fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-2011)

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1 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / NUCLER ND PRTICLE PHYSICS NET/JRF (JUNE-) 64 Q. Th adius of a 9Cu nuclus is masud to b cm. (). Th adius of a 7 Mg nuclus can b stimatd to b.86 - cm (b) 5. - cm.6 - cm cm Solution: Sinc R R ( ) / / / RMg Mg 7 RCu Cu 64 RMg RMg cm. RCu 4 4 (B). Th oot-man-squa (.m.s) ngy of a nuclon in a nuclus of atomic numb in its gound stat vais as: 4/ / / / (b) Q. bam of pions (π ) is incidnt on a poton tagt, giving is to th pocss π p n π π (). ssuming that th dcay pocds though stong intactions, th total isospin I and its thid componnt I fo th dcay poducts, a 5 5 I, I (b) I, I 5 I, I I, I 5 Solution: π p n π π ; I :, I : (B). Using isospin symmty, th coss-sction fo th abov pocss can b latd to that of th pocss π n pπ π (b) π p nπ π π n pπ π π p nπ π Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com

2 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES NET/JRF (DEC-) 5 89 Q. ccoding to th shll modl th spin and paity of th two nucli 5 Sb and 8 S a, spctivly, 5 and 5 (b) 5 and and 7 7 and Q4. Th diffnc in th Coulomb ngy btwn th mio nucli 4 C and Mn 5 is 6.MV. ssuming that th nucli hav a sphically symmtic chag distibution and that is appoximatly. MV-fm, th adius of th 49 5 Mn nuclus is m 5. - m (b) m m 5 ΔW (b) R ( Z Z ) ( 5 4 ) 4.9 m. NET/JRF (JUNE-) 7 Q5. Th gound stat of Pb nuclus has spin-paity 5 J p, whil th fist xcitd stat p has J.Th lctomagntic adiation mittd whn th nuclus maks a tansition fom th fist xcitd stat to gound stat a E and E (b) M o E E o M M o M Solution: No paity chang; ΔJ, Fo Fo E typ, ( ) l l l Δπ, (fo no paity chang l ) l M typ, Δ ( ) π, (fo no paity chang l ) ΔJ, No paity chang E ; ΔJ, No paity chang M Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com

3 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Q6. Th dominant intactions undlying th following pocsss. K p π, B. K K μ μ, C. Σ p π a : stong, B: lctomagntic and; C: wak (b) : stong, B: wak and; C: wak : wak, B: lctomagntic and; C: stong : wak, B: lctomagntic and; C: wak () K p π (Stong intaction) I : (Consvd) (B) μ μ K K (Elctomagntic intaction) (C) Σ p π (Wak intaction) I : (Not consvd) NET/JRF (JUNE-) Q7. Th binding ngy of a light nuclus ( Z, ) in MV is givn by th appoximat fomula B (, Z ) wh givn is 4 ( N Z ) / / 6 Z N Z is th nuton numb. Th valu of Z of th most stabl isoba fo a / 6 / (b) 64 4 / B Solution: Z Z Z Z / 6 Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com

4 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Q8. spin-/ paticl undgos th dlay B C D wh it is known that B andc a also spin-/ paticls. Th complt st of allowd valus of th spin of th paticl D is 5,,,,,,... (b), 5 7 only,,,,... Solution: Spin of th lft sid and combind spin of th poducts must b sam to consv th spin angula momntum consvation law. Q9. Muons a poducd though th annihilation of paticl a and its antiplaticl, namly th pocss a a μ μ muon has a st mass of 5 MV/c and its pop lif tim is μ s. If th cnt of mass ngy of th collision is. GV in th laboatoy fam that coincids with th cnt-of-mass fam, thn th faction of muons that will dcay bfo thy ach a dtcto placd 6 km away fom th intaction point is (b) (b) Solution: N t λt N λt γτ N N 6 whτ s,. γ and t sc. 8 t N Thus. γτ N Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com 4

5 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES JRF/NET-(DEC-) Q. Th intinsic lctic dipol momnt of a nuclus Z X incass with Z, but indpndnt of (b) dcass with Z, but indpndnt of is always zo incass with Z and Q. ccoding to th shll modl, th total angula momntum (in units of ) and th paity 7 of th gound stat of th Li nuclus is with ngativ paity (b) with positiv paity with positiv paity 7 with ngativ paity Solution: Z, N 4 Z /, l Fo odd ; ( s )( p ) / / j and paity ( ). NET/JRF (JUNE-4) Q. Th cntly-discovd Higgs boson at th LHC xpimnt has a dcay mod into a photon and a Z boson. If th st masss of th Higgs and Z boson a 5 GV/c and 9 GV/c spctivly, and th dcaying Higgs paticl is at st, th ngy of th photon will appoximatly b 5 GV (b) 5 GV GV 5 GV Solution: ssum H is symbol of Higgs boson, H E γ EH E E H Z ( 5) ( 9) 5 GV Z γ Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com 5

