PHYSICAL SCIENCE

NUCLEAR & PARTICLE PHYSICS

Previous Year Questions

CSIR-NET/JRF,GATE,JEST,TIFR

DPHYSICS KRISHNA CHOWK, NEW SANGAVI, PUNE-27 CONTACT: 8830156303

1
NO TOPIC PAGE NO:
1. Basic Nuclear Properties 3
2. Properties Of Nuclear Force 5
3. Nuclear Model 7
4. Deuteron Nuclei 16
5. Nuclear Radioactive Decays 18
6. Radioactivity 25
7. Nuclear Reaction 27
8. Nuclear Detector 32
9. Particle Physics 33
10. Miscellaneous 49

2
 NUCLEAR PHYSICS: Basic Nuclear Properties
❖ CSIR-NET PYQ the empirical observation of the charge radii, the
1. The radius of a 6429 Cu nucleus is measured to be volume of the 54 Xe128 nucleus, assumed to be
−13 spherical is
4.8 × 10 cm.
27 [GATE 2008]
(A) The radius of a 12 Mg nucleus can be estimated
to be (a) 8 V (b) 2 V
[CSIR JUNE 2011]
−13
(a) 2.86 × 10 cm (b) 5.2 × 10−13 cm (c)6.75 V (d) 1.89 V

(c)3.6 × 10−13 cm (d) 8.6 × 10−13 cm 5. Consider a nucleus with N neutrons and Z protons.
If mp , mn and BE represent the mass of the proton
(B) The root-mean-square (rms) energy of a the mass of the neutrons and the binding energy of
nucleon in a nucleus of atomic number A in its the nucleus respectively and c is the velocity of
ground state varies as light in free space, the mass of the nucleus is given
[CSIR JUNE 2011] by
4/3
(a) A (b) A1/3 [GATE 2009]
(a) Nmn + Zmp (b) Nmp + Zmn
(c)A−1/3 (d) A−2/3
BE BE
(c)Nmn + Zmp + (d) Nmp + Zmn +
❖ GATE PYQ c2 c2
1. The volume of a nucleus in an atom is proportional
to the 6. The mean kinetic energy of a nuclear in a nucleus
[GATE 2004] of atomic weight A varies as An , where n is (upto
(a) mass number (b) proton number two decimal places)
(c)neutron number (d) electron number [GATE 2015]

2. The form factor ❖ JEST PYQ

r 1. The binding energy of the k-shell electron in a
F(q
⃗ ) = ∫ exp (iq⃗ ⋅ ) ρ‾(r)d3 r Uranium atom (Z = 92, A = 238) will be modified
ℏ
of Rutherford scattering is obtained by choosing a due to
delta function for the charge density ρ(r). The (i) screening caused by other electrons and (ii) the
value of the form factor is finite extent of the nucleus as follows:
[GATE 2004] [JEST 2013]
(a) unity (b) infinity (a) Increases due to (i), remains unchanged due
to (ii).
(c)zero (d) undefined
(b) Decreases due to (i), decreases due to (ii).
3. The order of magnitude of the binding energy per
nucleon in a nucleus is (c)Increases due to (i), increases due to (ii).
[GATE 2006]
−5
(a) 10 MeV −3
(b) 10 MeV (d) Decreases due to (i), remains unchanged due
to (ii).
(c)0.1MeV (d) 10MeV 1 189
2. The stable nucleus that has the radius of Os
3
16
4. An O nucleus is spherical and has a charge radius nucleus is,
4 [JEST 2015]
R and a volume V = 3
πR3 . According to
7 16
(a) Li (b) O

3
 (c) 4 He (d) 14
N

❖ Answer Key
CSIR-NET
1. c 2. c 3. 4. 5.
GATE
1. a 2. a 3. d 4. a 5. c
6. - 0.66
JEST
1. b 2. a

4
 NUCLEAR PHYSICS: Properties Of Nuclear Force
❖ CSIR-NET PYQ 4. The tensor component of the nuclear force may be
1. In a classical model, a scalar (spin-0) meson inferred from the fact that deuteron nucleus
consists of a quark and an antiquark bound by a 2
1H [CSIR JUNE 2022]
potential (a)has only one bound state with total spin S = 1
b
V(r) = ar +
r (b)has a non-zero electric quadrupole moment in
where a = 200MeVfm−1 and b = 100MeVfm. If its ground state
the masses of the quark and antiquark are
negligible, the mass of the meson can be estimated (c)Is stable while triton 13 H is unstable
as approximately
[CSIR JUNE 2014] (d)Is the only two nucleon bound state
(a) 141MeV/c 2 (b) 283MeV/c 2
5. As one moves along the of stability from 56 Fe to
2 2
(c)353MeV/c (d) 425MeV/c 235
U nucleus, the nuclear binding energy per
particle decreases from about 8.8MeV to 7.6MeV.
2. The range of the nuclear force between two This trend is mainly due to the
nucleons due to the exchange of pions is 1.40fm. If (a) short range nature of the nuclear forces
the mass of the pion is 140MeV/c 2 and the mass of
the rho-meson is 770MeV/c 2, then the range of the (b) long range nature of the Coulomb forces
force due to exchange of rho mesons is
[CSIR JUNE 2017] (c)tensor nature of the nuclear forces
(a) 1.40fm (b) 7.70fm
(d) spin dependence of the nuclear forces
(c)0.25fm (d) 0.18fm
❖ GATE PYQ
3. The strong nuclear force between a neutron and a 1. With reference to nuclear forces which of the
proton in a zero orbital angular momentum state following statements is NOT true? The nuclear
is denoted by Fnp (r), where r is the separation forces are
between them. Similarly, Fnn (r) and Fpp (r) denote [GATE 2005]
the forces between a pair of neutrons and protons, (a) short range
respectively, in zero orbital momentum state.
Which of the following is true on average if the (b) charge independent
inter-nucleon distance is 0.2fm < r < 2fm ?
[CSIR DEC 2019] (c)velocity dependent
(a) Fnp is attractive for triplet spin state, and
Fnn , Fpp are always repulsive. (d) spin independent

(b) Fnn and Fnp are always attractive and Fpp is 2. Weak nuclear forces act on
repulsive in this triplet spin state. [GATE 2006]
(a) both hadrons and leptons
(c)Fpp and Fnp are always attractive and Fnn is
always repulsive. (b) hadrons only

(d) All three forces are always attractive. (c)all particles

(d) all charged particle

5
3. A heavy nucleus is found to contain more neutrons
than protons. This fact is related to which one of
the following statements.
[GATE 2008]
(a) The nuclear force between neutrons is
stronger than that between protons.

(b) The nuclear force between protons is of a

shorter range than those between neutrons, so
that a smaller number of protons are held
together by the nuclear force.

(c)Protons are unstable, so their number in a

nucleus diminishes

(d) It costs more energy to add a proton to a

(heavy) nucleus than a neutron because of the
coulomb repulsion between protons

4. Pick the wrong [GATE 2009]

(a) The nuclear force is independent of electric
charge

(b) The Yukawa potential is proportional to

mc
r −1 exp (
ħ
r), where r is the separation
betweeing two nucleus

(c)The range of nuclear force is of the order of

10−15 m − 10−14 m

(d) The nucleons interact among each other by

the exchange of mesons

❖ Answer Key
CSIR-NET
1. b 2. c 3. b 4. b 5. a
GATE
1. d 2. c 3. d 4. b

6
 NUCLEAR PHYSICS: Nuclear Model
❖ CSIR-NET PYQ (a) increases with Z, but independent of A
1. According to the shell model the spin and parity of (b) decreases with Z, but independent of A
the two nuclei 125 89
51 Sb and 38 Sr are, respectively. (c)is always zero
[CSIR DEC 2011] (d) increases with Z and A
5 + 5 + 5 + 7 +
(a) (2) and (2) (b) (2) and (2)
6. According to the shell model, the total angular
momentum (in units of ℏ ) and the parity of the
7 + 5 + 7 ∗ 7 +
(c)(2) and (2) (d) (2) and (2)
ground state of the 73 Li nucleus is
2. The difference in the Coulomb energy between the [CSIR DEC 2013]
49 3
mirror nuclei 49
24 Cr and 25 Mn is 6.0MeV. Assuming (a) with negative parity
2
that the nuclei have a spherically symmetric
charge distribution and that e2 is approximately 3
1.0MeV-fm, the radius of the 99 (b) with positive parity
25 Mn nucleus is 2
[CSIR DEC 2011]
(a) 4.9 × 10−13 m (b) 4.9 × 10−15 m 1
(c) with positive parity
2
−13 −15
(c)5.1 × 10 m (d) 5.1 × 10 m
7
(d) with negative parity
3. The single particle energy difference between the 2
p-orbitals (i.e. p3/2 and p1/2 ) of the nucleus
114 7. A permanently deformed even-even nucleus with
50 Sn is3 MeV . The energy difference between
JP = 2+ has rotational energy 93keV. The energy of
the states in its 1𝑓 orbital is
the next excited state is
[NET Dec. 2012]
[CSIR JUNE 2014]
(a) -7 MeV (b) 7 MeV
(a) 372keV (b) 310keV

(c)5 MeV (d) -5 MeV

(c)273keV (d) 186keV

4. The binding energy of a light nucleus (Z, A) in MeV

8. If the binding energy B of a nucleus (mass number
is given by the approximate formula
A and charge Z ) is given by
3 (N − Z)2 2 2
B(A, Z) ≈ 16A − 20A2/3 − Z2 A−1/3 + 30 (2Z − A) ac Z
4 A B = aV A − aS A2/3 − asym − 1/3
where N = A − Z is the neutron number. The value A A
where aV = 16MeV, aS = 16MeV, asy m = 24MeV
of Z of the most stable isobar for a given A is
and at = 0.75MeV, then the Z for the most stable
[CSIR JUNE 2013]
−1 isobar for a nucleus with A = 216 is
A A2/3 A
(a) (1 − ) (b) [CSIR DEC 2014]
2 160 2 (a) 68 (b) 72
(c)84 (d) 92
−1
A A2/3 A A4/3
(c) (1 − ) (d) (1 + )
2 120 2 64 9. The electric quadrupole moment of an odd
proton nucleus is
5. The intrinsic electric dipole moment of a nucleus (2𝑗 − 1) 2
⟨𝑟 ⟩
A
zX
2(𝑗 + 1)
, where 𝑗 is the total angular momentum. Given
that 𝑅0 = 1.2fm, what is the value, in barn, of the

7
 27 [CSIR DEC 2017]
quadrupole moment of the Al nucleus in the
shell model? 1 − 3 − 5 + 7 +
(a) (2) and (2) (b) (2) and (2)
[NET Dec. 2015]
3 + 5 + 3 − 5 −
(a) 0.043 (b) 0.023 (c)(2) and (2) (d) (2) and (2)
(c)0.915 (d) 0
15. The first excited state of the rotational spectrum of
10. Let us approximate the nuclear potential in the the nucleus 238
92 U has an energy 45keV above the
shell model by a 3-dimensional isotropic harmonic ground state. The energy of the second excited
oscillator. Since the lowest two energy levels have state (in keV), is
angular momenta l = 0 and l = 1 respectively, [CSIR DEC 2017]
which of the following two nuclei have magic (a) 150 (b) 120
numbers of protons and neutrons? (c)90 (d) 60
[CSIR JUNE 2015]
4 16
(a) 2 He and 8 O (b) 12 D and 84 Be 16. The low lying energy levels due to the vibrational
excitations of an even-even nucleus are shown in
(c) 42 He and 84 Be (d) 42 He and 12
6 Be the figure below. [CSIR DEC 2018]

11. Of the nuclei of mass number A = 125, the binding

energy calculated from the liquid drop model
(given that the coefficients for the Coulomb and
the asymmetry energy are ac = 0.7MeV and asynt
= 22.5MeV respectively) is a maximum for
[CSIR DEC 2015]
125
(a) 54 Xe (b) 125
53 I
The spin-parity jp of the level E1 is
(c) 125
52 Te (d) 125
51 Sb (a) 1+ (b) 1−

12. According to the shell model, the nuclear (c)2− (d) 2+

27
magnetic moment of the 13 Al nucleus is (Given
that for a proton 𝑔𝑖 = 1, 𝑔𝑖 = 5.586, and for a 17. The Bethe-Weizsäecker formula for the binding
neutron 𝑔𝑖 = 0, 𝑔𝑖 = −3.826). energy (in MeV ) of a nucleus of atomic number Z
[NET June 2016] and mass number A is [CSIR DEC 2019]
(a) −1.913𝜇𝑁 (b) 14.414𝜇𝑁 Z(Z − 1) (A − 2Z)2
15.8A − 18.3A2/3 − 0.714 − 23.2
A1/3 A
(c)4.793𝜇𝑁 (d) 0 The ratio Z/A for the most stable isobar of A = 64
nucleus, is nearest to
13. Let ES denote the contribution of the surface [CSIR DEC 2019]
energy per nucleon in the liquid drop model. The (a) 0.30 (b) 0.35
27
ratio ES ( 13 Al): ES ( 64
30 Zn) is
[CSIR JUNE 2016] (c)0.45 (d) 0.50
(a) 2: 3 (b) 4: 3
18. The Bethe-Weizsacker formula for the binding
(c)5: 3 (d) 3: 2 energy (in MeV ) of a nucleus of atomic number 𝑍
and mass number 𝐴 is
𝑍(𝑍 − 1) (𝐴 − 2𝑍)2
14. The spin-parity assignments for the ground and 15.8𝐴 − 18.3𝐴2/3 − 0.714 − 23.2
𝐴1/3 𝐴
first excited states of the isotropy 57
28 Ni, in the
singlo particle shell model, are

