QUESTION PAPER PHYSICS-PH. 1. Which one of the following is an allowed electric dipole transition? ), the unit vector ˆ.

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1 GATE-PH 8 Q. Q.5 : arry ONE mark ach. PHYSIS-PH. Which on of th following is an allowd lctric diol transition? S S P D D P P 5 D / 5/ 5/ /. In shrical olar coordinat ( r,, ), th unit vctor ˆ at,, 4 is ˆk ˆ ˆ ˆj k ˆ ˆ ˆ j k j k. Among lctric fild ( E ), magntic fild ( B ), angular momntum ( L ), and vctor otntial ( A ), which is/ar odd undr arity (sac invrsion) oration? E only E and A only E and B only B and L only 4. Th scal factors corrsonding to th covariant mtric tnsor g i j in shrical olar coordinats ar, r, r sin,,sin r,,, r, r sin 5. In th contt of small oscillations, which on of th following dos NOT aly to th normal coordinats? Each normal coordinat has an ign-frquncy associatd with it Th normal coordinats ar orthogonal to on anothr Th normal coordinats ar all indndnt Th otntial nrgy of th systm is a sum of squars of th normal coordinats with constant cofficints 6. A light bam of intnsity I is falling normally on a surfac. Th surfac absorbs % of th intnsity and th rst is rflctd. Th radiation rssur on th surfac is givn by I / c, whr is (u to on dcimal lac). Hr c is th sd of light. 7. For th givn unit clls of a two dimnsional squar lattic, which otion lists all th rimitiv clls? 5 4 and, and,, and 4,,, 4 and 5 8. Th high tmratur magntic susctibility of solids having ions with magntic momnts can b dscribd by T whr T as absolut tmratur and as constant. Th thr bhaviors i.., aramagntic, frromagntic and anti-frromagntic ar dscribd, rsctivly, by,,,,,,,, 9. Th ignvalus of a Hrmitian matri ar all ral imaginary of modulus on ral and ositiv. At low tmratur ( T ), th scific hat of common mtals is dscribd by (with and as constants)? 5 T T T ( / T ) T T

2 GATE-PH 8. Th numbr of indndnt comonnts of a gnral lctromagntic fild tnsor is.. Match th hysical ffcts and ordr of magnitud of thir nrgy scals givn blow, whr 4 fin structur constant ; m and m ar lctron and roton mass, rsctivly. Grou-II Grou-I P. Lamb shift. ~ O( mc ) 4 Q. Fin structur. ~ O( mc ) 4 R. Bohr nrgy. ~ O( m c / m) 5 S. Hyrfin structur 4. ~ O( mc ) P-, Q-, R-, S-4 P-, Q-, R-, S-4 P-4, Q-, R-, S- P-, Q-4, R-, S- c is. Which on of th following rrsnts th radial wav function of hydrogn atom? ( a is th Bohr radius) r/ a r/ a r/ a r/ a 4. For an orational amlifir (idal) circuit shown blow, 4 k V k +V V 5 k V R L V if V V and V V, th valu of V is V (u to on dcimal lac). 5. Th logic rssion AB AB AB AB can b simlifid to A OR A AND 6. An infinitly long straight wir is carrying a stady currnt I. Th ratio of magntic nrgy dnsity at distanc r to that at r ( r ) from th wir is. 7. Th rssion for th scond ovrton frquncy in th vibrational absortion sctra of a diatomic molculs in trms of th harmonic frquncy and anharmonicity constant is ( ) ( ) ( ) ( 4 )

3 GATE-PH 8 8. Th lmntary articl is lacd in th baryon dcult, shown blow, at + + Strangnss P Q R comonnt of isosin P Q R S rd S 9. For nuclus 64 Er, a stat is at 9 kv. Assuming 64 Er to b a rigid rotor, th nrgy of its 4 + stat is kv. (u to on dcimal lac). j. Th intrinsic/rmannt lctric diol momnt in th ground stat of hydrogn atom is ( a is th Bohr radius). a zro a a. A sacshi is travlling with a vlocity of.7c away from a station. Th sacshi jcts a rob with a vlocity.59c oosit to its own vlocity. A rson in th sac station would s th rob moving at a sd c, whr th valu of is (u to thr dcimal lacs).. In a -to- multilr as shown blow, th outut A if, and A if. A A Which on of th following is th corrct imlmntation of this multilr? A A A A A A A. If is th dimnsionality of a fr lctron gas, th nrgy (E) dndnc of dnsity of stats is givn by E Y, whr Y is. 4. In th dcay, v, what is? v v v A

