NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-) 64 Q. Th radius of a 9Cu nuclus is masurd to b 4.8 - cm. (A). Th radius of a 7 Mg nuclus can b stimatd to b.86 - cm (b) 5. - cm (c).6 - cm (d) 8.6 - cm (c) / / / RMg AMg 7 Solution: Sinc R R A RCu ACu 64 RMg RMg 4.8.6 cm. RCu 4 4 (B). Th root-man-squar (r.m.s) nrgy of a nuclon in a nuclus of atomic numbr A in its ground stat varis as: 4/ A / (b) A / (c) A / (d) A (c) Q. A bam of pions (π + ) is incidnt on a proton targt, giving ris to th procss pn (A). Assuming that th dcay procds through strong intractions, th total isospin I and its third componnt I for th dcay products, ar 5 5 I, I (b) I, I 5 (c) I, I (d) I, I (c) 5 Solution: p n ; I :, I : (B). Using isospin symmtry, th cross-sction for th abov procss can b rlatd to that of th procss n p (b) p n (c) n p (d) p n (c) H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
NET/JRF (DEC-) 5 89 Q. According to th shll modl th spin and parity of th two nucli 5 Sb and 8 Sr ar, rspctivly, 5 and 5 (b) 5 and 7 Solution: 7 (c) (d) Z 5 5 and 5 5 Sb ; Z 5 and N 74 7 (d) 7 and s p p d s d f p f p g g 4 6 4 8 4 6 / / / 5/ / / 7/ / 5/ / 9/ 7/ 7 j and l 4. Thus spin and parity 7 89 8 Sr ; Z 8 and N 5 N 5: s p p d s d f p f p g g 4 6 4 8 4 6 / / / 5/ / / 7/ / 5/ / 9/ 7/ 7 j and l 4. Thus spin and parity 7 49 49 Q4. Th diffrnc in th Coulomb nrgy btwn th mirror nucli 4 Cr and Mn 5 is 6.MV. Assuming that th nucli hav a sphrically symmtric charg distribution and that is approximatly. MV-fm, th radius of th 49 5 Mn nuclus is 4.9 - m (c) 5. - m (b) 4.9-5 m (d) 5. -5 m 5 W 5 6 5 5 (b) R Z Z 5 4 4.9 m. H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
NET/JRF (JUNE-) 7 Q5. Th ground stat of Pb nuclus has spin-parity J p, whil th first xcitd stat 5 p has J.Th lctromagntic radiation mittd whn th nuclus maks a transition from th first xcitd stat to ground stat ar E and E (b) M or E (c) E or M (d) M or M (c) Solution: No parity chang; J, For For E typ, l l l, (for no parity chang l ) l M typ,, (for no parity chang l ) J, No parity chang E ; J, No parity chang M Q6. Th dominant intractions undrlying th following procsss A. K p, B. K K, C. p ar A: strong, B: lctromagntic and; C: wak (b) A: strong, B: wak and; C: wak (c) A: wak, B: lctromagntic and; C: strong (d) A: wak, B: lctromagntic and; C: wak (A) K p (Strong intraction) I : (Consrvd) (B) K K (Elctromagntic intraction) (C) p (Wak intraction) I : (Not consrvd) H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
NET/JRF (JUNE-) Q7. Th binding nrgy of a light nuclus Z, A in MV is givn by th approximat formula whr givn A is / / N Z BA, Z 6A A Z A 4 A N A Z is th nutron numbr. Th valu of Z of th most stabl isobar for a / A A 6 (b) A (c) / A A (d) A A 64 4 / / B A A Solution: Z Z Z Z 6 Q8. A spin-/ particl A undrgos th dlay A B C D, whr it is known that B andc ar also spin-/ particls. Th complt st of allowd valus of th spin of th particl D is 5 5 7,,,,,,... (b), (c) only (d),,,,... (c) Solution: Spin of th lft sid and combind spin of th products must b sam to consrv th spin angular momntum consrvation law. Q9. Muons ar producd through th annihilation of particl a and its anti-particl, namly th procss a a. A muon has a rst mass of 5 MV/c and its propr lif tim is s. If th cntr of mass nrgy of th collision is. GV in th laboratory fram that coincids with th cntr-of-mass fram, thn th fraction of muons that will dcay bfor thy rach a dtctor placd 6 km away from th intraction point is (b) (b) (c) (d) Solution: N t t N t N N 6., whr s, and 5 t 6 5 8 sc. Thus t N N. H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 4