8
 The ratio 𝑍/𝐴 for the most stable isobar of a 𝐴 = 22. The energy (in keV) and spin-parity values E(JP )
64 nucleus, is nearest to of the low-lying excited states of a nucleus of mass
(a) 0.30 (b) 0.35
number A = 152 are
+ ), + ), + )and + ).
(c)0.45 (d) 0.50 122(2 366(4 707(6 1125(8 It may
be inferred that these energy levels correspond to
19. The binding energy 𝐵 of a nucleus is a [CSIR JUNE 2023]
approximated by a formula: (a) rotational spectrum of a deformed nucleus
(b) rotational spectrum of a spherically symmetric
𝐵 = 𝑎1 𝐴 − 𝑎2 𝐴2/3 − 𝑎3 𝑍 2 𝐴−1/3 − 𝑎4 (𝐴 nucleus
− 2𝑍)2 𝐴−1 (c)vibrational spectrum of a deformed nucleus
[NET Nov. 2020] (d) vibrational spectrum of a spherically
where 𝑍 is the atomic number and 𝐴 is the mass symmetric nucleus
𝑎
number of the nucleus. If 4 = 30, the atomic
𝑎3
number 𝑍 for naturally stable isobars (constant 23. In a shell model description, neglecting Coulomb
value of 𝐴 ) is effects, which of the following statements for the
30𝐴 30𝐴 energy and spin-parity is correct for the first
(a) (b)
60 + 𝐴 2/3 30 + 𝐴2/3 excited state of 𝐴 = 12 isobars 12 12 12
5 B, 6 C, 7 N ?
[CSIR DEC 2023]
60𝐴 120𝐴 12 12
(a)same for 5 B, 6 C and 7 N12
(c) (d)
120 + 𝐴2/3 60 + 𝐴2/3
12 12 12
(b)different for each 5 B, 6 C and 7 N
20. The magnetic moments of a proton and a neutron
are 2.792μN and −1.913μN , where μN is the 12 12 12
(c)same for 6 C and 7 N, but different for 5 B
nucleon magnetic moment. The values of the
magnetic moments of the mirror nuclei 19 9 F10 and 12 12 12
19 (d)same for 5 B and 7 N, but different for 6 C
10 Ne 9 , respectively, in the Shell model, are
closest to
❖ GATE PYQ
[CSIR DEC 2020]
1. The nuclear spins of 6 C14 and 12 Mg
25
nuclei are
(a) 23.652μN and −18.873μN
respectively
[GATE 2002]
(b) 26.283μN and −16.983μN
(a) zero and half-integer
(c)−2.628μN and 1.887μN
(b) half-integer and zero
(d) 2.628μN and −1.887μN
(c)an integer and half-integer
21. A60 Co nucleus 𝛽-decays from its ground state
(d) both half-integers
with 𝐽𝑝 = 5+ to a state of 60 Ni with 𝐽𝑝 = 4+ . From
the angular momentum selection rules, the
2. The spin and parity of 4 Be9 nucleus, as predicted
allowed values of the orbital angular momentum
by the shell model, are respectively.
𝐿 and the totalspin 𝑆 of the electron-antineutrino
[GATE 2002]
pair are
(a) 3/2 and odd (b) 1/2 and odd
[NET June 2021]
(a) 𝐿 = 0 and 𝑆 = 1 (b) 𝐿 = 1 and 𝑆 = 0
(c)3/2 and even (d) 1/2 and even
(c)𝐿 = 0 and 𝑆 = 0 (d) 𝐿 = 1 and 𝑆 = 1

9
3. The single particle states occupied by the last [GATE 2005]
proton and the last neutron, respectively, are 3+ 1+
given by (a) (b)
2 2
[GATE 2004]
(a) d5/2 and f7/2 (b) d3/2 and f5/2 3− 1−
(c) (d)
2 2
(c)d5/2 and f5/2 (d) d3/2 and f7/2
7. The experimentally measured sping factors of
Common Data for Q. 4 and Q.5: proton and a neutron indicate that
The nucleus 41 Ca can be described by the single [GATE 2006]
particle shell model. (a) Both proton and neutron are elementary
point particles
4. The ground state angular momentum and parity of
41
Ca are (b) Both proton and neutron are not elementary
[GATE 2004] point particles
7 3
(a) − (b) +
2 2 (c)While proton is an elementary point particle,
neutron is not
5 5
(c) (d)
2+ 2−
(d) While neutron is an elementary point particle,
proton is not
5. Which of the following expressions for total
binding energy B of a nucleus is correct
8. According to the shell model the ground state spin
(a1 , a2 , a3 , a4 > 0) ?
of the 17 O nucleus is
[GATE 2005]
[GATE 2007]
3 + 5 +
Z(Z − 1)
(a)B = a1 A − a2 A2/3 − a3 (a) (b)
A1/3 2 2
(A − 2Z)2
− a4 +δ 3− 5−
A
(c) (d)
2 2
Z(Z − 1)
(b)B = a1 A + a2 A2/3 − a3
A1/3 9. The following gives a list of pairs containing (I ) a
(A − 2Z)2 nucleus (ii) one of its properties. Find the pair
− a4 +δ
A which is inappropriate.
[GATE 2008]
Z(Z − 1) (A − 2Z)2 20
(a) ( I ) 10 Ne nucleus;
(c)B = a1 A + a2 A1/3 − a3 − a 4
A1/3 A (ii) stable nucleus
+δ
(b) (I ) A spheroidal nucleus;
1/3
Z(Z − 1)
(d)B = a1 A − a2 A − a3 (ii) an electric quadrupole moment
A1/3
(A − 2Z)2
− a4 +δ (c)( I ) 8 O16 nucleus;
A
(ii) nuclear spin J = 1/2
6. According to the shell model, the ground state of
15 (d) ( I ) U 238 nucleus;
8 O nucleus is
(ii) Binding energy = 1785MeV (approximately)

10
10. The four possible configuration of neutrons in the 13. In the nuclear shell model the spin parity of 15 N
ground state of 4 Be9 nucleus, according to the is given by
shell model, and the associated nuclear spin are [GATE 2010]
listed below. Choose the correct one: 1 − 1+
[GATE 2008] (a) (b)
2 2
2 3
(a) (1s1/2 ) (1p3/2 ) ; J = 3/2
3− 3+
2 2 1 (c) (d)
(b) (1s1/2 ) (1p1/2 ) (1p3/2 ) ; J = 3/2 2 2

228
1 4 14. The first three energy levels of Th90 are show
(c)(1s1/2 ) (1p3/2 ) ; J = 1/2
below
2 2 1
(d) (1s1/2 ) (1p3/2 ) (1p1/2 ) ; J = 1/2

11. The mass difference between the pair of mirror The expected spin-pairty and energy of the next
nuclei 6 C11 and 5 B11 is given to be ΔMeV/c 2 . level are given by
According to the semi-empirical mass formula, the [GATE 2010]
mass difference between the pair of mirror nuclei (a) (6+ ; 400keV) (b) (6+ ; 300keV)
17
9F and 8 O17 will approximately be (rest mass
of proton mp = 938.27MeV/c 2 and rest mass of (c)(2+ ; 400keV) (d) (4+ ; 300keV)
neutron mn = 939.57MeV/c 2 )
[GATE 2008] 15. The semi − empirical mass formula for the
(a) 1.39ΔMeV/c 2 binding energy of nucleus contains a surface
correction term. This term depends on the mass
number A of the nucleus as
(b) (1.39Δ + 0.5)MeV/c 2
[GATE 2011]
−1/3 1/3
(c)0.86ΔMeV/c 2 (a) A (b) A

(d) (1.6Δ + 0.78)MeV/c 2 (c)A2/3 (d) A

12. Consider the following expression for the mass of 16. According to the single particle nuclear shell
a nucleus with Z protons and A nucleons: model, the spin parity of the ground state of 17
8 O is
1 [GATE 2011]
M(A, Z) = 2 (f(A) + yZ + zZ2 ) 1− 3−
c (a) (b)
. Here f(A) is a function of A 2 2
y = −4a
z = ac A−1/3 + 4aA A−1 3+ 5+
aA and ac are constants of suitable dimensions. For (c) (d)
2 2
a fixed A, the expression of Z for the most stable
nucleus is 17. Total binding energies of 𝑂15 , 𝑂16 and 𝑂17 are
[GATE 2009] 111.96MeV, 127.62MeV and 131.76 MeV ,
A/2 A/2 respectively. The energy gap between 1 𝑝1/2 and
(a)Z = ac 2/3 (b) Z = a
1 + (a ) A 1 + (4ac ) A2/3 1
𝑑1/2 neutron shells for the nuclei whose mass
A A
number is close to 16 , is: [GATE 2012]
A A (a) 4.1 MeV (b) 11.5 MeV
(c)Z = a
(d) Z = 1+A2/3
1+( c )A2/3
4aA

11
 and isospin assignments for the ground state of
(c)15.7 MeV (d) 19.8 MeV 13
C is
[GATE 2015]
Statement for Linked Answer Q. 09 and Q.10: 1 1 1 +
1
In the Schmidt modei of nuclear magnetic (a) ; − (b) ;−
2 2 2 2
moments, we have,
𝑒ℏ 3 1 3 1
𝜇= (𝑔 𝑙 + 𝑔𝑠 𝑆) (c) ; (d) ;−
2𝑀𝑐 𝑙 2 2 2 2
where the symbols have their usual meaning
22. According to the nuclear shell model, the
18. For the case J = l + 1/2, where J is the total respective ground state spin-parity values of 15
8 O
angular momentum, the expectation value of S⃗ ⋅ J 17
and 8 O nuclei are
in the nuclear ground state is equal to [GATE 2016]
[GATE 2013] 1 1 1 5+
−

(J − 1) (J + 1) (a) , (b) ,
(a) (b) 2 2 2 2
2 2
3− 5+ 3− 1−
J J (c) , (d) ,
(c) (d) − 2 2 2 2
2 2
23. JP for the ground state of the 13
C6 nucleus is
19. For the O17 nucleus (A = 17, Z = 8), the effective [GATE 2017]
magnetic moment is given by 3
eħ (a) 1+ (b)
⃗ eff =
μ gJ, 2
2Mc
where g is equal to, (g s = 5.59 for proton and
3+ 1
−3.83 for neutron) (c) (d)
[GATE 2013] 2 2
(a) 1.12 (b) −0.77
24. For nucleus 164 Er, a Jπ = 2+state is at 90 keV .
(c)−1.28 (d) 1.28 Assuming 164 Er to be a rigid rotor, the energy of
its 4+ state is keV (up to one decimal place)
20. A nucleus X undergoes a first forbidden β-decay to [GATE 2018]
a nucleus Y. If the angular momentum (I) and
parity
7− 25. 4MeV𝛾-rays emitted by the de-excitation of 10 F
(P) denoted by I P as for X, which of the
2 are attributed, assuming spherical symmetry, to
following is a possible I P value for Y ? the transition of protons from 1 d32 state. If the
[GATE 2014] contribution of spin-orbit term to the total energy
1 1−
(a) (b) is written as C(𝑙ˆ− 𝑠̅ ), the magnitude of 𝐶 is…………
2 2 MeV (up to one decimal place).
[GATE 2018]
3+ 3−
(c) (d)
2 2 26. The nuclear spin and parity of 40
20 ,
Ca in its ground state is [GATE 2019]
21. In the nuclear shell model, the potential (a) 0+ (b) 0−
1
is modeled as V(r) = mω2 r 2 − λL ⃗ ⋅ ⃗S, λ
2 (c)1+ (d) 1−
> 0. The correct spin parity

12
27. The total angular momentum j of the ground state of the uniform and spherical charge distribution
of the 17
8 O nucleus is in the nucleus is 3 fm , the corresponding atomic
[GATE 2020] number (rounded off to the nearest integer) is
1 𝑒2
(a) (b) 1 [ Given: = 1.44MeVfm]
2 4𝜋𝜀0

3 5 [GATE 2021]
(c) (d)
2 2
31. In an experiment, it is seen that an electric-dipole
28. According to the Fermi gas model of nucleus, the (𝐸1) transition can connect an initial nuclear
nucleons move in a spherical volume of radius state of spin parity 𝐽𝑖𝜋 = 2+ to final state 𝐽𝑓𝜋 . All
1 possible values of 𝐽𝑓𝜋 are
R (= R 0 A3 , where A is the mass number and R 0 is
[GATE 2021]
an empirical constant with the dimensions of + +
(a) 1 , 2 , 3 +
(b) 1 , 2−
−
length). The Fermi energy of the nucleus EF is
proportional to (c)1− , 2− , 3− (d) 1+ , 2+
[GATE 2020]
1
(a)R20 (b) 32. Under parity and time reversal transformations,
R0
which of the following statements is (are) TRUE
about the electric dipole moment 𝑝 and the
1 1
(c) (d) magnetic dipole moment 𝜇 ?
R20 R30
[GATE 2023]

29. For the given sets of energy levels of nuclei 𝑋 and (a) 𝑝 is odd under parity and 𝜇 is odd under time
𝑌 whose mass number are odd and even, reversal
respectively, choose the best suited
interpretation. (b) 𝑝 is odd under parity and 𝜇 is even under
[GATE 2021] time reversal

(c)𝑝 is even under parity and 𝜇 is odd under time

reversal

(d) 𝑝 is even under parity and 𝜇 is even under

time reversal
(a) Set-I: Vibrational band of X
Set-II: Rotational band of Y 33. According to the nuclear shell model, the absolute
value of the difference in magnetic moments of
15 15
(b) Set-I: Rotational band of Y 8 O and 7 N, in the units of nuclear magneton
Set-II: Vibrational band of X (μN ) is a/3. The magnitude of a is (in integer).
[GATE 2024]
(c)Set-I: Rotational band of X
Set-II: Vibrational band of Y
❖ TIFR PYQ
(d) Set-I: Vibrational band of Y
1. In the semi-empirical mass formula, the volume
Set-II: Rotational band of X
(𝑉), surface (𝑆), coulomb (𝐶), and pairing (𝑃)
contributions to the binding energy of a nucleus
30. The Coulomb energy component in the binding 𝐴
2 𝑋 vary with mass number 𝐴 as
energy of a nucleus is 18.432 MeV . If the radius

13
 [TIFR 2015]
(a) 𝑉 ∝ 𝐴, 𝑆 ∝ 𝐴2/3 , 𝐶 ∝ 𝐴−1/3 , 𝑃 ∝ 𝐴−3/4 (c)17.92 keV (d) 19.2 MeV

(b) 𝑉 ∝ 𝐴, 𝑆 ∝ 𝐴1/3 , 𝐶 ∝ 𝐴−1/3 , 𝑃 ∝ 𝐴−3/4 4. In the shell model of the nucleus, it is known that
orbitals get filled in the order
(c)𝑉 ∝ 𝐴, 𝑆 ∝ 𝐴−2/3 , 𝐶 ∝ 𝐴1/3 , 𝑃 ∝ 𝐴−3/4
1𝑠1/2 1𝑝3/2 1𝑝1/2 1𝑑5/2 2𝑠1/2 1𝑑3/2 and so on … ..
(d) 𝑉 ∝ 𝐴2 , 𝑆 ∝ 𝐴2/3 , 𝐶 ∝ 𝐴−1/3 , 𝑃 ∝ 𝐴−3/4 [TIFR 2022]
18
For a nucleus of 8 O the two neutrons outside the
2. The Weizäcker semi-empirical mass formula for doubly-magic core of 16
8 O will occupy the same
an odd nucleus with 𝑍 protons and 𝐴 nucleons orbital.
may be written as 𝑀(𝑍, 𝐴) = 𝛼1 𝐴 + 𝛼2 𝐴2/3 + The allowed value of 𝐽𝑝 will be
𝛼3 𝑍 + 𝛼4 𝑍 2 where the 𝛼𝑖 are constants (a) 5+ (b) 4+
independent of 𝑍, 𝐴. For a given 𝐴, if 𝑍𝐴 is the
number of photons of the most stable isobar, the (c)3+ (d) 2−
total energy released when an unstable nuclide
undergoes a single 𝛽 − decay to (𝑍𝐴 , 𝐴) is 5. The binding energy 𝜀𝑏 of a nuclide 𝐴𝑍 𝑋 with atomic
[TIFR 2016] number 𝑍 and mass number 𝐴 is given by the
(a) 𝛼3 (b) 𝛼4 semiempirical formula:
|TIFR2023]
(c)𝛼4 − 𝛼3 (d) 𝛼1 + 𝛼2 𝑍(𝑍 − 1) (𝐴 − 2𝑍)2
𝜀𝑏 = 𝑎𝑉 𝐴 − 𝑎𝑆 𝐴2/3 − 𝑎𝐶 + 𝑎𝐴
𝐴1/3 𝐴
3. The semi-empirical mass formula for a heavy
nucleon (𝑍, 𝐴) can be written, to some where the constant parameters and source of
approximation, as effect for each term are:

𝑀(𝑍, 𝐴)𝑐 2 = 𝑍𝑀𝑝 𝑐 2 + (𝐴 − 𝑍)𝑀𝑛 𝑐 2 − 𝜆4 𝐴

Volume Surface Coulomb Asymmetry
𝑍(𝑍 − 1)
− 𝜆2 𝐴2/3 − 𝜆3 term term term term
𝐴1/3
2
(𝐴 − 2𝑍) 𝜆5
− 𝜆4 − 1/2 𝑎𝑉 𝑎𝑆 𝑎𝐶 𝑎𝐴
𝐴 𝐴

where 𝑀𝑝 𝑐 2 = 938MeV, 𝑀𝑛 𝑐 2 = 939MeV, and 15.56 17.8

0.7 MeV 23.29 MeV
𝜆1 = 16, 𝜆2 = 18, 𝜆3 = 0.7, 𝜆4 = 23, all in MeV , MeV MeV
where
+12 MeV for even - even nuclei
𝜆5 = {−12 MeV for odd - odd nuclei What is the mass difference between the two-
0 for others mirror nuclei 13 13
6 C and 7 N ? It is known that
Now, consider a spontaneous fission reaction both of them are spherical in shape and have a
uniform charge distribution.
238 146 91
92 U → 56 Ba + 36 Kr + 10 n (a) 2.62 MeV (b) 3.40 MeV

The energy released in this reaction will be close (c)1.84 MeV (d) 0.78 MeV
to
[TIFR 2019] 6. The binding energy 𝜀𝑏 of a nuclide 𝑧 𝑋 𝐴 with
(a) 190 MeV (b) 170 MeV atomic number and mass number 𝐴 is given by
the semi-empirical formula
𝑎𝑐 𝑍(𝑍 − 1) (𝐴 − 2𝑍)2
𝜀𝑏 = 𝑎𝑣 𝐴 − 𝑎𝑠 𝐴2/3 − + 𝑎𝑎
𝐴1/3 𝐴
14
 where the constant parameters and source of Answer Key
effect for each term are CSIR-NET PYQ
1. d 2. b 3. b 4. a 5. c
Volume Surface Coulomb Asymmetry 6. a 7. b 8. c 9. a 10. a
term term term term 11. c 12. c 13. b 14. d 15. a
16. d 17. c 18. c 19. c 20. d
𝑎𝑣 𝑎𝑠 𝑎𝑐 𝑎𝑎 21. a 22. a 23. d
GATE PYQ
15.56 17.8 1. a 2. a 3. d 4. a 5. a
0.7 MeV 23.29 MeV
MeV MeV 6. d 7. b 8. b 9. c 10. a
11. b 12. c 13. a 14. a 15. c
16. d 17. b 18. b 19. b 20. c
For a spherical neutron star consisting of only 21. a 22. b 23. d 24. 300 25.
neutrons and having uniform nuclear density 26. a 27. d 28. c 29. d 30.
throughout its volume, the Coulomb term is
31. c 32. a 33. 2
replaced by gravitational energy. What would be
the smallest radius of this neutron star? TIFR PYQ
(a) 4.34 km (b) 10.435 km 1. a 2. b 3. a 4. b 5. a
6. a 7. a
(c)2.165 km (d) 4.345 km

7. Oxygen (O) nuclei (𝑍 = 8) can be approximated

as non-interacting protons and neutrons filling
up orbitals in the following order.

1𝑠1/2 , 1𝑝3/2 , 1𝑝1/2 , 1𝑑5/2 , 2𝑠1/2 , 1𝑑3/2 , …

where the subscript specifies the J quantum

number. Given the binding energy of O (𝐴 = 15)
is 111.96MeV, O(𝐴 = 16) is 127.62MeV, and
O(𝐴 = 17) is 131.76MeV, what is the difference
between the energies of the 1𝑝1/2 and the 1𝑑5/2
orbitals? |TIFR2024]
(a) 11.52MeV (b) 15.66MeV

(c)4.14MeV (d) 19.81MeV

15
 NUCLEAR PHYSICS: Deuteron Nuclei
❖ CSIR-NET PYQ (a) It has a non-zero quadruple moment
1. The tensor component of the nuclear force may
be inferred from the fact that deuteron nucleus (b) The neutron-proton potential is non central
2
1H [CSIR JUNE 2022]
(a)has only one bound state with total spin S = 1 (c)The orbital wave function is not spherically
symmetric
(b)has a non-zero electric quadrupole moment in
its ground state (d) The Hamiltonian does not conserve the total
angular momentum
(c)Is stable while triton 13 H is unstable
4. Deuteron has only bound state with spin parity
(d)Is the only two nucleon bound state 1+ , isospin 0 and electric quadruple moment
0.286efm2. These data suggest that nuclear forces
❖ GATE PYQ are having
1. Deuteron in its ground state has a total angular [GATE 2012]
momentum J = 1 and a positive parity. The (a) only spin and isospin dependence.
corresponding orbital angular momentum L and
spin S combinations are (b) no spin dependence and no tensor
[GATE 2004] components.
(a) L = 0, S = 1 and L = 2, S = 0
(b) no spin dependence but no tensor
(b) L = 0, S = 1 and L = 1, S = 1 components.

(c)L = 0, S = 1 and L = 2, S = 1 (d) spin dependence along with tensor

components.
(d) L = 1, S = 1 and L = 2, S = 1
5. Consider the scattering of neutrons by protons at
2. To explain the observed magnetic moment of very low energy due to a nuclear potential of range
deuteron (0.8574μN ), its ground state r0 . Given that,
wavefunction is taken to be an admixture of S and γ
cot (kr0 + δ) ≈ −
D states. The expectation values of the z- k
Where δ is the phase shift, k the wave number and
component of the magnetic moment in pure S and
(−γ) the logarithmic derivative of the deuteron
pure D states are 0.8797μN and 0.3101μN
ground sate wave function the phase shift is
respectively. The contribution of the D state to the
[GATE 2013]
mixed ground state is approximately
k γ
[GATE 2006] (a)δ ≈ − − kr0 (b) δ ≈ − − kr0
γ k
(a) 40% (b) 4%
π π
(c)0.4% (d) 0.04% (c)δ ≈ − kr0 (d) δ ≈ − − kr0
2 2

3. The ground state wave function of deuteron is 6. Which of the following statements is NOT
in a superposition of s and d states. Which of the correct?
following is not true as a consequence? [GATE 2016]
[GATE 2010] (a) A deuteron can be disintegrated by irradiating
it with gamma rays of energy 4MeV

16
 (b) A deuteron has no excited states

(c)A deuteron has no electric quadrupole

moment

(d) The 1 S0 state of deuteron cannot be formed.

7. The deuteron is a bound state of a neutron and a

proton. Which of the following statements is(are)
CORRECT? [GATE 2023]
(a) The deuteron has a finite value of electric
quadrupole moment due to nonspherical
electronic charge distribution

(b) The magnetic moment of the deuteron is equal

to the sum of the magnetic moments of the
neutron and the proton

(c)The deuteron state is an admixture of 3 S1 and

3
D1 states

(d) The deuteron state is an admixture of 3 S1 and

3
P1 states

❖ Answer Key
CSIR-NET PYQ
1. b
GATE PYQ
1. c 2. b 3. d 4. d 5. a
6. c 7. ac

17
 NUCLEAR PHYSICS: Nuclear Radioactive Decays
❖ CSIR-NET PYQ 5. An excited state of a 84 Be nucleus decays into two
207
1. The ground state of 82 Pb nuclcus has spin-parity α particles which are in a spin-parity 0+ state. If the
P
J =
1
,
5
while the first excited state has JF = 2. The mean life-time of this decay is 10−22 s, the spin-
2
parity of the excited state of the nucleus is
electromagnetic radiation emitted when the
[CSIR JUNE 2019]
nucleus makes a transition from the first excited +
(a) 2 (b) 3+
state to the ground state are
[CSIR JUNE 2012]
(c) 0− (d) 4−
(a) E2 and E3 (b) M2 and E3

6. The nuclei of 137 Cs decay by the emission of 𝛽-

© E2 and M3 (d) M2 and M3
particles with a half of 30.08 years. The activity
(in units of disintegrations per second or Bq ) of a
2. A radioactive element 𝑋 decays to 𝑌, which in
turn decays to a stable element 𝑍. The decay 1mg source of 137 Cs, prepared on January 1 ,
constant from 𝑋 to 𝑌 is 𝜆1 , and that from 𝑌 to 𝑍 is 1980 as measured on January 1, 2021 is closest to
𝜆2 . If, to begin with, there are only 𝑁0 atoms of 𝑋, [CSIR JUNE 2021]
16
at short times (𝑡 ≪ 1/𝜆1 as well as 1/𝜆2 ) the (a) 1.79 × 10 (b) 1.79 × 109
number of atoms of 𝑍 will be
[CSIR JUNE 2016] (c) 1.24 × 1016 (d) 1.24 × 109
1 𝜆1 𝜆2
(a) 𝜆1 𝜆2 𝑁0 𝑡 2 (b) 𝑁𝑡 7. A 60 Co nucleus β-decays from its ground state
2 2(𝜆1 + 𝜆2 ) 0
with JP = 5+ to a state of 60 Ni with JP = 4+ . From
(c)(𝜆1 + 𝜆2 )2 𝑁0 𝑡 2 (d) (𝜆1 + 𝜆2 )𝑁0 𝑡 the angular momentum selection rules, the
allowed values of the orbital angular momentum L
3. If in a spontaneous α-decay of 232 and the total spin S of the election-antineutrino
92 U at rest, the
total energy released in the reaction is Q, then the pair are
energy carried by the α-particle is [CSIR JUNE 2021]
[CSIR JUNE 2017] (a) L = 0 and S = 1 (b) L = 1 and S = 0
57Q Q
(a) (b) (c) L = 0 and S = 0 (d) L = 1 and S = 1
58 57

Q 23Q 8. The Q-value of the α-decay of 232 Th to the ground

(c) (d)
58 58 state of 228 Ra is 4082keV. The maximum possible
kinetic energy of the α-particle is closest to
4. A nucleus decays by the emission of a gamma ray [CSIR JUNE 2021]
from an excited state of spin-parity 2+ to the (a) 4082keV (b) 4050keV
ground state with spin-parity 0+ . What is the type
of the corresponding radiation ? (c) 4035keV (d) 4012keV
[CSIR DEC 2018]
(a) magnetic dipole 9. The ground state of 207
82 Pb nucleus has spin-parity
1 −
Jπ = ( )
(b) electric quadrupole 2
,while the first excited state has
−
© electric dipole 5
Jπ = ( )
2
(d) m a g netic quadrupole . For the transition from the first excited state to

18
 the ground state, possible multipolarities of [GATE 2006]
emitted electromagnetic radiation are (a) (E0 − E) (b) p(E0 − E)
[CSIR DEC 2023]
(a)E2, E3 (b)M2, M3 © p2 (E0 − E)2 (d) p(E0 − E)2

©M2, E3 (d)E2, M3 5. Which of the following configurations of the decay

products correspond to the largest energy of the
❖ GATE PYQ antineutrino v‾ ? (rest mass of electron me =
1. The evidence for the non-conservation of parity in 0.51MeV/c 2, rest mass of proton mp =
β-decay has been obtained from the observation 938.27MeV/c 2 and rest mass of neutron mn =
that the β intensity [GATE 2005] 939.57MeV/c 2 )
(a) antiparallel to the nuclear spin directions is [GATE 2008]
same as that along the nuclear spin direction (a) In the laboratory proton is produced at rest

(b) antiparallel to the nuclear spin direction is not (b) In the laboratory, momenta of proton electron
the same as that along the nuclear spin direction and the anti-neutrino all have the same
magnitude.
© shows a continuous distribution as a function of
momentum © In the laboratory, proton and electron fly-off
with (nearly) equal and opposite momenta
(d) is independent of the nuclear spin direction
(d) In the laboratory, electron is produced at rest
2. A nucleus having mass number 240 decays by α
emission to the ground state of its daughter 6. Using the result of the above problem answer the
nucleus. The Q value of the process is 5.26MeV. following. Which of the following represents
The energy (in MeV ) of the α particle is approximately the maximum allowed energy of
[GATE 2005] the anti-neutrino v‾ ?
(a) 5.26 (b) 5.17 [GATE 2008]
(a) 1.3MeV (b) 0.8MeV
© 5.13 (d) 5.09
© 0.5MeV (d) 2.0MeV
3. The number of final states states of electrons
corresponding to momenta between p and p + dp 7. The disintegration energy is defined to be the
is difference in the rest energy between the initial
(c) independent of p and final states. Consider the following process:
240 236 4
94 Pu → 92 U + 2 He
(b) proportional to pdp The emitted 𝛼 particle has a kinetic energy
5.17MeV. The value of the disintegration energy is
© proportional to p2 dp [GATE 2009]
(a) 5.26MeV (b) 5.17MeV
(d) proportional to p3 dp
© 5.08MeV (d) 2.59MeV
4. The number of emitted electrons with momentum
p and energy E, in the allowed approximation, is 8. In the β decay process, the transition 2+ → 3+ , is
proportional to ( E0 is the total energy given up by [GATE 2013]
the nucleus). (a) allowed both by Fermi and Gamow-Teller
selection rule

19
 13. A radioactive element 𝐗 has a half-life of 30
(b) allowed by Fermi and but by Gamow-Teller hours. It decays via alpha, beta and gamma
selection rule emissions with the branching ratio for beta decay
being 0.75 . The partial half-life for beta decay in
© not allowed by Fermi by allowed by Gamow- unit of hours is [GATE 2018]
Teller selection rule

(d) not allowed by Fermi but allowed by Gamow- 14. Assumethat 13 N(Z =
Teller selection rule 7)undergoesfirstforbiddenβ+
decay from its ground state with spin −
9. A nucleus X undergoes a first forbidden 𝛽-decay parity Jiπ , to a final state Jfπ . The possible values for
to a nucleus Y. If the angular momentum (I) and Jiπ and Jfπ , respectively, are
parity [GATE 2021]
(P) denoted by 𝐼 𝑃 as
7−
for X, which of the 1− 5+ 1+ 5+
2 (a) , (b) ,
2 2 2 2
following is a possible I P value for Y ?
[GATE 2014] 1− 1− 1+ 1−
1 1− (c) , (d) ,
(a) (b) 2 2 2 2
2 2
15. In an experiment, it is seen that an electric-dipole
3+ 3− (E1) transition can connect an initial nuclear state
© (d)
2 2 of spin-parity Jiπ = 2+ to a final state Jfπ . All
possible values of Jfπ are
10. A beam of X-ray of intensity I0 is incident [GATE 2021]
normally on a metal sheet of thickness 2 nm. The (a) 1+ , 2+ (b) 1+ , 2+ , 3+
intensity of the transmitted beam is 0.025𝐼0 . The
linear absorption coefficient of the metal sheet © 1− , 2− (d) 1− , 2− , 3−
(inm−1 ) is (© one decimal place)
[GATE 2015] 16. Match the order of β-decays given in the left
1844.4 column to appropriate clause in the right column.
Here X(I π ) and Y(I π ) are nuclei with intrinsic spin
13 13 I and parity π.
11. In the nuclear reaction C6 + ve → N7 + X, the
particle X is [GATE 2022]
+ +
[GATE 2017] 1 1
1. X ( ) → Y ( )
(a) an electron (b) an anti-electron 2 2

