs coopr imilr ovr xtn my ovrlppg pir coopr on For ovrlps. 6 covrs it Tus pirs. or pirs. coopr numbr lrg union ls It suprconucr. volum ntir i pir coopr sgl ny by ncountr stnc r or ction comb by ovrcom s union. irs p not o y mtrils, pirs coopr form flow lctrons Wn conuctivity wors or or vns fcr rstnc n scttrg ny ncountr fity wic coms b. suprconuctivity ll s c lctron stt suprconuctg n I - coulomb tn strongr trction ponon y pots. lttic by scttr not r pirs Coopr lctrons. ttrction forc nrgy ir s own slow witout frly rvl t not o y t Du trnsfrr. not os p. rstivity ny lctricl s s nsur glss cl wit nor b.5 x rfrctiv fibr glss An opticl. 5 wit trvllg ligt cont will tt rflction trnl o Wt x. fibr clg? llow for rfrction ximum x m Mrks 4 (

89 E ngrg Pysics:PHY 85 B y gnrl n lw rfrction s 9 = ns 85 n =.49 M y/jun 6. i Suprconucr suprconuctg stt bv s A Monovlnt mtls B Frromgntic mtrils C Goo conucrs t room tmprtur D Dimgntic mtrils Ans D Dimgntic mtrils i i A suprconucr mtril, on bg subjct criticl fil, cngs A Criticl conucr B suprconuctg wic pnnt tmprtur C Norml stt D rms unflunc. Ans C Norml stt iii Frctionl x cng opticl fibr n rfrctiv x cor r.55 n.5 rspctivly. c lg rfrctiv x A.49 B.55 C.499 D.5 Ans B.55 i v Attnution opticl fibr cus u A Absorption B Scttrg C Dprsion D All tr Ans D All tr b. Wt i s Msnr ffct? Expl BCS ory suprconucr. M snr ffct: ( 6 Mrks A suprconuctg mtril kpt mgntic fil xpls mgntic flux out its b oy wn it cool blow criticl tmprtur n tus bcoms prfct imgnt. T ffct cll Msnr ffct. Brn, Coopr n Scriffr (BCS 957 xpl pnomnon s uprconuctivity bs on formtion coopr pirs. It cll BCS ory. It q untum mcnicl concpt. Wn currnt flow suprconucr, lctrons com nr positiv ion cor lttic, u ttrctiv forc. ion cor lso gts plc from its position, wic cll l ttic rtion. T lttic vibrtions r quntiz trm cll P onons. Now D prtmnt Pysics, SJBIT, Bnglor-6 Pg 89

90 E ngrg Pysics:PHY n lctron wic coms nr tt plc will trct wit rt lttic. T tns ruc nrgy lctron. It quivlnt trction btwn two lctrons troug lttic. T ls formtion coopr pirs. C oopr pirs r boun pir lctrons form by trction btwn lctrons wit opposit sp n m omnt ponon fil. Accorg quntum mcnics coopr pir trt s sgl ntity. A wv function ssocit wit c coopr pir. T ols goo ovr lrg volum wit fit vlu for its mplitu. wv function similr coopr pirs 6 ovrlps. For on coopr pir ovrlppg my xtn ovr or pirs. Tus it covrs ntir volum suprconucr. It ls union lrg numbr coopr pirs. rstnc ncountr by ny sgl coopr pir ovrcom by comb ction or p irs union. W n lctrons flow form coopr pirs mtrils, ncountr ny scttrg n rstnc fcr vns or or wors b coms fity wic cll s suprconuctivity. y o not conuctivity In suprconuctg stt lctron- p onon trction strongr tn coulomb forc ttrction lctrons. Coopr pirs r not scttr by lttic pots. y trvl frly witout slow own s ir nrgy not trnsfrr. Du t y o not p osss ny lctricl rstiv ity. c. Driv xprssion for numricl prtur n opticl fibr. (6 Mrks Consir ligt ry AO cint t n ngl θ ntrs fibr. Lt θ b ngl r frction for ry OB. rfrct ry OB cint t criticl ngl (9 - θ t B grzs trfc btwn cor n clg long BC. If ngl cinc grtr tn criticl ngl, it unrgos tl trnl rflction. Tus θ cll wvgui ccptnc ngl n sθ i s cll numric l prtur. Lt n, n n n b rfrctiv ics mium, cor n clg r spctivly. F rom Snll s n o lw, s θ = s θ n ( At B ngl cinc (9 - θ D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

