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9.%20Nuclear and Particle Physics NET-JRF VKS

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics

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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-2011) Q1. The radius of a Cu nucleus is measured to be 4.8 10-13 cm. 64 29 (A). The radius of a 27 12 Mg nucleus can be estimated to be (a) 2.86 10-13 cm Ans: (b) 5.2 10-13 cm (c) 3.6 10-13 cm (d) 8.6 10-13 cm (c) Solution: Since R R0 A 1/ 3 RMg RMg RCu AMg A Cu 1/ 3 27 64 1/ 3 3 3 RMg 4.8 10 13 3.6 10 13 cm. RCu 4 4 (B). The root-mean-square (r.m.s) energy of a nucleon in a nucleus of atomic number A in its ground state varies as: (a) A4 / 3 (c) A 1/ 3 (b) A1/ 3 (d) A 2 / 3 Ans: (c) Q2. A beam of pions ( +) is incident on a proton target, giving rise to the process +p n + + + + (A). Assuming that the decay proceeds through strong interactions, the total isospin I and its third component I3 for the decay products, are 3 (a) I , I 3 2 5 (c) I , I 3 2 Ans: 3 2 3 2 5 5 (b) I , I 3 2 2 1 1 (d) I , I 3 2 2 (c) Solution: p n ; I : 1 5 1 3 1 1 , I3 : 1 1 2 2 2 2 (B). Using isospin symmetry, the cross-section for the above process can be related to that of the process (a) n p (c) n p Ans: (b) p n (d) p n (c) Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q3. NET/JRF (DEC-2011) According to the shell model the spin and parity of the two nuclei 125 51 Sb and 49 24 Cr and 89 38 Sr are, respectively, 5 7 (b) and 2 2 7 7 (d) and 2 2 5 5 (a) and 2 2 7 5 (c) and 2 2 Ans: (d) Q4. The difference in the Coulomb energy between the mirror nuclei 49 25 Mn is 6.0 MeV . Assuming that the nuclei have a spherically symmetric charge distribution and that e2 is approximately 1.0 MeV-fm, the radius of the 49 25 Mn nucleus is (a) 4.9 10-13 m (c) 5.1 10-13 m Ans: (b) 4.9 10-15 m (d) 5.1 10-15 m R (b) 3e 2 3 1 10 15 2 Z 12 Z 2 25 2 24 2 4.9 10 15 m . 5 W 5 6 NET/JRF (JUNE-2012) Q5. The ground state of 207 12 Pb nucleus has spin-parity J p 1 , while the first excited state 2 5 has J .The electromagnetic radiation emitted when the nucleus makes a transition 2 p from the first excited state to ground state are (a) E2 and E3 Ans: (b) M2 or E3 (c) E2 or M3 (d) M2 or M3 (c) Solution: No parity change; J 2,3 For E l type, 1 , (for no parity change l 2 ) l For M l type, 1 , (for no parity change l 3 ) l 1 J 2 , No parity change E2 ; J 3 , No parity change M 3 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 2 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q6. The dominant interactions underlying the following processes A. K p , B. K K , C. p 0 are (a) A: strong, B: electromagnetic and; C: weak (b) A: strong, B: weak and; C: weak (c) A: weak, B: electromagnetic and; C: strong (d) A: weak, B: electromagnetic and; C: weak Ans: (a) (A) K p (Strong interaction) 1 1 I 3 : 1 1 (Conserved) 2 2 (B) K K (Electromagnetic interaction) (C) p 0 (Weak interaction) I3 :1 1 0 2 (Not conserved) NET/JRF (JUNE-2013) Q7. The binding energy of a light nucleus Z, A in MeV is given by the approximate formula B A, Z 16 A 20 A 2 / 3 N Z 3 2 1 / 3 Z A 30 4 A 2 where N A Z is the neutron number. The value of Z of the most stable isobar for a given A is A A2 / 3 1 (a) 2 160 A A2 / 3 1 (c) 2 120 Ans: 1 1 (b) A 2 A A4 / 3 1 (d) 2 64 1 (a) B Solution: Z Z Z A A2 / 3 0 Z 1 2 160 1 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 3 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q8. A spin-1/2 particle A undergoes the delay A B C D where it is known that B and C are also spin-1/2 particles. The complete set of allowed values of the spin of the particle D is (a) (b) 0, 1 (c) Ans: 1 3 5 ,1, , 2, , 3, ... 2 2 2 1 only 2 (d) 1 3 5 7 , , , ,.... 2 2 2 2 (c) Solution: Spin of the left side and combined spin of the products must be same to conserve the spin angular momentum conservation law. Q9. Muons are produced through the annihilation of particle a and its antiplarticle, namely the process a a A muon has a rest mass of 105 MeV/c2 and its proper life time is 2 s . If the center of mass energy of the collision is 2.1 GeV in the laboratory frame that coincides with the center-of-mass frame, then the fraction of muons that will decay before they reach a detector placed 6 km away from the interaction point is (a) e 1 (c) 1 e 2 Ans: (b) 1 e 1 (d) e 10 (b) t Solution: N N 0 e t N e t e N0 where 2 10 6 s , 6 10 3 2.1 2 10 5 sec . 