© a muon (d) a pion 1− 5+

2. X ( ) → Y( )
2 2
12. An α particle is emitted by a 230 90 Th nucleus.
Assuming the potential to be purely Coulombic 3. X(3+ ) → Y(0+ )
beyond the point of separation, the height of the
Coulomb barrier is MeV (up to two decimal 4. X(4− ) → Y(0+ )
places). [GATE 2018] (i) First forbidden β-decay
2
e (ii) Second forbidden β-decay
( = 1.44MeV-fm, r0 = 1.30fm)
4πϵ0 (iii) Third forbidden β-decay
(iv) Allowed β-decay
(a) 1 – i, 2 – ii, 3 – iii, 4 – iv

20
 (b) 1 – iv, 2 – i, 3 – ii, 4 – iii

(c)1 – i, 2 – iii, 3 – ii, 4 – iv

(d) 1 – iv, 2 – ii, 3 – iii, 4 – i

17. A 60 Co nucleus emits a β-particle and is converted

to 60 Ni∗ with JP = 4+ , which in turn decays to the
60
Ni ground state with JP = 0+ by emitting two
photons in succession, as shown in the figure.
Which one of the following statements is
CORRECT? [GATE 2023]

❖ JEST PYQ
1. 238 U decays with a half life of 4.51 × 109 years,
the decay series eventually ending at 206 Pb,
which is stable. A rock sample analysis shows
that the ratio of the numbers of atoms of 206 Pb
to 238 U is 0.0058 . Assuming that all the 206 Pb
has been produced by the decay of 238 U and that
all other half-lives in the chain are negligible, the
(c) 4+ → 2+ is an electric octupole transition age of the rock sample is [JEST 2013]
6
(a) 38 × 10 years (b) 48 × 106 years
(b) 4+ → 2+ is a magnetic quadrupole transition
© 38 × 107 years (d) 48 × 107 years
+ +
© 2 → 0 is an electric quadrupole transition
2. In the mixture of isotopes normally found on the
+ +
(d) 2 → 0 is a magnetic quadrupole transition earth at the present time, 238
92 𝑈 has an abundance
235
of 99.3% and 92 𝑈 has an abundance of 0.7%.
18. Let Ne and Te , respectively, denote number and The measured lifetimes of these isotopes are
kinetic energy of electrons produced in a nuclear 6.52 × 109 years and 1.02 × 109 years,
beta decay. Which one of the following respectively. Assuming that they were equally
distributions is correct? abundant when the earth was formed, the
estimated age of the earth, in years is
[JEST 2014]
9
(a) 6.0 × 10 (b) 1.0 × 109

© 6.0 × 108 (d) 1.0 × 108

3. The half-life of a radioactive nuclear source is 9

days. The fraction of nuclei which are left

21
 undecayed after 3 days is: [JEST 2014] (b) electric dipole magnetic dipole
7 1 OR
(a) (b) (E1) (M1)
8 3
(c)electric magnetic
OR
5 1 quadrupole (E2) quadrupole (M2)
(c) (d) 1
6 (d) electric magnetic dipole
23 OR
quadrupole (E2) (M1)
❖ TIFR
1. A detector is used to count the number of 𝛾 rays 4. A standard radioactive source is known to decay
emitted by a radioactive source. If the number of by emission of 𝛾 rays. The source is provided to a
counts recorded in exactly 20 seconds is 10000 , student in a thick sealed capsule of unbreakable
the error in the counting rate per second is plastic and she is asked to find out the half-life.
[TIFR 2010] Which of the following would be the most useful
(a) ±5.0 (b) ±22.4 advice to the student? [TIFR 2014]
(a) The half-life cannot be measured because the
(c)±44.7 (d) ±220.0 initial concentration of the source is not given.

2. A lead container contains 1gm of a 6027 Co (b) Mount the source in front of a gamma ray
radioactive source. It is known that a 60
27 Co detector and count the number of photons
nucleus emits a 𝛽 particle of energy 316KeV detected in one hour.
followed by two 𝛾 emissions of energy 1173 and
1333KeV respectively. Which of the following (c)Measure the mass of the source at different
experimental methods would be the best way to times with an accurate balance having a least
determine the lifetime of this 60
27 Co source? count of 1mg. Plot these values on a curve and fit
[TIFR 2010] it with an exponential decay law.
(a) Measure the change in temperature of the
source (d) Mount the source in front of a gamma ray
detector and count the number of photons
(b) Measure the weight of the source now and detected in a specific time interval. Repeat this
again after one year experiment at different times and note how the
count changes.
(c)Measure the recoil momentum of the nucleus
during 𝛽 emission 5. Which of the following radioactive decay chains is
it possible to observe? [TIFR 2015]
(d) Measure the number of 𝛾 photons emitted by 206 202 202
(a) 82 Pb → 80 Hg → 79 Au
this source
210 210 206
(b) 83 Bi → 84 Po → 82 Pb
3. An excited atomic electron undergoes a
spontaneous transition (c) 214
88 Ra →
210
86 Rn → 207
82 Pb
3𝑑3/2 → 2𝑝1/2
The interaction responsible for this transition 206 202 202
(d) 82 Pb → 80 Hg → 79 Au
must be of the type [TIFR 2011]
(a) electric dipole magnetic 6. In an experiment, 197
79 Au nuclei were bombarded
OR
(E1) quadrupole (M2) with neutrons leading to formation of 198
79 Au,
198
which is unstable. The half-life of 79 Au was
measured to be 2.25 days and it was found later

22
 that this measured half-life was an underestimate 9. Natural potassium contains a radioactive
by 10%. The corresponding percentage error in component of 40 K that has two decay modes.
the estimated population of 198
79 Au after 9 days is • In the first mode, 40 K undergoes a 𝛽 decay to
[TIFR 2015] the ground state of 40 Ca.
(a) 10% (b) 25% • In the second mode, 40 K undergoes an
electron capture to the excited state of 40 Ar,
(c)2.5% (d) 15% followed by a single 𝛾 transition to the
ground state of 40 Ar.
7. Cosmic ray muons, which decay spontaneously
The amount of radioactive 40 K in a natural
with proper lifetime 2.2𝜇s, are produced in the
potassium (atomic weight of 39.089) sample is
atmosphere, at a height of 5 km above sea level.
known to be 0.0118 percent. It is also known that
These move straight downwards at 98% of the
in the decay of 40 K, for every 100𝛽 particles
speed of light.
emitted, there number of 𝛾-photons emitted is 12
Find the percent ratio 100 × (𝑁𝐴 /𝑁𝐵 ) of the
If the number of 𝛽-particles emitted per second
number of muons measured at the top of two
by 1 kg of natural potassium is 2.7 × 104 , the
mountains 𝐴 and 𝐵, which are at heights 4,848 m
mean lifetime of 40 K in years is [TIFR 2022]
and 2,682 m respectively above mean sea level.
(a) 1.9 × 109 (b) 1.3 × 109
[TIFR 2017]

(c)1.7 × 109 (d) 1.1 × 108

8. Consider the nuclear decay chain of radio-
Bismuth to Polonium to Lead, i.e. 10. A beam of neutrons is incident normally upon a
219 210 206
83 Bi → 84 Po → 82 Pb thick sheet of Cadmium. The mass density of
where Pb − 206( 20682 Pb) is a stable nucleus, and Cadmium is 𝜌 = 8.6 g cm−3 . The absorption
Bi-210 ( 83 Bi) and Po-206 ( 210
219
84 Po) are cross-section of neutrons on Cadmium nuclei is
radioactive nuclei with half lives of about 5 days 2.5 × 10−20 cm2 . The atomic weight of Cadmium
and 138 days respectively. is known to be 112.40 g/mol. You may take 𝑁𝐴 =
If we start with a sample of pure Bi − 210( 219
83 Bi), 6.02 × 1023 .
then a possible graph for the time evolution of the At what depth is the intensity of the beam
number of nuclei of these three species will be reduced by a factor 1/𝑒 ? [TIFR 2024]
[TIFR 2020] (a) 9𝜇m (b) 9fm

(c)9 nm (d) 900fm

23
 ❖ Answer Key
CSIR-NET PYQ
1. c 2. a 3. a 4. b 5. a
6. d 7. a 8. d 9. d
GATE PYQ
1. a 2. b 3. c 4. b 5. d
6. b 7. a 8. c 9. c 10. 1844.4
11. a 12. 13. 40 14. b 15. d
16. b 17. c 18. c
JEST PYQ
1. a 2. a 3. d
TIFR PYQ
1. b 2. d 3. a 4. d 5. b
6. b 7. 194 8. a 9. a 10. a

24
 NUCLEAR PHYSICS: Radioactivity
❖ CSIR-NET PYQ [GATE 2006]
1. A radioactive element X decays to Y, which in turn (a) Thorium series (b) Neptunium series
decays to a stable element Z. The decay constant
from X to Y is λ1 , and that from Y to Z is λ2 . If, to (c)Uranium series (d) Actinium series
begin with, there are only N0 atoms of X, at short
times (t ≪ 1/λ1 as well as 1/λ2 ) the number of 3. Fission fragments are generally radioactive as
atoms of Z will be [GATE 2007]
[CSIR JUNE 2016] (a) they have excess of neutrons
1 λ1 λ2
(a) λ1 λ2 N0 t 2 (b) N t
2 2(λ1 + λ2 ) 0 (b) they have excess of protons

(c)(λ1 + λ2 )2 N0 t 2 (d) (λ1 + λ2 )N0 t (c)they are products of radioactive nuclides

2. The nuclei of 137 Cs decay by the emission of β- (d) their total kinetic energy is of the order of
particles with a half of 30.08 years. The activity (in 200MeV
units of disintegrations per second or Bq ) of a
1mg source of 137 Cs, prepared on January 1 , 1980 4. Half life of a radio-isotope is 4 × 108 years. If there
as measured on January 1, 2021 is closest to are 103 radioactive nuclei in a sample today, the
[CSIR JUNE 2021] number of such nuclei in the sample 4 × 109 years
16
(a) 1.79 × 10 (b) 1.79 × 109 ago were
[GATE 2007]
(c)1.24 × 1016 (d) 1.24 × 109 (a) 128 × 103 (b) 256 × 103

❖ GATE PYQ (c)512 × 103 (d) 1024 × 103

1. The plot of log A vs. time t, where A is activity, as
shown in the figure, corresponds to decay 5. A radioactive element 𝐗 has a half-life of 30 hours.
[GATE 2005] It decays via alpha, beta and gamma emissions
with the branching ratio for beta decay being 0.75
. The partial half-life for beta decay in unit of hours
is [GATE 2019]

❖ JEST PYQ
1. 238 U decays with a half life of 4.51 × 109 years, the
decay series eventually ending at 206 Pb, which is
(a) from only one kind of radioactive nuclei stable. A rock sample analysis shows that the ratio
having same half life of the numbers of atoms of 206 Pb to 238 U is
(b) from only neutron activated nuclei 0.0058 . Assuming that all the 206 Pb has been
(c)from a mixture of radioactive nuclei having produced by the decay of 238 U and that all other
different half lives half-lives in the chain are negligible, the age of the
(d) which is unphysical rock sample is
[JEST 2013]
6
2. Which one of the following disintegration series of (a) 38 × 10 years (b) 48 × 106 years
the heavy elements will give 209 Bi as a stable
nucleus ? (c)38 × 107 years (d) 48 × 107 years

25
2. In the mixture of isotopes normally found on the
earth at the present time, 238
92 U has an abundance
238
of 99.3% and 92 U has an abundance of 0.7%. The
measured lifetimes of these isotopes are 6.52 ×
109 years and 1.02 × 109 years, respectively.
Assuming that they were equally abundant when
the earth was formed, the estimated age of the
earth, in years, is
[JEST 2014]
(a) 6.0 × 109 (b) 1.0 × 109

(c)6.0 × 108 (d) 1.0 × 108

3. The half-life of a radioactive nuclear source is 9

days. The fraction of nuclei which are left
undecayed after 3 days is:
[JEST 2016]
7 1
(a) (b)
8 3

5 1
(c) (d) 1
6
23

❖ Answer Key
CSIR-NET
1. a 2. d
GATE
1. c 2. b 3. a 4. d 5. 40
JEST
1. a 2. a 3. d

26
 NUCLEAR PHYSICS: Nuclear Reaction
❖ CSIR-NET PYQ 5. The elastic scattering of a neutrino ve by an
1. An atom of mass M can be excited to a state of mass electron e− , i.c. the reaction ve + e− → ve + e− ,
M + Δ by photon capture. The frequency of a can be described by the interaction Hamiltonian
photon which can cause this transition is: Hint
[CSIR DEC 2011] 1
= GF ∫ d3 x(ψ‾ e (x)γμ ψve (x))(ψ‾ ve (x)γμ ψe (x))
2
(a) Δc /2h (b) Δc 2 /h √2
The cross-section of the above process depends on
(c)Δ2 c 2 /2Mh (d) Δ(Δ + 2M)c 2 /2Mh the centre of mass energy E, as depends on the
centre of mass energy E, as
2. What should be the minimum energy of a photon [CSIR JUNE 2019]
2
for it to split an α-particle at rest into a tritium and (a) 1/E (b) E 2
a proton?
4 3 H
(The masses of 2 He, 1 H and 1 H are (c)E (d) √E
4.0026amu, 3.0161amu and 1.0073amu,
respectively, and 1 amu ≈ 938MeV ). ❖ GATE PYQ
[CSIR DEC 2016] 1. The reaction 3 H(p, n)2 He has a Q value of
(a) 32.2MeV (b) 3MeV −0.764MeV. Calculate the threshold energy of
incident protons for which neutrons are emitted in
(c)19.3MeV (d) 931.5MeV the forward direction. [GATE 2001]

63
3. The reaction Cu29 + p → 63 Zn30 + n is 2. Typical energies released in a nuclear fission and
followed by a prompt β-decay of zinc 63 Zn30 → a nuclear fusion reaction are respectively
63
Cu29 + e+ + ve . If the maximum energy of the [GATE 2002]
position is 2.4MeV, the Q-value of the original (a) 50MeV and 1000MeV
reaction in MeV is nearest to
[Take the masses of electrons, proton and neutron (b) 200MeV and 1000MeV
to be 0.5MeV/c 2 , 938MeV/c 2 and 939.5MeV/c 2 ,
respectively]. (c)1000MeV and 50MeV
[CSIR JUNE 2018]
(a) -4.4 (b) -2.4 (d) 200MeV and 10MeV