91 E ngrg Pysics:PHY F rom Snll s lw, n s(9-θ = ns 9 n F rom qn ( n S n U sg cosθ n = cosθ = n / n ( s = n n o qn ( ( cos θ ( S n n n n surroung m ium ir, n o = = n n (4 n o S Wr sθi i s cll numricl prtur. n n N.A= n n T rfor for ny ngl cinc qul θ bl propgt. i qul or lss tn θ, cint ry θ i < θ S i S sθi < N. A i s conition for propgtion sθi < n n D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

92 E ngrg Pysics:PHY. An opticl fibr s cor RI.5 n RI clg % lss tn cor x. C lcult numricl prtur, ngl ccptnc n trnl criticl ccptnc ngl. (4 Mrks Givn: n=.5, n = % lss tn n = =. 455, N.A =?, θ =? N.A= n n N.A = N.A=.646 sθ = N. A θ θ = s = s - - θ =.4 N.A ( n sθ = n sθ θ = s n sθ n θ = s.5 s.4 θ = 4 J nury 6. i criticl tmprtur mrcury A 4.k B 6.k C 7.8K A ns A 4.k D k ii tmprtur suprconucr kpt wk mgntic fil ruc blow c riticl tmprtur, n A R=;B B R ; B= C R ; B D R=; B= A ns D R=; B= iii numricl prtur n opticl fibr ir., numricl prtur wtr (n = 4/ A.4 A ns B.4 B.4 C.64 D.96 i v Gr x fibr cn b A Sgl mo fibr only C bot sgl mo n multimo B multimo fibr o nly B multimo fibr only D p ns on surroung m ium. Ans D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

93 E ngrg Pysics:PHY b. Df trms: i ngl ccptnc ii numricl prtur i ii Frctionl x cng iv mos propgtion. (4 Mrks I f ngl cinc t O lss tn o n rfrct ry unr go tl trnl rflction n propgts fibr. If ngl cinc grtr tn o. n rfrct ry pss troug clg n it will b lost. Tus i s cll ccptnc ngl s ccptnc ngl o or ccptnc con lf ngl cll numricl prtur i.. N.A = S o. Frctionl Inx Cng ( : It rtio rfrctiv x iffrnc btwn cor n c lg rfr ctiv x cor n opticl fibr. = n n n N umbr wvs propgtg troug n opticl fibr cll mos propgtion. c. Expl BCS ory suprconuctivity. Writ sort not on mglv vicls. ( 8 Mrks Brn, Coopr n Scriffr (BCS 957 xpl pnomnon suprconuctivity bs on formtion coopr pirs. It cll BCS ory. It q untum m cnicl concpt. Wn currnt flow suprconucr, lctrons com nr positiv ion cor lttic, u ttrctiv forc. ion cor lso gts plc from its position, wic cll l ttic rtion. lttic vibrtions r quntiz trm cll P onons. Now n lctron wic coms nr tt plc will trct wit rt lttic. T tns r uc nrgy lctron. It quivlnt trction btwn two lctrons troug lttic. T ls formtion coopr pirs. C oopr pirs r boun pir lctrons form by trction btwn lctrons wit opposit sp n m omnt ponon fil. Accorg quntum mcnics coopr pir trt s sgl ntity. A wv function ssocit wit c coopr pir. T ols goo ovr lrg volum wit fit vlu for its mplitu. wv function similr coopr pirs 6 ovrlps. For on coopr pir ovrlppg my xtn ovr or pirs. Tus it covrs ntir volum suprconucr. It ls union lrg numbr coopr pirs. rstnc ncountr by ny sgl coopr pir ovrcom by comb ction or p irs union. W n lctrons flow form coopr pirs mtrils, y o not ncountr ny scttrg n rstnc fcr vns or or wors conuctivity b coms fity wic cll s suprconuctivity. In suprconuctg stt lctron-p onon trction strongr tn coulomb forc ttrction lctrons. Coopr pirs r not scttr by lttic pots. y trvl f rly witout slow own s ir nrgy not trnsfrr. D prtmnt Pysics, SJBIT, Bnglor-6 Pg 9