NET/JRF -(DEC-) Q. Th intrinsic lctric dipol momnt of a nuclus A Z X incrass with Z, but indpndnt of A (b) dcrass with Z, but indpndnt of A (c) is always zro (d) incrass with Z and A (d) Q. According to th shll modl, th total angular momntum (in units of ) and th parity 7 of th ground stat of th Li nuclus is with ngativ parity (b) with positiv parity (c) with positiv parity (d) 7 with ngativ parity Solution: Z, N 4 Z /, l For odd ; s p / / j and parity. NET/JRF (JUNE-4) Q. Th rcntly-discovrd Higgs boson at th LHC xprimnt has a dcay mod into a photon and a Z boson. If th rst masss of th Higgs and Z boson ar 5 GV/c and 9 GV/c rspctivly, and th dcaying Higgs particl is at rst, th nrgy of th photon will approximatly b 5 GV (b) 5 GV (c) GV (d) 5 GV (c) Solution: Assum H is symbol of Higgs boson, H E EH E E H Z 5 9 5 GV Z H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 5
Q. In a classical modl, a scalar (spin-) mson consists of a quark and an antiquark bound b by a potntial V r ar r, whr - a MV fm and b MV fm. If th masss of th quark and antiquark ar ngligibl, th mass of th mson can b stimatd as approximatly 4 MV/c (b) 8 MV/c (c) 5 MV/c (d) 45 MV/c (b) Solution: At quilibrium sparation th potntial is minimum, thus th quilibrium sparation can b dtrmind as dv r dr rr b a r b MVfm r fm a MVfm Th quilibrium sparation btwn particls is also stimatd by uncrtainty principl r ct r c ( whr, Et ) E Whr, c is th vlocity of th virtual mson MV. fm r c E E MV Using abov two rlation E 8MV th mass of th mson MV. fm E MV E m c E m c MV / fm 8 c NET/JRF (DEC-4) Q4. Considr th four procsss (i) p n v (ii) p v (iii) v (iv) which of th abov is/ar forbiddn for fr particls? only (ii) (b) (ii) and (iv) (c) (i) and (iv) (d) (i) and (ii) (d) H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 6
Solution: (i) fiziks p n [Not allowd] It violat nrgy consrvation. Th mass of proton is lss than mass of nutron. Fr proton is stabl and can not dcay to nutron. Proton can dcay to nutron only insid th nuclus, whr nrgy violation is takn car by Hisnbrg uncrtainty principl. (ii) [Not allowd]. In this dcay charg is not consrvd p (iii) [allowd through Wak intraction] (iv) [allowd through Elctromagntic intraction] Q5. In dp inlastic scattring lctrons ar scattrd off protons to dtrmin if a proton has any intrnal structur. Th nrgy of th lctron for this must b at last 9 6 8.5 V (b).5 V (c).5 V (d).5 V (b) Solution: Th intrnal structur of proton can only b dtrmind if th wavlngth of th incoming lctron is narly qual to th siz of th proton... i.. / 5 R A fm fm m h According to d-brogli rlation, p h me 5 This can b also writtn as E V 5 5 EV.4 5. E.4 Th bt suitabl answr is option (b). Q6. If th binding nrgy B of a nuclus (mass numbr A and charg Z ) is givn by V whr Z A az C / / BaV AaS A asym A A av 6 MV, as 6 MV, asym 4 MV and a C. 75MV, thn for th most stabl isobar for a nuclus with A 6 is 68 (b) 7 (c) 84 (d) 9 (c) H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 7
db Solution: For th most stabl isobar for a nuclus / Z A az C / A dz asym A Z 6 Z 4 Z 6 Z 4.75 6 6 9 4 6 4Z 6 Z 9 4 6 Z 6 9Z 4Z 66 Z 8. NET/JRF (JUNE-5) Q7. Th raction D D 4 H cannot procd via strong intractions bcaus it Ans. Solution: violats th consrvation of angular momntum (c) baryon numbr (d) D D H (Not consrvd) 4 I : (b) lctric charg (d) isospin This isopin is not consrvd in abov raction. Q8. Lt us approximat th nuclar potntial in th shll modl by a thr dimnsional isotropic harmonic oscillator. Sinc th lowst two nrgy lvls hav angular momnta Ans. l and l rspctivly, which of th following two nucli hav magic numbrs of protons and nutrons? 4 6 H and O (b) D and 8 B (c) 4 H and 8 B (d) 4 8 4 4 H and C 6 Solution: and 4 H has Z, N 6 8O has Z 8, N 8 magic numbrs,8,,8,5,8,6 Q9. Th charm quark S assignd a charm quantum numbr C. How should th Gllmann-Nishijima formula for lctric charg b modifid for four flavors of quarks? I BS C (b) I BS C (c) I BS C (d) I BS C H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 8