(c)-4.8 (d) -3.4 3. Calculate the minimum kinetic energy that the
neutron should have in order to induce the
4. Assume that pion-nucleon scattering at low reaction O16 (n1 , He4 )C13
energies, in which isospin is conserved, is in which C13 is left in an excited state of energy
described by the effective interaction potential 1.79 MeV. Given:
Veff = F(r)Ix ⋅ IN , where F(r) is a function of the [GATE 2002]
16
radial separation r and Im and IN denote, Mass of O = 16.000000amu
respectively, the isospin vectors of a pion and the Mass of n1 = 1.008986amu
nucleon. The ratio σI=3/2 /σI−ν/2 of the scattering Mass of He4 = 4.003874amu
cross-sections corresponding to total isospins I = Mass of C13 = 13.007490amu
3/2 and 1/2, is
[CSIR DEC 2018] 4. The masses of a hydrogen atom, neutron and
238
(a) 3/2 (b) ¼ U92 are given by 1.0078,1.0087 and 238.0508
respectively. The binding energy of 238 U92 is
(c)5/4 (d) 1/2

27
 therefore approximately equal to (taking 1 a.m.u. [GATE 2007]
= 931.64MeV ) (a) tritium is radioactive
[GATE 2003]
(a) 120MeV (b) 1500MeV (b) more nucleons participate in fusion

(c)1600MeV (d) 1800MeV (c)the Coulomb barrier is lower for the d + t

system than d + d system
Data for Q. No. 5 to 6
An atomic bomb consisting of 235 U explodes and (d) the reaction product 4 He is more tightly
releases an energy of 1014 J. It is known that each bound
235
U which undergoes fission releases 3 neutrons
and about 200MeV of energy. Further, only 20% of 10. The energy released in the fission of 1kg Uranium
the 235 U atoms in the bomb undergo fission. (Approximately [in joule] [GATE 2008]
14 17
(a)10 (b)10
5. The total number of neutrons released is about
[GATE 2003] (c)1016 (d)1010
24
(a) 4.7 × 10 (b) 9.7 × 1024
11. A neutron scatters elastically from a heavy
(c)1.9 × 1025 (d) 3.7 × 1025 nucleus. The initial and final states of the neutron
have the
235
6. The mass of U in the bomb is about [GATE 2007]
[GATE 2003] (a) same energy
(a) 1.5 kg (b) 3.0 kg
(b) same energy and linear momentum
(c)6.1 kg (d) 12 kg
(c)same energy and angular momentum
7. A thermal neutron having speed v impinges on a
235
U nucleus. The reaction cross-section is (d) same linear and angular momenta
proportional to
[GATE 2004] 12. The neutrons are observed at the rate of 1.806 ×
−1
(a) v (b) v 108 s−1. If the density of rhodium is approximated
as 104 kg m−3 the cross-section for the reaction
(c)v1/2 (d) v −1/2 (in barns) is
[GATE 2007]
8. The threshold temperature above which the (a) 0.1 (b) 0.2
thermonuclear reaction 32 He + 32 He → 42 He +
2 11 H + 12.86MeV can occur is (use e2/4πε0 = (c)0.4 (d) 0.8
1.44 × 10−15 MeVm )
[GATE 2005] 13. The disintegration energy is defined to be the
10
(a) 1.28 × 10 K (b) 1.28 × 109 K difference in the rest energy between the initial
and final states. Consider the following process:
(c)1.28 × 108 K (d) 1.28 × 107 K 240 236 4
94 Pu → 92 U + 2 He
The emitted α particle has a kinetic energy
9. In the deuterium + tritium (d + t) fusion more 5.17MeV. The value of the disintegration energy is
energy is released as compared to deuterium + [GATE 2009]
deuterium (d + d) fusion because (a) 5.26MeV (b) 5.17MeV

28
 19. Consider the induced nuclear fission reaction
(c)5.08MeV (d) 2.59MeV 235 93 141
92 U + n → 37 Rb + 55 Cs + 2n where neutron
momenta in both initial and final states are
14. Total binding energies of O15 , O16 and O17 are negligible. The ratio of the kinetic energies
111.96MeV, 127.62MeV and 131.76MeV (KE) of the daughter nuclei,
respectively. The energy gap between 1 p1/2 and KE( 93
37 Rb)
1d5/2 neutron shells for the nuclei whose mass KE( 114
55 Cs)
number is close to 16 is is
[GATE 2012] [GATE 2024]
(a) 4.1MeV (b) 11.5MeV 93 141
(a) (b)
141 93
(c)15.7MeV (d) 19.8MeV
(c)1 (d) 0
15. The atomic masses of 152 152 1
63 Eu, 62 Sm, 1 H and
20. Binding energy and rest mass energy of a two-
neutron are 151.921749,151.919756,1.007825
nucleon bound state are denoted by B and mc 2 ,
and 1.008665 in atomic mass units (amu)
respectively, where c is the speed of light. The
respectively. Using the above information the Q-
minimum energy of a photon required to
value of the reaction 152 152
03 Eu + n → 02 Sm + p
dissociate the bound state is
is_____________ × 10−3 am (upto three decimal
[GATE 2024]
places) B
[GATE 2015] (a)B (b)B (1 + )
2mc 2
2.833
B
16. Consider the reaction 54 − 54 (c)B (1 − ) (d) B − mc 2
25 Mn + e → 24 Cr + X. 2mc 2
The particle X is
[GATE 2016] ❖ JEST PYQ
(a) γ (b) ve 1. Consider a point particle A and mass mA colliding
elastically with another point particle B of mass
(c)n (d) π0 mB at rest, where mB /mA = γ. After collision, the
ratio of the kinetic energy of particle B to the initial
17. Protons and α − particles of equal initial kinetic energy of particle A is given by
momenta are scattered off a gold foil in a [JEST 2017]
Rutherford scattering experiment. The scattering 4 2
(a) (b)
cross sections for proton on gold and α-particle on γ + 2 + 1/γ γ + 1/γ
gold are σp and σα respectively. The ratio σα /σp
is__________.
[GATE 2016] 2 1
(c) (d)
γ + 2 − 1/γ γ
18. An α-particle is emitted from the decay of
Americium (Am) at rest, i.e., 241 237 ❖ TIFR
94 Am → 92 U + α.
The rest masses of 241 237 1. The binding energy per nucleon for 235 U is
94 Am, 92 U and α are
224.544GeV/c 2 , 220.811 GeV/c 2 and 3.728GeV/ 7.6MeV. The 235 U nucleus undergoes fission to
c 2 respectively. What is the kinetic energy (in produce two fragments, both having binding
MeV/c 2, rounded off to two decimal places) of the energy per nucleon 8.5MeV. The energy released,
α-particle? [GATE 2023] in Joules, from the complete fission of 1Kg of
235
U is, therefore,

29
 [TIFR 2013]
(a) 8000 (b) 1035

(c)450 (d) 20000

(e) 8.7 × 1013 (f) 5.0 × 108

2. A fast-moving 14 N nucleus collides with an 𝛼

particle at rest in the laboratory frame, giving rise
to the reaction
14
N + 𝛼 → 17 O + 𝑝
Given the masses 14.00307 a.m.u. and 16.99913
a.m.u. for 14 N and 17 O nuclei respectively, and
The detector D is capable of detecting either
4.00260 a.m.u. and 1.00783 a.m.u. for 𝛼 and 𝑝
electrons (𝛽 − )or positrons (𝛽 + ). Now the
respectively, the minimum kinetic energy in the
𝛽 − source is replaced with a 𝛽 + source, and we
laboratory frame of the 14 N nucleus must be
would like to measure the energy of the positrons
[TIFR 2011]
(𝛽 + )using the same setup. Which of the following
(a) 4.20MeV (b) 1.20MeV
is correct? [TIFR 2014]
(a) This can be done quite easily, if the polarity of
(c)5.41MeV (d) 1.55MeV
current in the coils of the electromagnet is
3. In a nuclear reactor, Plutonium ( 239 reversed.
94 Pu) is used as
fuel, releasing energy by its fission into isotopes
of Barium ( 146 91 (b) This can be done trivially, without changing
54 Ba) and Strontium ( 38 Sr) through
anything, since the detector D can detect either
the reaction
239 1 146 91 1 𝛽 − or 𝛽 + .
94 Pu + 0 n ⟶ 56 Ba + 38 Sr + 3 × 0 n
The binding energy (B.E.) per nucleon of each of
(c)There is no way to do this with the given set
these nuclides is given in the table below:
up, since 𝛽 + will have to be converted into 𝛽 − ,
239 146 91
Nuclide 94 Pu 54 Ba 38 Sr which is obviously not possible.

B.E. per nucleon (d) This cannot be done since the magnet does
7.6 8.2 8.6
(MeV) not have a symmetric shape.
Using this information, one can estimate the
5. It is well-known that the energy of the Sun arises
number of such fission reactions per second in a
from the fusion of hydrogen nuclei (protons)
100 MW reactor as [TIFR 2012]
18 inside the core of the Sun. This takes place
(a) 3.9 × 10 (b) 7.8 × 1018
through several mechanisms, each resulting in
emission of energy.
(c)5.2 × 1019 (d) 5.2 × 1018
Which of the following reactions is NOT possible
during the proton fusion inside the Sun?
(e) 8.9 × 1017
[TIFR 2014]
1 1 2
(a) 1 H + 1 H → 2 He
4. In a beta decay experiment, an electromagnet M
and a detector D are used to measure the energy
(b) 12 H + 11 H → 32 He
of electrons (𝛽 − ), as shown in the figure.

(c) 11 H + 11 H → 12 H + 𝑒 + + 𝑣𝑒

30
 If the Q-value of the reaction is −30MeV, the
(d) 11 H + 11 H + 11 H + 11 H → 42 He + 2𝑒 + excitation energy of the compound nucleus can
be estimated as [TIFR 2020]
6. Consider a process in which atoms of Actinium- (a) 81MeV (b) 170MeV
226 ( 226
89 Ac) get converted to atoms of Radium-
226 ( 226 (c)330MeV (d) 270MeV
BB Ra) and the yield of energy is 0.64MeV
per atom. This occurs through [TIFR 2016]
Both 𝑝 → 𝑛 + 𝑒 + + 𝑣𝑒
❖ Answer Key
(a) and 𝑝 + 𝑒 − → 𝑛 + 𝑣𝑒
CSIR-NET PYQ
Both 𝑝 → 𝑛 + 𝑒 + + 𝑣𝑒 1. d 2. c 3. a 4. 5. b
6. 7. 8. 9. 10.
(b) and 𝑛 → 𝑝 + 𝑒 − + 𝑣‾𝑒 11. 12. 13. 14. 15.
GATE PYQ
(c)Only 𝑝 → 𝑛 + 𝑒 + + 𝑣𝑒 1. 2. d 3. 4. d 5. b
6. c 7. a 8. a 9. a 10. a
(d) Only 𝑝 + 𝑒 − → 𝑛 + 𝑣𝑒 11. a 12. b 13. a 14. b 15. 2.833
16. b 17. a 18. 19. b 20. b
7. A deuteron of mass 𝑀 and binding energy 𝐵 is JEST PYQ
struck by a gamma ray photon of energy 𝐸𝛾 , and 1. a
is observed to disintegrate into a neutron and a TIFR PYQ
proton. If 𝐵 ≪ 𝑀𝑐 2 , the minimum value of 𝐸𝛾 1. e 2. c 3. a 4. a 5. d
must be [TIFR 2017] 6. d 7. d 8. d 9. b
2
𝐵 𝐵2
(a)2𝐵 + (b)𝐵 +
2𝑀𝑐 2 𝑀𝑐 2

1 𝐵2 1 𝐵2
(c) (3𝐵 + ) (d) (2𝐵 + )
2 𝑀𝑐 2 2 𝑀𝑐 2

8. Let 𝐸𝑁 be the energy released when one mole of

pure 235 U undergoes controlled fission, and 𝐸𝐶
be the energy released when one mole of pure
carbon undergoes complete combustion. The
ratio 𝐸𝑁 /𝐸𝐶 will have the order of magnitude
[TIFR 2013]
(a) 104 (b) 108

(c)109 (d) 106

9. Two atomic nuclei A and B have masses such that

𝑚(𝐵) = 2𝑚(𝐴). in the laboratory frame, the
nucleus 𝐵 is kept stationary, while the nucleus 𝐴
is given a kinetic energy 300MeV and made to
collide with B. It is found that the two nuclei fuse
to form a compound nucleus C.

31
 NUCLEAR PHYSICS: Nuclear Detector
❖ CSIR-NET PYQ
1. Thermal neutrons may be detected most
efficiently by a
[CSIR JUNE 2022]
6
(a)Li loaded plastic scintillator

(b)Geiger-Müller counter

(c)inorganic scintillatorCaF2

(d) silicon detector

❖ GATE PYQ
1. The Geiger-Muller counter is a device to detect α, β
and γ radiations. It is a cylindrical tube filled with
monatomic gases like argon, and polyatomic gases
such as ethyl alcohol. The inner electrode is along
the axis of the cylindrical tube and the outer
electrode is the tube. Which of the following
statements is (are) CORRECT?
[GATE 2023]
(a) Argon is used so that ambient light coming
from the surroundings do not produce any signal
in the detector