94 E ngrg Pysics:PHY Mgnticlly Lvit t Vicls (Mglv vicls : Mgnticlly lvit t vicls r cll Mglv vicls. mgntic lvit tion bs on prcipl Msnr ffct. mgntic fil prouc by suprconuctg mgnt n lctric currnt. s uprconuctg mgnt kpt si vicl n lctric currnt Alumum gui wy. vicl on Alumum gui wy. vicl provi wit rtrctbl wls. vicl runs on gui wy, onc it lvit t ir wls r r trct boy. igt wic vicl lvit t bov guiwy bout 5cm. Wil sppg, wls r rwn out n vicl slowly sttls on gui wy by runng tnc. s ny lctricl rstivity.. rfrctiv ics cor n clg r.5 n.48 rspctivly n opticl f ibr. F numricl prtur n ngl ccptnc. (4 Mrks Givn: n=.5, n =. 48, N.A =?, θ =? N.A= n n N.A = N.A=.44 sθ = N. A θ θ = s = s - - θ = 4 N.A (.44 J un/july 6. i conuctivity suprconucr A fit B Zro C fit D non s A ns A fit ii rltion btwn suprconuctg trnsition tmprtur(tc n mic w igt(μ op A T C α μ B TC α / μ C TC α μ D T C α / μ Ans C TC α μ i ii If opticl fibr kpt mium R.I μ ( > st ir, ccptnc ngl A Dcrss B Incrss C Rms constnt D Non s. A ns A Dcrss i v In gr x fibr, R.I clg vris D prtmnt Pysics, SJBIT, Bnglor-6 Pg 94

95 E ngrg Pysics:PHY A Exponntilly B lrly C prboliclly D non s A ns D non s b. Dcuss typs opticl fibrs n mos propgtion usg suitbl igrm. ( 6 Mrks F ollowg r iffrnt typs fibrs:. S gl mo fibr. S tp x multimo fibr. G r x multimo fibr S gl mo fibr: Rfrctiv x cor n clg s uniform vlu; r n i ncrs rfrctiv x from clg cor. y r us submr.. S tp x multimo fibr: It similr sgl mo fibr but cor s lrg imtr. I t cn propgt lrg numbr mos s sown figur. Lsr or LED us s sourc o f ligt. It s n ppliction t lks.. G r x multimo fibr: It lso cll GRIN. rfrctiv x cor crss from x wrs cor clg trfc. rfrctiv x pril D prtmnt Pysics, SJBIT, Bnglor-6 Pg 95

96 E ngrg Pysics:PHY sown figur. cint rys bns n tks prioic pt long x. rys v iffrnt pts wit sm prio. Lsr or LED us s sourc ligt. It xpnsiv ll. I t us tlpon trunk btwn cntrl fics. c. Dtgu btwn typ-i n typ- I I suprconucrs. ( 5 Mrks Typ- I suprconucrs: Typ- I suprconucrs xibit complt Msnr ffct. Blow criticl fil it bvs s prfct imgnt. If xtrnl mgntic fil crss byon Hc suprconuctg spcimn gts convrt norml stt. mgntic flux pntrts n rstnc crs from zro som vlu. As criticl fil vry low for typ- I s uprconucrs, y r not us construction solnois n suprconuctg mgnts. Typ-I I suprconucrs Typ-I I suprconucrs r r suprconucrs. y xt tr stts S uprconuctg stt M ix stt Norml s tt D prtmnt Pysics, SJBIT, Bnglor-6 Pg 96