Ans. (d) Solution: From Gll-Mann-Nishijima formula Q I B S For Quark it is gnralizd as Q I BS C NET/JRF (DEC-5) Q. Considr th following procsss involving fr particls (i) n p v (ii) pn (iii) (iv) p n p v n Which of th following statmnts is tru? Procss (i) obys all consrvation laws (b) Procss (ii) consrvs baryon numbr, but violats nrgy-momntum consrvation (c) procss (iii) is not allowd by strong intraction but is allowd by wak intractions (d) Procss (iv) consrvs baryon numbr, but violats lpton numbr consrvation Ans.: (b) Solution: (i) spin n p v q (consrvd) (not consrvd) L (not consrvd) (ii) Baryon numbr is consrvd but nrgy and momntum consrvation violatd. (iii) spin is not consrvd (iv) obys all consrvation laws. Q. Of th nucli of mass numbr A 5, th binding nrgy calculatd from th liquid drop modl (givn that th cofficints for th Coulomb and th asymmtry nrgy ar ac.7 MV and a.5 MV rspctivly) is a maximum for 5 54 Ans.: (c) sym X (b) 4 5 5 5 I (c) 5 T (d) Sb 5 H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 9
Solution: fiziks Z 4a a A 4a Aa A / / a c a c / / aa c 8aA a 8aa aa c Z 4.55.7 5 8.5.7 5 / / 5 7.5 67.5 Z 5.4 Z 5 8 5 5 NET/JRF (JUNE-6) Q. A radioactiv lmnt X dcays toy, which in turn dcays to a stabl lmnt Z. Th dcay constant from X to Y is, and that from Y to Z is. If, to bgin with, thr ar only N atoms of X, at short tims ( t as wll as ) th numbr of atoms of Z will b Nt (b) (c) Nt (d) Nt X Y Z Solution: t N t N N N t dn dn Rat quations N N, N N, N dt dt t t N N t t N t t t t t t N t t t N N Nt Nt H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
Q. In th larg hadron collidr LHC, two qual nrgy proton bams travrs in opposit dirctions along a circular path of lngth 7 km. If th total cntr of mass nrgy of a proton-proton pair is4 TV, which of th following is th bst approximation for th propr tim takn by a proton to travrs th ntir path? ns (b). s (c). ns (d). s Solution: Th proton travl at narly spd of light in LHC, thrfor d 7 t 8 c 5 9 sc Sinc, proton is rlativistic, t t v t 6 mc 98 MV 98 V E m c E 7TV 7 V t 5 4 8 Thus, t 9.4. sc ns c.4 4 Q4. Lt E S dnots th contribution of th surfac nrgy pr nuclon in th liquid drop modl. Th ratio 7 64 S : S E Al E Zn is : (b) 4: (c) 5: (d) : (b) Solution: E S B A A A A ES Al 7 64 4 ES Z n 64 7 Q5. According to th shll modl, th nuclar magntic momnt of th 7 Al nuclus is (Givn that for a proton g, g 5.586, and for a nutron g, g.86 ) l s l s.9 N (b) 4.44 N (c) 4.79 N (d) (c) 7 Solution: Al : Z, N 4for Magntic momnt, 4 5 Z, S/, P/, P/, d5/ j 5, l 5 j g S N 5.586 N 4.79 N H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
NET/JRF (DEC-6) Q6. What should b th minimum nrgy of a photon for it to split an -particl at rst into a tritium and a proton? (Th masss of H, 4 H and rspctivly, and amu 98MV ) H ar 4.6 amu,.6amu and.7amu. MV (b) MV (c) 9.MV (d) 9.5MV Ans. : (c) Solution: From consrvation of nrgy E mc m c m c H H or E m m m 98 MV 9.5 MV H H Q7. Which of th following raction(s) is/ar allowd by th consrvation laws? (i) n K (ii) p K both (i) and (ii) (c) only (ii) Ans. : Solution: (i) n q : K (b) only (i) (d) nithr (i) nor (ii) B : S : Raction is allowd (ii) p K q : B : S : Raction is allowd H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
Q8. A particl, which is a composit stat of thr quarks ud, and s, has lctric charg, spin and strangnss rspctivly, qual to,, (b),, (c),, (d), Ans. : (c) Solution: charg, spin and strangrs of Quarks ud, & s ar givn as U D S Total Charg Spin or Strangnss If a particl x is a composit of ud, & s, thn nt charg, spin and strangnss on x is nt charg nt spin or and nt strangnss NET/JRF (JUNE-7) Q9. If in a spontanous - dcay of 9 U at rst, th total nrgy rlasd in th raction is Q, thn th nrgy carrid by th - particl is 57 Q / 58 (b) Q /57 (c) Q / 58 (d) Q / 58 Ans. : Solution: Enrgy carrid by th particl is A 4 8 57 KE Q Q Q A 58 Q. Th rang of th nuclar forc btwn two nuclons du to th xchang of pions is Ans. : (c).4 fm. If th mass of pion is 77 / 4 / MV c and th mass of th rho-mson is MV c, thn th rang of th forc du to xchang of rho-msons is.4 fm (b) 7.7 fm (c).5 fm (d).8 fm H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498
c Solution: Rang for nuclar forc btwn nuclon will b Rct and c99mvfm mc 99MVfm R.5 fm MV 77 c c Q. A baryon X dcays by strong intraction as X, whr is a mmbr of th isotriplt,,. Th third componnt I of th isospin of X is Ans. : Solution: (b) / (c) (d) / X I : I for X is. H.No. 4 D, Ground Floor, Jia Sarai, Nar IIT, Hauz Khas, Nw Dlhi 6 Phon: 6865455/+9 98745498 4