(b) Ethyl alcohol is used as a quenching gas

(c)The electric field strength decreases from the

axis to the edge of the tube and the direction of the
field is radially outward

(d) The electric field increases from the axis to the

edge of the tube and the field direction is radially
inward

Answer Key
CSIR-NET PYQ
1. a
GATE PYQ
1. abc

32
 NUCLEAR PHYSICS: Particle Physics
❖ CSIR-NET PYQ
1. A beam of pions (π+ )is incident on a proton target, Mπ c Mτ c
(c) (d)
giving rise to the process π+ p → n + π+ + π+ Mτ Mπ
(A) Assuming that the decay proceeds through
strong interactions, the total isospin I and its third 4. The elastic scattering of a neutrino 𝑣𝑒 by an
component I3 for the decay products, are electron 𝑒 − , i.e. the reaction 𝑣𝑒 + 𝑒 − → 𝑣𝑒 + 𝑒 − ,
[CSIR JUNE 2011] can be described by the interaction Hamiltonian
3 3 5 5 𝐻𝑖𝑛𝑡
(a)I = , I3 = (b) I = , I3 = 1
2 2 2 2
= 𝐺𝐹 ∫ 𝑑3 𝑥(𝜓‾𝑒 (𝑥)𝛾 𝜇 𝜓𝑣𝑒 (𝑥))(𝜓‾𝑣𝑒 (𝑥)𝛾𝜇 𝜓𝑒 (𝑥))
√2
5 3 1 1 The cross-section of the above process depends
(c)I = , I3 = (d) I = , I3 = −
2 2 2 2 on the centre of mass energy 𝐸, as depends on the
centre of mass energy 𝐸, as
(B) Using isospin symmetry, the cross-section for [NET June 2019]
the above process can be related to that of the (a) 1/𝐸 2
(b) 𝐸 2
process
[CSIR JUNE 2011]
− − −
(c)𝐸 (d) √𝐸
(a) π n → pπ π (b) π− p‾ → n‾π− π−
5. The strong nuclear force between a neutron and a
(c)π4 n → pπ+ π− (d) π+ p‾ → nπ+ π−
proton in a zero orbital angular momentum state
is denoted by 𝐹𝑛𝑝 (𝑟), where 𝑟 is the separation
2. An atom of mass 𝑀 can be excited to a state of
between them. Similarly, 𝐹𝑛𝑛 (𝑟) and 𝐹𝑝𝑝 (𝑟)
mass 𝑀 + Δ by photon capture. The frequency of
denote the forces between a pair of neutrons and
a photon
protons, respectively, in zero orbital momentum
which can cause this transition is:
state. Which of the following is true on average if
[NET Dec. 2011]
the inter-nucleon distance is 0.2fm < 𝑟‾ < 2fm ?
(a) Δ𝑐 2 /2 h (b) Δ𝑐 2 /h
[NET Dec. 2019]
(a) 𝐹𝑛𝑝 is attractive for triplet spin state, and
(c)Δ2 𝑐 2 /2𝑀ℎ (d) Δ(Δ + 2M)c 2 /2Mh
𝐹𝑛𝑛 , 𝐹𝑝𝑝 are always repulsive.
3. Consider the decay process τ− → π− + vτ in the
rest frame of the τ− . The masses of τ− , π− and vτ (b) 𝐹𝑛𝑛 and 𝐹𝑛𝑝 are always attractive and 𝐹𝑝𝑝 is
are Mt , Mπ and zero respectively. repulsive in this triplet spin state.
(A) The energy of π− is:
[CSIR JUNE 2011] (c)𝐹𝑝𝑝 and 𝐹𝑛𝑝 are always attractive and 𝐹𝑛𝑛 is
2 2
(Mτ − Mπ )c 2 (Mr2 + Mπ2 )c 2 always repulsive.
(a) (b)
2Mτ 2Mr
(d) All three forces are always attractive.
(c)(Mr − Mπ )c 2 (d) √Mτ Mπ c 2
6. hermal neutrons may be detected most efficiently
by a
(B) The velocity is π− is: [CSIR JUNE 2011]
[NET June 2022]
(Mτ2 − Mπ2 )c (Mr2 − Mπ2 )c (a) 6 Li loaded plastic scintillator
(a) (b)
Mτ2 + Mπ2 Mr2 − Mπ2
(b) Geiger-Müller counter

(c)inorganic scintillator CaF2

33
 105MeV/c 2 and its proper life time is 2μs. If the
(d) silicon detector center of mass energy of the collision is 2.1GeV in
the laboratory frame that coincides with the
7. An electron of energy 27GeV collides with a proton center-of-mass frame, then the fraction of muons
of energy 820GeV. The heaviest particle which can that will decay before they reach a detector placed
6 km away from the interaction point is
be produced in this collision has mass close to [CSIR JUNE 2013]
−1
[CSIR DEC 2011] (a) e (b) 1 − e−1
(a) 300GeV (b) 821GeV
(c)1 − e−2 (d) e−10
(c)850GeV (d) 1127GeV
12. A spin- 1/2 particle A undergoes the decay A →
8. The dominant interactions underlying the B + C + D where it is known that B and C are also
following processes spin- 1/2 particles. The complete set of allowed
[CSIR JUNE 2012] values of the spin of the particle D is
− − +
A. K + p → Σ + π , [CSIR JUNE 2013]
B. μ− + μ+ → K − + K ′ → 1 3 5
(a) , 1, , 2, , 3, … … (b) 0,1
C. Σt → p + π0 are 2 2 2
(a) A: strong, B: electromagnetic and C : weak
1 1 3 5 7
(c) only (d) , , , ,…
(b) A:strong, B: weak and C: weak 2 2 2 2 2

(c)A: weak, B: electromagnetic and C : strong 13. Consider the following ratios of the partial decay
widths
(d) A: weak, B: electromagnetic and C: weak Γ(ρ+ → π+ + π0 )
R1 =
Γ(ρ− → π− + π0 )
9. The muon has mass 105MeV/c 2 and mean lifetime and
2.2μs in its rest frame. The mean distance Γ(Δ++ → π+ + p)
R2 =
traversed by muon of energy 315MeV/c 2 before Γ(Δ− → π− + n)
decaying is approximately . If the effects of electromagnetic and weak
[CSIR DEC 2012] interactions are neglected, then R1 and R 2 are,
5 respectively,
(a) 3 × 10 km (b) 2.2 cm
[CSIR DEC 2013]
(c)6.6μm (d) 1.98 km (a) 1 and √2 (b) 1 and 2

10. Consider the following particles: the proton p, the (c)2 and 1 (d) 1 and 1
neutron n, the neutral pion π0 and the delta
resonance Δ+ . When ordered in terms of 14. The recently-discovered Higgs boson at the LHC
decreasing lifetime, the correct arrangement is as experiment has a decay mode into a photon and a
follows: Z boson. If the rest masses of the Higgs and Z boson
[CSIR DEC 2012] are 125GeV/c 2 and 90GeV/c 2 respectively, and
0 ∗
(a) π , n, p, Δ (b) p, n, Δ+ , π0 the decaying Higgs particle is at rest, the energy of
(c)p, n, π0 , Δ+ (d) Δ+ , n, π0 , p the photon will approximately be
[CSIR JUNE 2014]
11. Muons are produced through the annihilation of (a) 35√3GeV (b) 35GeV
particle a and its antiparticle, namely the process
a + a̅ → μ+ + μ− . A muon has a rest mass of (c)30GeV (d) 15GeV

34
 (ii) 𝑝‾ + 𝑛 → 𝜋 −
15. In a classical model, a scalar (spin-0) meson (iii) 𝑝 + 𝑛 → 𝜋 + + 𝜋 0 + 𝜋 0
consists of a quark and an antiquark bound by a (iv)𝑝 + 𝑣‾𝑒 → 𝑛 + 𝑒 +
potential
Which of the following statements is true?
𝑏
𝑉(𝑟) = 𝑎𝑟 + [CSIR DEC 2015]
𝑟
(a) Process (i) obeys all conservation laws
where 𝑎 = 200MeVfm−1 and b = 100MeVfm. If
the masses of the quark and antiquark are
(b) Process (ii) conserves baryon number, but
negligible, the mass of the meson can be
violates energy-momentum conservation
estimated as approximately[CSIR JUNE 2014]
(a) 141MeV/c 2 (b) 283MeV/c 2
(c)Process (iii) is not allowed by strong
interactions, but is allowed by weak interactions
(c)353MeV/c2 (d) 425MeV/c 2

(d) Process (iv) conserves baryon number, but

16. Consider the four processes
violates lepton number conservation
(i) p+ → n + e+ + ve
20. In the large hadron collider (LHC), two equal
(ii) Λ0 → p+ + e+ + ve energy proton beams traverse in opposite
(iii) π∗ → e+ + ve directions along a circular path of length 27 km. If
(iv) π0 → γ + γ the total center of mass energy of a proton-
Which of the above is/are forbidden for free proton pair is 14 TeV, which of the following is
particles? [CSIR DEC 2014] the best approximation for the proper time taken
(a) only (ii) (b) (ii) and (iv) by a proton to traverse the entire path?
[CSIR JUNE 2016]
(c)(i) and (iv) (d) (i) and (ii) (a) 12 ns (b) 1.2𝜇s

17. The charm quark is assigned a charm quantum (c)1.2 ns (d) 0.12𝜇s
number C = 1. How should the Gellmann-
Nishijima formula for electric charge be modified 21. Which of the following reaction(s) is/are allowed
for four flavours of quarks? by the conservation laws ?
[CSIR JUNE 2015] [CSIR DEC 2016]
1 1
(a)I3 + (B − S − C) (b)I3 + (B − S + C) (i) π+ + n → Λ0 + K +
2 2
(ii) π− + p → Λ0 + K 0
1 1 (a) Both (i)and(ii) (b) Only (i)
(c)I3 + (B + S − C) (d)I3 + (B + S + C)
2 2
(c)Only (ii) (d) Neither(i)nor(ii)
18. The reaction 12 D + 12 D → 42 He + π0 cannot
proceed via strong interactions because it violates 22. A particle, which is a composite state of three
the conservations of quarks u, d and s, has electric charge, spin and
[CSIR JUNE 2015] strangeness respectively, equal to
(a) angular momentum (b) electric charge [CSIR DEC 2016]
1
(a)1, , −1 (b) 0,0, −1
(c)baryon number (d) isospin 2

1 1
19. Consider the following processes involving free (c)0, , −1 (d) − 1, − , +1
2 2
particles
(i) 𝑛‾ → 𝑝‾ + 𝑒 + + 𝑣‾𝑒

35
23. SA baryon X decays by strong interaction as X →
Σ+ + π− + π0 , where Σ+ is a member of the (a) The spin of both 𝐵 and 𝐶 may be ½
isotriplet (Σ∗ , Σ0 , Σ− ). The third component I3 of
the isospin of X is (b) The sum of the masses of 𝐵 and 𝐶 is greater
[CSIR JUNE 2017] than the mass of 𝐴
(a) 0 (b) 1/2
(c)The energy of 𝐵 is uniquely determined by the
(c)1 (d) 3/2 masses of the particles

24. Which of the following processes is not allowed by (d) The spin of both 𝐵 and 𝐶 may be integral
the strong interaction but is allowed by the weal
interaction? 28. Assume that pion-nucleon scattering at low
[CSIR DEC 2017] energies, in which isospin is conserved, is
0 ‾
(a) K + π → K + π + π−
0 0 + described by the effective interaction potential
𝑉eff = 𝐹(𝑟)𝐼𝑥 ⋅ 𝐼𝑁 , where 𝐹(𝑟) is a function of the
(b) p + n → d + p + p‾ radial separation r and 𝐼𝑚 and 𝐼𝑁 denote,
respectively, the isospin vectors of a pion and the
(c)Δ+ + K 0 → p + n nucleon. The ratio 𝜎𝐼=3/2 /𝜎𝐼−𝜈/2 of the scattering
cross-sections corresponding to total isospins 𝐼 =
(d) p + Δ+ → n‾ + Δ++ 3/2 and 1/2, is [CSIR DEC 2018]

25. Which of the following elementary particle (a) 3/2 (b) 1/4
processes does not conserve strangeness ?
[CSIR JUNE 2018] (c)5/4 (d) ½
0 + 0
(a) π + p → K + Λ (b) π− + p → K 0 + Λ0
29. The mean life-time of the following decays:
(c)Δ0 → π0 + n (d) K 0 → π+ + π− ρ0 → π+ + π− , π0 → γ + γ, μ− → e− + v‾e + vα
, are τp , τπ and τμ , respectively. They satisfy
26. A deuteron d captures a charged pion π− in the l = [CSIR JUNE 2019]
1 state, and subsequently decays into a pair of (a) τπ < τρ < τμ (b) τμ < τρ < τs
neutrons ( n ) via strong interaction. Given that the
intrinsic parities of π− , d and n are −1, +1 and +1
(c)τp < τπ < τμ (d) τρ < τμ < τπ
respectively, the spin-wavefunction of the final
state neutrons is a
30. Which of the following decay processes is allowed
[CSIR JUNE 2018]
?
(a) linear combination of a singlet and a triplet.
[CSIR DEC 2019]
0 + −
(a) K → μ + μ (b) μ → e− + γ
(b) singlet

(c)n → p + π− (d) n → π+ + π−
(c)triplet

31. Charged pions π− decay to muons μ− and anti-

(d) doublet
muon neutrinos v⃗ μ ; π− → μ− + v⃗ μ . Take the rest
27. Consider the decay 𝐴 → 𝐵 + 𝐶 of a relativistic masses of a muon and a pion to be 105MeV and
1 140MeV, respectively. The probability that the
spin − 2 particle 𝐴. Which of the following
measurement of the muon spin along the direction
statements is true in the rest frame of the particle of its momentum is positive, is closest to
𝐴? [CSIR DEC 2018]

36
 [CSIR DEC 2020] [CSIR JUNE 2022]
(a) 0.5 (b) 0.75 (a)0.01 milli-barn (b)1 milli-barn,

(c)1 (d) 0 (c)0.1 barn, (d) 10 barn,

32. A particle of mass

1GeV
and its antiparticle, both 36. A neutral particle X 0 is produced in π− + p → X 0 +
c2
n by s-wave scattering. The branching ratios of the
moving with the same speed v, produce a new
10GeV decay of X 0 to 2γ, 3π and 2π are 0.38,0.30 and less
particle X of mass in a head-on collision. The
c2 than 10−3, respectively. The quantum numbers JCP
minimum value of v required for this process is of X 0 are
closest to [CSIR JUNE 2023]
[CSIR JUNE 2021] (a) 0 −+
(b) 0+−
(a) 0.83c (b) 0.93c
(c)1−+ (d) 4 ⋅ 1+−
(c)0.98c (d) 0.88c
37. Atmospheric neutrinos are produced from the
33. In an experiment, the velocity of a non-relativistic cascading decays of cosmic pions (𝜋 ± )to stable
neutron is determined by measuring the time (∼ particles. Ignoring all other neutrino sources, the
50 ns) it takes to travel from the source to the ratio of muon neutrino (𝑣𝜇 + 𝑣‾𝜇 ) flux to electron
detector kept at a distance L. Assume that the
neutrino (𝑣𝑒 + 𝑣‾𝑒 ) flux in atmosphere is expected
error in the measurement of L is negligibly small.
to be closest to [CSIR-DEC 2023]
If we want to estimate the kinetic energy T of the
δT
(a)2: 3 (b)1: 1
neutron to within 5% accuracy i.e., | T | ≤ 0.05, the
maximum permissible error |δT| in measuring the (c)1: 2 (d)2: 1
time of flight is nearest to
[CSIR JUNE 2021] 38. The nucleus of 40 K (of spin-parity 4+ in the
(a) 1.75 ns (b) 0.75 ns ground state) is unstable and decays to 40 Ar. The
mass difference between these two nuclei is
(c)2.25 ns (d) 1.25 ns Δ𝑀𝑐 2 = 1504.4keV. The nucleus 40 Ar has an
excited state at 1460.8 keV with spin-parity 2+ .
34. In the reaction p + n → p + K + + X, mediated by The most probable decay mode of 40 K is by
strong interaction, the baryon number B, [CSIR JUNE 2023]
strangeness S and third component of isospin I3 of (a) a 𝛽 + -decay to the 2+ state of 40 Ar
the particle X are, respectively
[CSIR JUNE 2021] (b) an electron capture to the 2+ state of 40
Ar
(a) −1, −1 and -1 (b) +1, −1 and -1
(c)an electron capture to the ground state of
1 40
Ar
(c)+1, −2 and − (d) −1, −1 and 0
2
(d) a 𝛽 + -decay to the ground state of 40
Ar
35. The elastic scattering process π− p → π− p may be
treated as a hard-sphere scattering. The mass of
1 ❖ GATE PYQ
π− , mπ ≃ mp 1. The cross-sections of the reactions p + Π − → Σ− +
6
, where mp ≃ 938MeV/c 2 is the mass of the K + and p− + Π + → Σ‾− + K − at a given energy are
proton. The total scattering cross-section is closest the same due to
to