97 E ngrg Pysics:PHY y r vg two criticl fils Hc n Hc. For fil lss n Hc, it xpls mgntic fil compltly n bcoms prfct imgntic. Btwn Hc n Hc flux strts pntrtg trougout spcimn. T stt cll vortx stt. Hc tims igr tn Hc. At Hc flux pntrts compltly n bcoms norml conucr. Typ- I I suprconucrs r us mnufcturg suprconuctg mgnts ig m gntic fils bov Tsl.. ngl ccptnc n opticl fibr wn kpt ir. F ngl ccptnc wn it mium R.I=.. ( 5 Mrks g ivn: θ =., n =.. T o f: Angl ccptnc wil fibr rfrctg mium, θ =. S olution: Sθ= n n n Wn surroung mium ir, n, n=, n θ S= n n D prtmnt Pysics, SJBIT, Bnglor-6 Pg 97 =.5= n n W n surroung mium rfrctiv x., lt θ b ccptnc ngl. N ow Eq( bcoms, Sθ = n n n Sθ = n n.

98 E ngrg Pysics:PHY. Sθ =n + n F rom Eqs( n (,. Sθ =. 5 θ = ccptnc ngl wn fibr mium rfrctiv x. UNIT-V II C rystl structur J un/july 9 7. i rltion btwn mic rius n lttic constnt fcc structur A =r B r C = (r/4 D 4r/ A ns B r i i Pckg fcr imon crystl structur A.68 B.74 C.5 D.4 A ns D.4. i ii A crystl ttrgonl lttic A =b=c B b c C = b c Ans D b= c D b= c iv For vry rottion by n ngl θ i n Brgg s spctromtr, tcr turns by n ngl A θ B θ C θ / D θ A ns θ b. Driv n xprssion for trplnr spcg trms Millr ics. ( 6 Mrks C onsir pln ABC wic blongs fmily plns., k, l r Millr ics t pln, wic rprsnts st plns. prpniculr ON from orig O pln rprsnts tr- plnr spcg =ON t fmily plns. Lt ON mk n ngl α, β, γ w it x, y, z xs rspctivly D prtmnt Pysics, SJBIT, Bnglor-6 Pg 98

99 E ngrg Pysics:PHY T trcpts pln on tr xs r O A= / ; OB= /k ; OC=/l W r lngt cub g. T n from figur, w v ON cos OA / cos OB / k cos OC / l y z From figur x k l cos cos cos But, cos cos cos for ortogonl c oorts Substitutg vlus cos, cos, cos i n qution (, W gt, OA OB OC k l k l k T rltion btwn tr- plnr spcg n g cub. It soul b n ot tt t formul pplicbl only primitiv lttics cubic, ortorombic n t trgonl systms. c. Wit nt figur, xpl crystl stru c tur NCl. ( 6 Mrks l T crystl structur soium clori si - imnsionl ortogonl rry. s soium ion n clor ions rrng rsult fc cntr cubic lttic. si by NCl crystl structur cn b consir b suprposition two FCC sublttics o n soium ions n or clor ions, bot sub lttics vg sm lttic prmtrs. suprposition suc tt on sub lttic trnslt troug tnc qul lf lttic prmtr long cub g fc cntr cubic lttic. In igrm sow n blow soium loss its outr lctron n gts n xcss positiv + crg n clor m ccpts lctron n bcoms ngtiv ion. N ion (Smll D prtmnt Pysics, SJBIT, Bnglor-6 Pg 99