4 GATE-PH Givn th following tabl, Grou-I Grou-II P. Stm-Grlach rimnt. Wav natur of articls Q. Zman ffct. Quantization of nrgy of lctrons in th atoms R. Frank-Hrtz rimnt. Eistnc of lctron sin S. Davisson-Grmr rimnt 4. Sac quantization of angular momntum Which on of th following corrctly matchs th rimnts from Grou-I to thir infrncs in Grou-II? P-, Q-, R-4, S- P-, Q-, R-, S-4 P-, Q-4, R-, S- P-, Q-, R-4, S- Q.6 Q.55 : arry TWO marks ach. 6. A -dod smiconductor slab carris a currnt I ma in a magntic fild B. T as shown. On masurs Vy.5 mv and V mv. Th mobility of hols in th smiconductor is m V s (u to two dcimal lacs). V y V I B l = mm y z t = mm w = 4 mm 7. Thr articls ar to b distributd in four non-dgnrat nrgy lvls. Th ossibl numbr of ways of distribution: (i) for distinguishabl articls, and (ii) for idntical Bosons, rsctivly, is (i) 4, (ii) 4 (i) 4, (ii) (i) 64, (ii) (i) 64, (ii) 6 8. An atom in its singl stat is subjctd to a magntic fild. Th Zman slitting of its 65 nm sctral lins is. nm. Th magnitud of th fild is Tsla (u to two dcimal lacs)..6, m 9. kg, c. ms Th artition function of an nsmbl at a tmratur T is N Z cosh, kbt whr k B is th Boltzmann constant. Th hat caacity of this nsmbl at T is Nk B, whr th valu k of is (u to two dcimal lacs).. A quartr wav lat introducs a ath diffrnc of /4 btwn th two comonnts of olarization aralll i ( kz t) and rndicular to th otic ais. An lctromagntic wav with E ( ˆ yˆ ) E is incidnt normally on a quartr wav lat which has its otic ais making an angl 5º with th -ais as shown. y B Otics ais 5º

5 GATE-PH 8 Th mrgnt lctromagntic wav would b llitically olarizd circularly olarizd linarly olarizd with olarization as that of incidnt wav linarly olarizd but with olarization at 9º to that of th incidnt wav. Two solid shrs A and B hav sam missivity. Th radius of A is four tims th radius of B, and tmratur of A is twic th tmratur of B. Th ratio of th rat of hat radiatd from A to that from B is. 5z z. Th absolut valu of th intgral, dz ovr th circl z.5 in coml lan, is z 4 (u to two dcimal lacs).. A long straight wir, having radius a and rsistanc r unit lngth r, carris a currnt I. Th magnitud and dirction of th Poynting vctor on th surfac of th wir is, rndicular to ais of th wir and ointing inwards. a, rndicular to ais of th wir and ointing outwards. a, rndicular to ais of th wir and ointing inwards. a, rndicular to ais of th wir and ointing outwards. a 4. An intrstllar objct has sd v at th oint of its shortst distanc R from a star of much largr mass M. Givn v GM / R, th trajctory of th objct is circl llis arabola hyrbola 5. Th ground stat nrgy of a articl of mass m in an infinit otntial wll is E. It changs to whn thr is a small otntial bum of hight V valu of is (u to two dcimal lacs). V( ) 5 ml 5 E ( ), and width a L/, as shown in th figur. Th a L V 6. onsidr an infinitly long solnoid with N turns r unit lngth, radius R and carrying a currnt I ( t) cost, whr is a constant and is th angular frquncy. Th magnitud of lctric fild at th surfac of th solnoid is NR sin t NR cos t NR sin t NR cost 7. Insid a larg nuclus, a nuclon with mass 99 MVc has Frmi momntum.4 fm at absolut zro tmratur. Its vlocity is c, whr th valu of is (u to two dcimal lacs).