103 20 and t 8 3 10 105 1 1 N Thus e 2 1 e 1 . 2 N0 t Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 4 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES JRF/NET-(DEC-2013) Q10. The intrinsic electric dipole moment of a nucleus A Z X (a) increases with Z , but independent of A (b) decreases with Z , but independent of A (c) is always zero (d) increases with Z and A Ans: (d) Q11. According to the shell model, the total angular momentum (in units of ) and the parity 7 Li nucleus is of the ground state of the 3 (a) (b) 3 with positive parity 2 (c) Ans: 3 with negative parity 2 1 with positive parity 2 (d) 7 with negative parity 2 (a) Solution: Z 3, N 4 1 1 For odd Z 3; s12/ 2 p3 / 2 j 3 / 2, l 1 and parity 1 1 . NET/JRF (JUNE-2014) Q12. The recently-discovered Higgs boson at the LHC experiment has a decay mode into a photon and a Z boson. If the rest masses of the Higgs and Z boson are 125 GeV/c 90 GeV/c 2 2 and respectively, and the decaying Higgs particle is at rest, the energy of the photon will approximately be (a) 35 3 GeV Ans: (b) 35 GeV (c) 30 GeV (d) 15 GeV (c) Solution: Assume H is symbol of Higgs boson, H E Z 2 2 EH EZ 125 2 90 2 30GeV 2E H 2 125 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 5 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q13. In a classical model, a scalar (spin-0) meson consists of a quark and an antiquark bound by a potential V r ar b r where a 200 MeV fm -1 and b 100 MeV fm . If the masses of the quark and antiquark are negligible, the mass of the meson can be estimated as approximately (a) 141 MeV/c 2 Ans: (b) 283 MeV/c 2 (c) 353 MeV/c 2 (d) 425 MeV/c 2 (b) Solution: At equilibrium separation the potential is minimum, thus the equilibrium separation can be determined as DV r b a 2 0 dr r r0 r0 r0 b 100MeVfm 1 1 fm 1 a 200MeVfm 2 The equilibrium separation between particles is also estimated by uncertainty principle r0 c t r0 c E ( where, E t ) Where, c is the velocity of the virtual meson r0 c 200 MeV . fm E E MeV Using above two relation 200 MeV . fm 1 fm E MeV 2 E 200 2 283 MeV E m c 2 the mass of the meson m E 283MeV / c 2 2 c Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 6 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES NET/JRF (DEC-2014) Q14. Consider the four processes (i) p n e ve (ii) 0 p e ve (iii) e ve (iv) 0 which of the above is/are forbidden for free particles? (a) only (ii) Ans: (b) (ii) and (iv) (c) (i) and (iv) (d) (i) and (ii) (d) Solution: (i) p n e e [Not allowed] It violate energy conservation. The mass of proton is less than mass of neutron. Free proton is stable and can not decay to neutron. Proton can decay to neutron only inside the nucleus, where energy violation is taken care by Heisenberg uncertainty principle. (ii) 0 p e e [Not allowed]. In this decay charge is not conserved (iii) e e [allowed through Weak interaction] (iv) 0 [allowed through Electromagnetic interaction] Q15. In deep inelastic scattering electrons are scattered off protons to determine if a proton has any internal structure. The energy of the electron for this must be at least (a) 1.25 109 eV Ans: (b) 1.25 1012 eV (c) 1.25 106 eV (d) 1.25 108 eV (b) Solution: The internal structure of proton can only be determined if the wavelength of the incoming electron is nearly equal to the size of the proton i.e. R 1.2 A1/ 3 fm 1.2 fm 1.2 10 15 m h p According to de-Broglie relation, 0 This can be also written as h 150 E eV 2mE Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 7 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES E eV 150 0 2 150 1.04 1012 E 1.04 1012 eV 1.2 10 5 2 The bet suitable answer is option (b). Q16. If the binding energy B of a nucleus (mass number A and charge Z ) is given by B aV A a S A 2/3 a sym 2Z A 2 aC Z 2 1/ 3 A A where aV 16 MeV , a S 16 MeV , a sym 24 MeV and aC 0.75 MeV , then for the most stable isobar for a nucleus with A 216 is (a) 68 Ans: (b) 72 (c) 84 (d) 92 (c) Solution: For the most stable isobar for a nucleus 24 2 2 Z A 2 2aC Z dB 1/ 3 0 0 asym A A dZ 4 2Z 216 3 2Z 2 2Z 216 2 2Z 0 0.75 0 1/ 3 9 4 6 216 216 4 2Z 216 Z 0 16 2Z 216 9Z 0 41Z 216 16 Z 82.3 9 4 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 8

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