100 E ngrg Pysics:PHY - Siz n Cl ion (Big Siz ttrct c or u lctrosttic forcs btwn crgs. But two ions cn pproc c or crt tnc; bcus strong f orcs rpulsion quilibrium obt wn n ttrction n rpulsion blnc. NCl c rystl s FCC structur KCl, PbS, MnO, AgBr ll v sm structur. For c m r r 6 quitnt nrst nigbours opposit k. Hnc co- o rtion numbr 6. r r nxt nrst nigbours sm k. r will b 4 ions on k n 4 ions or k blong unit cll. Tus r r 4 N + Cl - ion p irs ( molculs pr unit cll. T A n rltion btwn mic rius n lttic constnt n=4 for fcc structur spc lttic constnt nm N A 8 r T molculr wigt NCl = =58.45 nsity NCl = 8 kg/m 6 Avgro numbr NA = 6. / k mol = 8 6. = tr- mic tnc NCl = / =.8A. mimum orr Brgg s rflction occurs t ngl i n pln ( F wvlngt X- r ys if lttic constnt.65 Å. ( 4 Mrks Givn: θ =, kl = (, =.65 Å, λ =? s = n λ = λ = s n s = +k +l n λ =.85 m. 65 s + + D prtmnt Pysics, SJBIT, Bnglor-6 Pg m

101 E ngrg Pysics:PHY D EC 9/JAN 7. i wic on followg crystl n xmpl monoclic? A Sno 4 B Ncl CCS o 4 D CuS o 4 A ns C C S o 4 i i I n simpl cubic lttic rtio : : A 6:: B : : C 6: : D : : A ns D : : i ii Wic on followg Brv lttics not foun cubic crystl? A Simpl cub B fc cntr C Boy cntr D Bs cntr A ns D Bs cntr i v pckg frction imon crystl structur A 4% B5% C68% D74% A ns A 4% b. Dcuss brv lttic n ny fiv crystl systms wit lp illustrtions. ( 8mrks A Brv lttic on wic ll ms t lttic pots r inticl or ll l ttic pots r quivlnt. A n o n - Brv lttic on wic som lttic pots r non quivlnt. A n on - Brv lttic lso known s lttic wit bs. Bs st ms loct n r Brv lttic. T 7 Crystl systms ( From Most symmtric l st symmtric. C ubi c o =b=c ;α=β=γ=9 E x: - Au, Cu, NCl, F cl C, N O s impl (SC P olonium T 4 Brv Lttics f c - b oy - c ntr (F C c ntr (B C C C NCL(Hlit Iron, or Rock Slt, Cromium lumium, & Tungstn c oppr, gol D prtmnt Pysics, S JBIT, Bnglor - 6 P g

102 E ngrg Pysics:PHY s impl boy-c ntr. T trgonl =b c ; α=β=γ=9 Ex: -SnO, TiO, NiSO4. o s impl bs-c ntr boy- c ntr fc- c ntr. O rtorombic o b c α=β=γ=9 Ex: - KNO,BSO4, M gso4. s impl bs-c ntr 4. M onoclic b c α=γ=9 o β Ex: - CSO4. H O, FSO4, N O S 4 5. T riclic b c α β γ 9 Ex: - K Cr O 7, CuSO4. 5HO 6. R omborl ( trigonl =b=c α=β=γ 9o Ex: - c lcit, qurtz, Bi t ourml, As,Sb, o c. Df coortion numbr n pckg fcr. Clcult pckg fcr for sc, f cc n bcc structurs. ( 8mrks. Co- o rtion numbr: It numbr nrst n igbours irctly surroung givn m wll wit c rystl.. A mic pckg fcr (APF D prtmnt Pysics, SJBIT, Bnglor-6 Pg