6 GATE-PH An articl is mittd by a 9Th nuclus. Assuming th otntial to b urly oulombic byond th oint of saration, th hight of th oulomb barrir is MV (u to two dcimal lacs) MV-fm, r. fm 9. A articl movs in on dimnsion undr a otntial V ( ) with som non-zro total nrgy. Which on of th following bst dscribs th articl trajctory in th has sac? 4. If H is th Hamiltonian for a fr articl with mass m, th commutator [, [, H ]] is m m ( m) ( m) 4. Givn : V ˆ ˆ ˆ ˆ ˆ i j and V i j k, which on of th following V maks ( V, V, V ) a comlt st for a thr dimnsional ral linar vctor sac? V ˆ ˆ i j 4kˆ V ˆ ˆ ˆ i j k V ˆ ˆ ˆ i j 6k V ˆ ˆ ˆ i j 4k 4. An lctromagntic lan wav is roagating with an intnsity I. Wm in a mdium with and. Th amlitud of th lctric fild insid th mdium is Vm (u to on dcimal lac) N m, 4 NA, c ms 5 4. An n-channl FET having Gat-Sourc switch-off voltag VGS(OFF) V is usd to invrt a 5 V squarwav signal as shown. Th maimum allowd valu of R would b k (u to two dcimal lacs). +5V 5 k 5 V V V in R k V out 5 V V V 44. For th transformation Q q cos, P q sin, (whr is a constant) to b canonical, th valu of is. 45. Amongst lctrical rsistivity ( ), thrmal conductivity ( ), scific hat ( ), Young s modulus ( Y ), and magntic susctibility ( ), which quantitis show a shar chang at th surconducting transition tmratur?,,, Y,,,,,, Y, d f ( ) d f ( ) 46. Givn : f ( ), and boundary conditions f () and f (), th valu of f (.5) d d is (u to two dcimal lacs).

7 GATE-PH A two-stat quantum systm has nrgy ignvalus corrsonding to th normalizd stats. At tim t, th systm is in quantum stat h stat at t (6 ) is (u to two dcimal lacs).. Th robability that th systm will b in th sam 48. Th nrgy disrsion for lctron in on dimnsional lattic with lattic aramtr a is givn by E( k) E W cos ka, whr W and E ar constants. Th ffctiv mass of th lctron nar th bottom of th band is Wa Wa Wa 49. Th trm symbol for th lctronic ground stat of oygn atom is 4Wa S D P P 5. An air-conditionr maintains th room tmratur at 7 º whil th outsid tmratur is 47 º. Th hat conductd through th walls of th room from outsid to insid du to tmratur diffrnc is 7 W. Th minimum work don by th comrssor of th air-conditionr r unit tim is W. 5. A uniform circular disc of mass m and radius R is rotating with angular sd about an ais assing through its cntr and making an angl º with th ais of th disc. If th kintic nrgy of th disc is m R, th valu of is (u to two dcimal lacs) MV -rays mittd by th d-citation of F ar attributd, assuming shrical symmtry, to th transition of rotons from d / stat. If th contribution of sin-orbit trm to th total nrgy is writtn as ( l s), th magnitud of is MV (u to on dcimal lac). 5. Th quantum ffcts in an idal gas bcom imortant blow a crtain tmratur T Q whn d-brogli wavlngth corrsonding to th root man squar thrmal sd bcoms qual to th intr-atomic saration. For such a gas of atoms of mass 6 kg and numbr dnsity m, T Q K (u to on dcimal lac). 54. A microcanonical nsmbl consists of atoms with ach taking ithr nrgy stat, or nrgy stat. Both stats ar non-dgnrat. If th total nrgy of this nsmbl is 4, its ntroy will b kb (u to on dcimal lac), whr k B is th Boltzmann constant. 55. A constant and uniform magntic fild B B ˆ k rvads all sac. Which on of th following is th corrct choic for th vctor otntial in oulomb gaug? B ( y) iˆ B ˆ ( y) j B ˆ j ˆ ˆ ( ) B i y j