37
 [GATE 2001]
(a) baryon number conservation (d) 14 up quarks and 14 down quarks

(b) time-reversal invariance 6. Which one of the following nuclear reactions is

possible?
(c)charge conjugation [GATE 2003]
14 13 +
(a) N7 → C6 + β + vc
(d) parity conservation
13 13
(b) N7 → C6 + β+ + vc
2. Which of the following functions describes the
nature of interaction potential V(r) between two (c) 13 N7 → 13
C6 + β+
quarks inside a nucleon? ( r is the distance
13 13
between the quarks and a and b positive constants (d) N7 → C7 + β+ + vc
of suitable dimensions)
[GATE 2001] 7. Suppose that a neutron at rest in free space decays
a a into a proton and an electron. This process would
(a)V(r) = + br (b) V(r) = − + br
r r violate
a a [GATE 2003]
(c)V(r) = − br (d) V(r) = − − br (a) conservation of charge
r r

3. Which of the following reactions violates lepton (b) conservation of energy

number conservation?
(c)conservation of linear momentum
(a) e+ + e− → v + v‾ (b) e− + p → v + n
(d) conservation of angular momentum
+ − −
(c)e + n → p + v (d) μ → e + v + v̅
8. If the photon were to have a finite mass, then the
4. The baryon number of proton, the lepton number Coulomb potential between two stationary
of proton, the baryon number of electron and the charges separated by a distance r would
lepton number of electron are respectively [GATE 2003]
[GATE 2002] (a) be strictly zero beyond some distance
(a) zero, zero, one and zero
(b) fall off exponentially for large values of r
(b) one, one, zero and one
(c)fall off as 1/r 3 for large values of r
(c)one, zero, zero and one
(d) fall off as 1/r for large values of r
(d) zero, one, one and zero
9. A stationary particle in free space is observed to
9
5. The nucleus of the atom Be4 consists of spontaneously decay into two photons. This
[GATE 2003] implies that [GATE 2003]
(a) 13 up quarks and 13 down quarks (a) the particle carries electric charge

(b) 13 up quarks and 14 down quarks (b) the spin of the particle must be greater than
or equal to 2
(c)14 up quarks and 13 down quarks
(c)the particle is a boson

38
 15. The strangeness quantum number is conserved
(d) the mass of the particle must be greater than in [GATE 2007]
or equal to the mass of the hydrogen atom (a) strong, weak and electromagnetic
interactions
10. The resonance widths Γ of ρ, ω and φ particle
resonances satisfy the relation Γp > Γω > Γφ . (b) weak and electromagnetic interactions only
Their life-times τ satisfy the relation
[GATE 2004] (c)strong and weak interactions only
(a) τp > τω > τip (b) τp < τω < τφ
(d) strong and electromagnetic interactions only
(c)τp < τω < τφ (d) τp > τω < τφ
16. A relativistic particle travels a length of 3 ×
11. Choose the particle with zero Baryon number 10−3 m in air before decaying. The decay process
from the list given below. of the particle is dominated by
[GATE 2004] [GATE 2007]
(a) pion (b) neutron (a) strong interactions

(c)proton (d) Δ+ (b) electromagnetic interactions

12. Which of the following decay is forbidden? (c)weak interactions

[GATE 2005]
(a) μ− → e− + vμ + v‾c (b) π+ → μ+ + vμ (d) gravitational interactions

17. The strange baryon Σ+ has the quark structure

(c)π+ → e+ + ve (d) μ− → e+ + e− + e−

13. The interaction potential between two quarks, (a) uds (b) uud
separated by a distance r inside a nucleon, can be
(c)uus (d) us‾
described by ( a, b and β are positive constants)
[GATE 2006]
a 18. According to the quark model, the K + meson is
(a)ae−βr (b) + br composed of the following quarks:
r
[GATE 2008]
(a) u ud (b) uc‾
a a
(c) − + br (d)
r r (c)us‾ (d) su‾

14. Which one of the following nuclear processes is 19. Choose the correct statement from the following
forbidden? [GATE 2008]
[GATE 2006] (a) The reaction K + K − → pp‾ can proceed
+
(a) v‾ + p → n + e irrespective of the kinetic energies of K + and K −

(b) π− → e− + ve + π0 (b) The reaction K + K − → pp‾ is forbidden by the

baryon number conservation
(c)π− + p− → n + K + + K −
(c)The reaction K + K − → 2γ is forbidden by
(d) μ− → e− + v‾e + vμ strangeness conservation

39
 23. In the nuclear shell model the spin parity of 15 N
0 + −
(d) The decay K → π π proceeds via weak is given by
interactions. [GATE 2010]
∗ +
(1) π → μ + vμ (i) Strong
20. A neutral pi meson ( π∘ ) has a rest-mass of (2) π0 → γ + γ (ii) Electromagnetic
approximately 140MeV/c 2 and a lifetime of τsec. (3) π0 + n → π− + p (iii) Weak
A πo produced in the laboratory is found to decay (a) (1,iii), (2,ii), (3,i) (b) (1, i), (2,ii), (3,iii)
after 1.25τsec into two photons. Which of the
following sets represents a possible set of energies (c)(1, ii), (2,i), (3,iii) (d) (1, iii), (2, i), (3,ii)
of the two photons as seen in the laboratory?
[GATE 2008] 24. The quark content of Σ + , K − , π and p is indicated:
(a) 70 MeV and 70 MeV |Σ⟩ = |uus⟩; |K − ⟩ = |su‾⟩; |π− ⟩ = |u‾d⟩; |p⟩ = |uud⟩
In the process, π− + p → K − + Σ− , considering
(b) 350 MeV and 100 MeV strong interactions only, which of the following
statements is true?
(c)75 MeV and 100 MeV [GATE 2010]
(a) The process is allowed because ΔS = 0
(d) 25 MeV and 150 MeV
(b) The process is allowed because ΔI3 = 0
21. In the quark model which one of the following
represents a proton? (c)The process is not allowed because ΔS ≠ 0 and
[GATE 2009] ΔI3 ≠ 0
(a) udd (b) uud
(d) The process is not allowed because the baryon
(c)ub‾ (d) cc‾ number is violated

37. Consider the operations 𝑃: 𝑟 → 𝑟 (parity) and 25. The ground state wavefunction of deuteron is in a
𝑇: 𝑡 → −𝑡 (time-reversal). For the electric and superposition of 𝑠 and 𝑑 states. Which of the
magnetic fields 𝐸‾ and 𝐵‾, which of the following following is NOT true as a consequence?
set of transformations is correct? [GATE 2010] [GATE 2010]
𝑃: 𝐸⃗ → −𝐸⃗ , 𝐵‾ → 𝐵⃗ (a) It has a non-zero quadruple moment
(a)
𝑇: 𝐸⃗ → 𝐸⃗ , 𝐵
⃗ → −𝐵 ⃗
(b) The neutron-proton potential is non-central
( b ) 𝑃: 𝐸⃗ → −𝐸⃗ , 𝐵
⃗ →𝐵⃗
(c)The orbital wavefunction is not spherically
𝑃: 𝐸⃗ → 𝐸⃗ , 𝐵
⃗ → −𝐵
⃗
symmetric

(c)𝑇: 𝐸⃗ → −𝐸⃗ , 𝐵
⃗ →𝐵
⃗ → −𝐵
⃗
(d) The Hamiltonian does not conserve the total
angular momentum
𝑃: 𝐸⃗ → 𝐸⃗ , 𝐵
⃗ → −𝐵
⃗
(d)
𝑇: 𝐸⃗ → −𝐸⃗ , 𝐵⃗ →𝐵
⃗ 26. A neutron passing through a detector is detected
because of
22. The basic process underlying the neutron β- [GATE 2011]
decay is [GATE 2010] (a) the ionization it produces
−
(a) d → u + e + v‾e (b) d → u + e−
(b) the scintillation light it produces
(c)s → u + e− + v‾e (d) u → d + e− + v‾e

40
 (c)the electron-hole pair it produces (b) no spin dependence and no tensor
components
(d) the secondary particles produced in a nuclear
reaction in the detector medium. (c)spin dependence but no tensor components

27. In the β − decay of neutron n → p + e− + v‾e , the (d) spin dependence along with tensor
anti-neutrino v‾e escapes detection. Its existence is components
inferred from the measurement of
[GATE 2011] 31. Choose the correct statement from the following
(a) energy distribution of electrons [GATE 2012]
(a) Neutron interacts through electromagnetic
(b) angular distribution of electrons interaction

(c)helicity distribution of electrons (b) Electron does not interact through weak
interaction
(d) forward-backward asymmetry of electrons
(c)Neutrino interacts through weak and
28. The isospin and the strangeness of Ω− baryon are electromagnetic interaction
[GATE 2011]
(a) 1, −3 (b) 0, −3 (d) Quark interacts through strong interaction
but not through weak interaction
(c)1,3 (d) 0,3 32. The decay process n → p+ + e− + v‾e violates
[GATE 2013]
29. In case of a Geiger-Muller (GM) counter, which (a) baryon number (b) lepton number
one of the following statements is CORRECT?
(a) Multiplication factor of the detector is of the (c)isospin (d) strangeness
order of 1010 .
[GATE 2012] 33. Consider the decay of a pion into a muon and an
(b) Type of the particles detected can be anti-neutrino 𝜋 −1 → 𝜇−1 + 𝑣‾𝜇 in the pion rest
identified. frame.
𝑚𝜋 = 139.6MeV/c 2 , 𝑚𝜇 = 105.7MeV/c 2 , 𝑚𝑣 ≈ 0
(c)Energy of the particles detected can be The energy (in MeV) of the emitted neutrino to
distinguished. the nearest integer is__________________.
[GATE 2013]

(d) Operating voltage of the detector is few tens

34. The isospin (I) and baryon number (B) of the up
of Volts.
quark is
[GATE 2013]
30. Deuteron has only one bound state : with spin
(a) I = 1, B = 1 (b) I = 1, B = 1/3
parity 1+ , isospin 0 and electric quadrupole
moment 0.286 efm2. These data suggest that the (c)I = 1/2, B = 1 (d) I = 1/2, B = 1/3
nuclear forces are having
[GATE 2012] 35. Which one of the following high energy processes
(a) only spin and isospin dependence is allowed by conservation laws?
[GATE 2014]
∘ ∘
(a) p + p‾ → Λ + Λ (b) π + p → π∘ + n
−

41
 (c)n → p + e− + ve (d) μ+ → e+ + γ

36. The value of the magnetic field required to

maintain non-relativistic protons of energy 1 MeV
in a circular orbit of radius 100 mm is Tesla.
[GATE 2014]
−27
(Given: 𝑚𝑝 = 1.67 × 10 kg, 𝑒 = 1.6 × 10−19 C
41. In the SU(3) quark model, the triplet of mesons
37. Which one of the following three-quark states (π+ , π0 , π− )has
(qqq) denoted by X, cannot be a possible baryon? [GATE 2016]
The corresponding electric charge is indicated in (a) Isospin = 0, Strangeness = 0
the superscript.
[GATE 2014] (b) Isospin = 1, Strangeness = 0
++ +
(a) X (b) X
(c)Isospin = 1/2, Strangeness = +1
(c)X − (d) X −−.
(d) Isospin = 1/2, Strangeness = −1
38. Consider the process μ+ + μ− → π+ + π− . The
minimum kinetic energy of the muons (μ) in the 42. Which of the following statements is NOT
centre of mass frame required to produce the pion correct?
(π) pairs at rest is_____________ MeV [GATE 2016]
2 2
(Given: mμ = 105MeV/c , mx = 140MeV/c ) (a) A deuteron can be disintegrated by irradiating
[GATE 2014] it with gamma rays of energy 4 MeV .

39. The decay μ+ → e+ + (b) A deuteron has no excited states

γ is forbidden, because it violates
[GATE 2015] (c)A deuteron has no electric quadrupole
(a) momentum and lepton number conservation moment

(b) baryon and lepton number conservation (d) The 1

S0 state of deuteron cannot be formed

(c)angular momentum conservation 43. An alpha particle is accelerated in a cyclotron. It

leaves the cyclotron with a kinetic energy of 16
(d) lepton number conservation MeV . The potential difference between the D
electrodes is 50 kilovolts. The number of
40. A particle of rest mass M is moving along the revolutions the alpha particle makes in its spiral
positive x-direction. It decays into two photons 𝛾1 path before it leaves the cyclotron is
and 𝛾2 as shown in the figure. The energy of 𝛾1 is
1GeV and the energy of 𝛾2 is 0.82GeV. The value [GATE 2016]
of M (in units of GeV/c 2 ) is_____ (Give your
answer upto two decimal places) 44. Electromagnetic interactions are:
[GATE 2017]
(a) C conserving

(b) C non-conserving but CP conserving

42
 (ii) e+ + ve → μ+ + vμ
(c)CP non-conserving but CPT conserving (a) both (i) and (ii) (b) only (i)

(d) CPT non-conserving (c)only (ii) (d) neither (i) nor (ii)

45. Which one of the following conservation laws is 50. A massive particle 𝐗 in free space decays
violated in the decay τ+ → μ+ μ+ μ− spontaneously into two photons. Which of the
[GATE 2017] following statements is true for 𝐗 ?
(a) angular momentum [GATE 2019]
(a) 𝐗 is charged
(b) total Lepton number
(b) Spin of 𝐗 must be greater than or equal to 2
(c)electric charge
(c)𝐗 is a boson
(d) tau number
(d) 𝐗 must be a baryon
+ †
46. The π decays at rest to μ and vμ . Assuming the
neutrino to be mass less, the momentum of the 51. Low energy collision (s-wave scattering) of pion
neutrino is ________MeV/c. (up to two decimal (π+ )with deuteron (d) results in the production
places) (mπ = 139MeV/c 2 , mμ = 105MeV/c 2 ). of two protons (π+ + d → p + p). The relative
[GATE 2017] orbital angular momentum (in units of ℏ ) of the
resulting two-proton system for this reaction is
47. The elementary particle Ξ 0 is placed in the baryon [GATE 2019]
decuplet, shown below, at [GATE 2018] (a) 0 (b) 1

(c)2 (d) 3

52. A particle X is produced in the process π+ + p →

K + + X via the strong interaction. If the quark
content of the K + is us‾, the quark content of X is
[GATE 2020]
(a) cs‾ (b) und
(a) P (b) Q
(c)uus (d) ud‾
(c)R (d) S
53. A particle Y undergoes strong decay Y → π− + π− .
48. In the decay, μ+ → e+ + ve + X, what is X ? The isospin of Y is [GATE 2020]
[GATE 2018]
(a) γ (b) v‾e 54. In the center of mass frame, two protons each
having energy 7000GeV, collide to produce
(c)vμ (d) v‾μ protons and anti-protons. The maximum number
of anti-protons produced is (Assume the proton
49. Considering baryon number and lepton number mass to be 1GeV/c 2 ) [GATE 2020]
conservation laws, which of the following
processes is/are allowed? 55. The Gell − Mann − Okuba mass formula defines
[GATE 2019] the mass of baryons as
(i) p → π0 + e+ + ve

43
 1
M = M0 + aY + b [I(I + 1) − Y 2 ]
4
, where M0 , a and b are constants, I represents the
isospin and Y represents the hypercharge. If the
mass of ∑ hyperons is same as that of Λ hyperons,
then the correct option(s) is(are)
[GATE 2021]
(a) M ∝ I(I + 1)

(b) M ∝ Y

(c)M does not depend on I

(d) M does not depend on Y

∗
56. The Ξ 0 particle is a member of the Baryon
decuplet with isospin state 58. A slow moving π− particle is captured by a
1 1 deuteron (d) and this reaction produces two
|I, I3 ⟩ = | , ⟩
2 2 neutrons (n) in the final state, i.e., π− + d → n + n,
and strangeness quantum number -2 . In the quark Neutron and deuteron have even intrinsic parities,
model, which one of the following is the flavour whereas π− has odd intrinsic parity. L and S are the
∗
part of the Ξ 0 wavefunction? orbital and spin angular momenta, respectively of
[GATE 2023] the system of two neutrons. Which of the following
1 statements regarding the final two-neutron state
(a) (uss − ssu)
√2 is (are) CORRECT?
[GATE 2023]
1 (a) It has odd parity (b) L + S is odd
(b) (uss + sus + ssu)
√3
(c)L = 1, S = 1 (d) L = 2, S = 0
1
(c) (uss + ssu)
√2 59. Let P, Q and R be three different nuclei. Which one
of the following nuclear processes is possible?
1
(d) (uss − sus + ssu) [GATE 2024]
√3 A
(a) ve + z P → A Q + e −1
z+1
0
57. In a hadronic interaction, π ,s are produced with
A
different momenta, and they immediately decay (b) ve + A
zP → z−1 R + e
+

into two photons with an opening angle θ between

them. Assuming that all these decays occur in one (c)ve + A
zP →
A
zP+e
+
+ e−
plane, which one of the following figures depicts
the behaviour of θ as a function of the π0 (d) ve + A
2P →
A
2P + γ
momentum p ? [GATE 2023]
60. Decays of mesons and baryons can be categorized
as weak, strong and electromagnetic decays
depending upon the interactions involved in the
processes. Which of the following option is/are
true?