103 E ngrg Pysics:PHY T frction spc occupi by ms unit cll known s mic pckg fcr. It rtio tl volum occupi by ms unit cll tl vilbl v olum unit cll.. S impl cubic structur (SC: T r only on lttic pot t c igt cornrs unit cll. In simpl cubic structur n m surroun by six quitnt nigbors. Hnc co- ortion numbr i s 6. Sc c m cornr sr by 8 unit clls, tl numbr ms on u nit cll (/8 8 = v 4r P ckg fcr P.F =.5 5% V 8r 6. B oy cntr cubic structur (BCC: In BCC structur igt ms r prsnt t igt cornrs n on m t cntr. co- o rtion numbr 8. numbr ms pr unit cll = [(/8 8]+ = 4 V olum ll ms pr unit cll v = r 64r Volum unit cll V = = v 8r A mic pckg fcr =.68 68% V 64r 8. F c cntr cubic structur (FCC: In FCC structur igt ms r t cornrs unit cll n six ms r prsnt t cntr six fcs. cntr m surroun by pots. co- ortion n umbr. Ec cornr m sr by 8 unit clls n fc cntr m sr b y surroung unit clls.... numbr ms pr unit cll = = 4 8 Volum 4 ll ms unit cll v = 4 r Volum unit cll V = = 64r v 6r V 64r... pckg fcr =.74 74% 6 M y/jun i Nrst n igbour tnc btwn two ms cs bcc structur ( /4 b / c ( / / A ns A ( /4 ii co-o rtion numbr cs simpl cubic crystl structur b 8 c 6 Ans D 6 D prtmnt Pysics, SJBIT, Bnglor-6 Pg

104 ngrg Pysics:PHY E Pysics, prtmnt D Bnglor JBIT, S - 6 g P 4 =b wit lttics crystl ii i n ngls c α=β=γ= 9 prsnts r Ttrgonl Ortorombic c Hxgonl b Cubic ns A D l Ttrgon ics millr cll. unit cubic simpl c b/,, t trcpts A pln iv r ln p (4 (4 c (4 b (4 ns A B 4 ( (6mrks imon. structur crystl Dscrib cll. n primitiv cll unit Df. b unit A n irctio long rptition on wic lttic, spc portion smllst cll itslf. lttic spc gnrts vcrs bs tr f o n non cll rimitiv P - l cl rimitiv p A non vrtics. t r it pots ll wit cll unit cll primitiv A - primitiv img n clls primitiv multipl tgrl n corports wic cll unit cll sk for nly o lttic rrngmnt symmtry vuliztion sy ots. p Dimon: structur rystl C on sublttics fcc suprposition s consir b cn lttic imon igon boy long or from plc ic w (/4 by cll unit l t lngt four wit ttrron, cntr t prsnt b m will crbon Tus igonl. cornrs four t loct nigbours nrst its s sublttic or ms crbon Tus ttrron. m s o c - crbon 8 b will r n 4 imon numbr ortion cll unit pr prsnt ms. 4 ttrron, cntr t m crbon c Tt.5A constnt lttic plns. opposit igonlly t r ms crbon o n l on b A 6.56 ngt o. structur. imon vg r G n Si lik smiconucrs T FCC n A. cll ms/unit 4 s ttic l two comprs lttic imon But FCC sub ntrpntrtg i -. ttic l ltt imon cll unit pr ms Numbr rfor, T. = 8 x4 c i = Fcr Pckg Amic n A % r r r

105 E ngrg Pysics:PHY c. Driv Brgg s lw. ( 4mrks Consir st prlll plns cll Brgg s plns. Ec m ctg s scttrg cntr. tnsity rflct bm t crt ngls will b mximum wn t pt iffrnc btwn two rflct wvs from two jcn t plns n tgrl m ultipl λ. Lt b tnc btwn two jcnt plns, 'λ b wvlngt i ncint x - ry, θ b glncg ngl. pt iffrnc btwn rys rflct t A & B givn by = CB + BD = sθ + s θ = s θ For rflct ligt tnsity b mximum, pt iffrnc sθ = nλ, wr n t orr scttrg. T cll Brgg s lw.. A monocromtic X - ry bm wvlngt.5 Å unrgos scon orr Brgg r flctio n from pln ( cubic crystl, t glncg ngl Clcult t lttic constnt. (8mrks G ivn: =.5 Å, =54. 8 s = n n s D prtmnt Pysics, S JBIT, Bnglor - 6 P g 5