6 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Q. In a classical modl, a scala (spin-) mson consists of a quak and an antiquak bound by a potntial b V () a - wh a MV fm and b MV fm. If th masss of th quak and antiquak a ngligibl, th mass of th mson can b stimatd as appoximatly 4 MV/c (b) 8 MV/c 5 MV/c 45 MV/c (b) Solution: t quilibium spaation th potntial is minimum, thus th quilibium spaation can b dtmind as DV d () b a b a MVfm MVfm fm Th quilibium spaation btwn paticls is also stimatd by unctainty pincipl cδt c ( wh, ΔEΔt ) ΔE Wh, c is th vlocity of th vitual mson MV. fm c ΔE ΔE ( MV ) Using abov two lation ΔE 8MV th mass of th mson MV. fm ΔE ( MV ) Δ E Δ m c fm ΔE Δ m 8MV / c c Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com 6

7 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Q4. Consid th fou pocsss (i) p n v NET/JRF (DEC-4) (ii) Λ p v Solution: (i) (iii) π v (iv) π γ γ which of th abov is/a fobiddn fo f paticls? only (ii) (b) (ii) and (iv) (i) and (iv) (i) and (ii) p n ν [Not allowd] It violat ngy consvation. Th mass of poton is lss than mass of nuton. F poton is stabl and can not dcay to nuton. Poton can dcay to nuton only insid th nuclus, wh ngy violation is takn ca by Hisnbg unctainty pincipl. (ii) Λ [Not allowd]. In this dcay chag is not consvd p ν (iii) π ν [allowd though Wak intaction] (iv) π γ γ [allowd though Elctomagntic intaction] Q5. In dp inlastic scatting lctons a scattd off potons to dtmin if a poton has any intnal stuctu. Th ngy of th lcton fo this must b at last V (b).5 V.5 V.5 V (b) Solution: Th intnal stuctu of poton can only b dtmind if th wavlngth of th incoming lcton is naly qual to th siz of th poton i.. λ ( ) / 5 R. fm. fm. m ccoding to d-bogli lation, h λ p h me This can b also wittn as λ Α 5 E V ( ) Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com 7

8 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES 5 5 E( V).4 5 (. λ Α ) E.4 Th bt suitabl answ is option (b). Q6. If th binding ngy B of a nuclus (mass numb and chag Z ) is givn by wh B a V a S a / sym ( Z ) a Z C / av 6 MV, as 6 MV, asym 4 MV and a C. 75MV, thn fo th most stabl isoba fo a nuclus with 6 is 68 (b) db Solution: Fo th most stabl isoba fo a nuclus ( Z ) ( ) / V Z az C / dz ( ) asym ( ) 6 Z 4 Z 6 Z ( Z 6) Z ( ) Z 6 9Z 4Z 6 6 Z 8. NET/JRF (JUNE-5) Q7. Th action D D 4 H π cannot pocd via stong intactions bcaus it ns. Solution: violats th consvation of angula momntum bayon numb D D H π (Not consvd) 4 I : This isopin is not consvd in abov action. (b) lctic chag isospin Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com 8

9 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES Q8. Lt us appoximat th nucla potntial in th shll modl by a th dimnsional isotopic hamonic oscillato. Sinc th lowst two ngy lvls hav angula momnta ns. l and l spctivly, which of th following two nucli hav magic numbs of potons and nutons? 4 6 H and O (b) D and 8 B 4 H and 8 B H and C 6 Solution: and 4 H has Z, N Z N magic numbs (,8,,8,5,8,6 ) 6 8O has 8, 8 Q9. Th cham quak s assignd a cham quantum numb C. How should th Gllmann- ns. Nishijima fomula fo lctic chag b modifid fo fou flavos of quaks? I ( BS C) (b) I ( B S C) I ( B S C) I ( B S C) Solution: Fom Gll-Mann-Nishijima fomula Q I ( B S) Fo Quak it is gnalizd as Q I ( B S C) NET/JRF (DEC-5) Q. Consid th following pocsss involving f paticls (i) n p v (ii) p n π (iii) p n π π π (iv) p v n Which of th following statmnts is tu? Pocss (i) obys all consvation laws (b) Pocss (ii) consvs bayon numb, but violats ngy-momntum consvation pocss (iii) is not allowd by stong intaction but is allowd by wak intactions Pocss (iv) consvs bayon numb, but violats lpton numb consvation Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com 9

10 Institut fo NET/JRF, GTE, IIT JM, JEST, TIFR and GRE in PHYSICL SCIENCES ns.: (b) Solution: (i) n p v spin q (consvd) (not consvd) L (not consvd) (ii) Bayon numb is consvd but ngy and momntum consvation violatd. (iii) spin is not consvd (iv) obys all consvation laws. Q. Of th nucli of mass numb 5, th binding ngy calculatd fom th liquid dop modl (givn that th cofficints fo th Coulomb and th asymmty ngy a ac ns.: Solution:.7 MV and a.5 MV spctivly) is a maximum fo 5 54 Z sym X (b) 4 5 4a a 4a a / / a c c / / a c 8a a 8aa a c ( ) ( ) Z / Z I 5 T Sb 5 / Z Had offic fiziks, H.No., G.F, Jia Saai, Na IIT, Hauz Khas, Nw Dlhi 6 Phon: / Banch offic nand Institut of Mathmatics, 8 B/6, Jia Saai, Na IIT Hauz Khas, Nw Dlhi 6 Wbsit: fiziks.physics@gmail.com