44
 [GATE 2024]
(a) π0 → γγ is a weak decay

(b) ∧0 → π0 + p is an electromagnetic decay

(c)K 0 → π+ + π− is a weak decay

(d) Δ++ → p + π+ is a strong decay

❖ JEST PYQ
1. A k meson (with a rest mass of 494MeV ) at rest
decays into a muon (with a rest mass of 106MeV )
2. 𝐴 spin- 1/2 particle 𝐴 decays to two other particles
and a neutrino. The energy of the neutrino, which
𝐵 and 𝐶. If 𝐵 and 𝐶 are of spin- 1/2 and spin-1
can be taken to be massless, is approximately
respectively, then a complete list of the possible
[JEST 2013]
values of the orbital angular momentum of the
(a) 120MeV (b) 236MeV
final state (i.e. B + C ) is
[TIFR 2013]
(c)300MeV (d) 388MeV 1 3
(a) 0,1 (b) ,
2 2
+ −
2. The reaction e − e → γ is forbidden because,
[JEST 2015] (c)0, 1, 2 (d) 0, ±1
(a) lepton number is not conserved
3. Cosmic ray muons generated at the top of the
(b) linear momentum is not conserved Earth's atmosphere decay according to the
radioactive decay law
(c)angular momentum is not conserved
0.693𝑡
𝑁(𝑡) = 𝑁(0)exp (− )
(d) charge is not conserved 𝑇1/2
[TIFR 2014]
3. The reaction 𝑒 + + 𝑒 − → 𝛾 is forbidden because, where 𝑁(𝑡) is the number of muons at time t , and
[JEST 2015] T1/2 = 1.52𝜇 s is the proper half-life of the muon,
(a) lepton number is not conserved Immediately after generation, most of these
muons shoot down towards the Eearth's surface.
(b) linear momentum is not conserved Some of these muons decay on the way, but their
interaction with the atmosphere is negligible.
(c)angular momentum is not conserved An observer on the top of a mountain of height 2.0
km above mean sea level detects muons with the
(d) charge is not conserved speed 0.98 c over a period of time and counts 1000
muons. The number of muons of the same speed
❖ TIFR PYQ detected by an observer at mean sea level in the
～
1. The process of electron capture same period of time would be .
(a) 232 (b) 539
𝑝 + 𝑒 − → 𝑛 + 𝑣𝑒
takes place at the quark level through the
(c)839 (d) 983
Feynman diagram [TIFR 2013]

4. A spin-2 nucleus absorbs a spin-1/2 electron and

is then observed to decay to a stable nucleus in

45
 two stages, recoiling against an emitted invisible 𝑝 + 𝑝 → 𝐴𝑧 𝑁 + 𝐴𝑧 𝑁‾ + 𝑝 + 𝑝
particle in the first stage and against an emitted The heaviest nucleus 𝐴𝑧 𝑁 that can be created has
spin-1 photons in the second stage. If the stable atomic mass number 𝐴 =
nucleus is spinless, then the set of all possible spin (a) 15 (b) 9
values of the invisible particle is (c)5 (d) 4
[TIFR 2014]
(a) {1/2,5/2} (b) {3/2,7/2} 8. Consider the hyperon decay (1) Λ → 𝑛 + 𝜋 0
followed by (2) 𝜋 0 → 𝛾𝛾. If the isospin component,
(c){1/2,3/2,5/2} (d) {1/2,3/2,5/2,7/2} baryon number and strangeness quantum
numbers are denoted by 𝐼𝑧 , 𝐵 and 𝑆 respectively,
5. The interaction strength of the recently- then which of the following statements is
discovered Higgs boson (mass approximately completely correct?
125GeV/c 2 ) with any other elementary particle is [TIFR 2016]
proportional to the mass of that particle. Which of (a) In (1)𝐼𝑧 is not conserved, 𝐵 is conserved, 𝑆 is
the following decayprocesses will have the not conserved;
greatest probability? In (2)𝐼𝑧 is conserved, 𝐵 is conserved, 𝑆 is
[TIFR 2014] conserved.
(a) Higgs boson decaying to a top quark +a top
anti-quark (b) In (1) 𝐼𝑧 is conserved, 𝐵 is not conserved, 𝑆 is
not conserved;
(b) Higgs boson decaying to a bottom quark + a
In (2) 𝐼𝑧 is conserved, 𝐵 is conserved, 𝑆 is
bottom anti-quark
conserved.

(c)Higgs boson decaying to an electron and a

(c)In (1)𝐼𝑧 is not conserved, 𝐵 is conserved, 𝑆 is
positron
not conserved;
In (2) 𝐼𝑧 is not conserved, 𝐵 is conserved, 𝑆 is
(d) Higgs boson decaying to a neutrino-
conserved.
antineutrino pair.
(d) In (1)𝐼𝑧 is not conserved, 𝐵 is conserved, 𝑆 is
6. Consider the following reaction involving
conserved;
elementary particles: [TIFR 2015]
− − +
In (2)𝐼𝑧 is conserved, 𝐵 is conserved, 𝑆 is
(A) 𝜋 + 𝑝 → 𝐾 + Σ
conserved.
(B) 𝐾 − + 𝑝 → 𝐾 − + 𝜌+
Which of the following statements is true for
9. A subatomic particle 𝜓 and its excited state 𝜓 ∗
strong interactions?
have rest masses 3.1GeV/𝑐 2 and 3.7GeV/𝑐 2
(a) (A) and (B) are both forbidden
respectively. A table of its assigned quantum
numbers is given below.
(b) (B) is allowed but (A) is forbidden
Angular C- Electri
Parit Isospi
(c)(A) is allowed but (𝐵) is forbidden Momentu Parit c
y n
m y charge
(d) (A) and (B) are both allowed
𝑃 𝐶
𝐽=1 𝐼=0 𝑄=0
7. In a fixed target experiment, a proton of total = −1 = −1
energy 200 GeV is bombarded on a proton at rest
If 𝜋 0∗⋅ is an excited state of 𝜋 0 with a mass about
and produces a nucleus 𝐴2 𝑁 and its anti-nucleus
2 ‾ 1.3GeV/𝑐 2, which of the following reaction is
𝐴𝑁

46
 possible when the above quantum numbers are 12. There are two conceivable channels by which a
conserved ? vector 𝜌0 meson can decay into a pair of pseudo
[TIFR 2017] scalar pions. These are 𝜌0 → 𝜋 0 + 𝜋 0 and 𝜌0 →
∗
(a) 𝜓 → 𝛾𝛾 (b) 𝜓 → 𝜓𝜋 + 𝜋 −
∗
𝜋 + + 𝜋 − . The probability that the decay takes
place through the process 𝜌0 → 𝜋 + + 𝜋 − is
approximately.
(c)𝜓 ∗ → 𝜋 0 𝜋 0 (d) 𝜓 ∗ → 𝜓𝜋 0∗ [TIFR 2022]
(a) 1 (b) Zero
10. The table below gives the properties of four
unstable particles 𝜇+ , 𝜋 + , 𝑛0 , Λ0 𝑚𝜋0 𝑚𝜋2 ∗
[TIFR 2019] (c) (d)
2𝑚𝜋+ 𝑚𝜌2
Mass
13. Consider an unstable bound state 𝐵 of a proton (𝑝)
(MeV Principal with an antiproton (𝑝‾), which is in the S-state (ℓ =
Particle Spin
/𝑐 2 ) decay mode 0) in the spin-singlet configuration. When this
state 𝐵 decays, which of the following final states
𝜇+ will NOT be possible?
muon 𝜇˙+ 105.66 1/2 → 𝑒 + + 𝑣𝜇+ [TIFR 2024]
+ 𝑣‾𝑒 (a) 𝛾 + 𝛾 + 𝛾 (b) 𝜇+ + 𝜇− + 𝛾

𝜋+ (c)𝛾 + 𝛾 (d) 𝑒 + + 𝑒 − + 𝛾
pion 𝜋 + 139.57 0
→ 𝜇+ + 𝑣˙𝜇

𝑛0
0
neutron 𝑛 939.56 1/2 → 𝑝+ + 𝑒˙ −
+ 𝑦‾𝑒

Lambda Λ0
1,115.68 1/2
hyperon Λ0 → 𝑝+ + 𝜋 +

If arranged in order of DECREASING decay

lifetime, the above list will read
(a) 𝑛0 , 𝜇+ , 𝜋 + , Λ0 (b) 𝜋 + , 𝑛0 , 𝜇+ , Λ0

(c)𝜇+ , Λ0 , 𝑛0 , 𝜋 + (d) 𝑛0 , Λ0 , 𝜇+ , 𝜋 +

11. Which of the following decays is forbidden?

[TIFR 2020]
0
(a) 𝜋 → 𝛾 + 𝛾

(b) 𝐾 0 → 𝜋 + + 𝜋 − + 𝜋 0

(c)𝜇− → 𝑒 − + 𝑣𝑒 + 𝑣‾𝜇

(d) 𝑛0 → 𝑝+ + 𝑒 − + 𝑣‾𝑒

47
 Answer Key
CSIR-NET PYQ
1. c/c 2. d 3. b/a 4. b 5. b
6. a 7. a 8. a 9. b 10. c
11. b 12. c 13. d 14. c 15. b
16. d 17. d 18. d 19. b 20. a
21. a 22. c 23. a 24. a 25. d
26. b 27. c 28. b 29. c 30. a
31. c 32. c 33. d 34. b 35. c
36. c 37. d 38. b
GATE PYQ
1. d 2. b 3. c 4. c 5. b
6. b 7. d 8. b 9. c 10. c
11. a 12. d 13. c 14. b 15. d
16. b 17. c 18. c 19. d 20. c
21. b 22. a 23. a 24. a 25. c
26. d 27. d 28. b 29. b 30. a
31. d 32. a 33. c 34. 30 35. d
36. b 37. 1.44 38. d 39. 35 40. d
41. 1.44 42. b 43. c 44. 80 45. a
46. d 47. 29.84 48. c 49. d 50. c
51. c 52. b 53. c 54. 2 55. 6999
56. bc 57. b 58. a 59. a,c 60. a
61. cd
JEST PYQ
1. b 2. b 3. b
TIFR PYQ
1. c 2. c 3. b 4. d 5. b
6. a 7. b 8. a 9. b 10. a
11. c 12. a 13. a

48
 NUCLEAR PHYSICS: Miscellaneous
❖ CSIR-NET PYQ (c)inorganic scintillator CaF2
1. An atom of mass 𝑀 can be excited to a state of
mass 𝑀 + Δ by photon capture. The frequency of a (d) silicon detector
photon
which can cause this transition is: ❖ GATE PYQ
[NET Dec. 2011] 1. The ground state wavefunction of deuteron is in a
2
(a) Δ𝑐 /2 h ` (b) Δ𝑐 2 /h superposition of 𝑠 and 𝑑 states. Which of the
following is NOT true as a consequence?
(c)Δ2 𝑐 2 /2𝑀ℎ (d) Δ(Δ + 2M)c 2 /2Mh [GATE 2010]
(a) It has a non-zero quadruple moment
2. The elastic scattering of a neutrino 𝑣𝑒 by an
electron 𝑒 − , i.e. the reaction 𝑣𝑒 + 𝑒 − → 𝑣𝑒 + 𝑒 − , (b) The neutron-proton potential is non-central
can be described by the interaction Hamiltonian
𝐻𝑖𝑛𝑡 = (c)The orbital wavefunction is not spherically
1
𝐺 ∫ 𝑑3 𝑥(𝜓‾𝑒 (𝑥)𝛾 𝜇 𝜓𝑣𝑒 (𝑥))(𝜓‾𝑣𝑒 (𝑥)𝛾𝜇 𝜓𝑒 (𝑥)). symmetric
√2 𝐹
The cross-section of the above process depends on (d) The Hamiltonian does not conserve the total
the centre of mass energy 𝐸, as depends on the angular momentum
centre of mass energy 𝐸, as
[NET June 2019] 2. A neutron passing through a detector is detected
(a) 1/𝐸 2 (b) 𝐸 2 because of
[GATE 2011]
(c)𝐸 (d) √𝐸 (a) the ionization it produces

3. The strong nuclear force between a neutron and a (b) the scintillation light it produces
proton in a zero orbital angular momentum state
is denoted by 𝐹𝑛𝑝 (𝑟), where 𝑟 is the separation (c)the electron-hole pair it produces
between them. Similarly, 𝐹𝑛𝑛 (𝑟) and 𝐹𝑝𝑝 (𝑟) denote
the forces between a pair of neutrons and protons, (d) the secondary particles produced in a nuclear
respectively, in zero orbital momentum state. reaction in the detector medium.
Which of the following is true on average if the
inter-nucleon distance is 0.2fm < 𝑟‾ < 2fm ? 3. In case of a Geiger-Muller (GM) counter, which one
[NET Dec. 2019] of the following statements is CORRECT?
(a) 𝐹𝑛𝑝 is attractive for triplet spin state, and (a) Multiplication factor of the detector is of the
𝐹𝑛𝑛 , 𝐹𝑝𝑝 are always repulsive. order of 1010 .
[GATE 2012]
(b) 𝐹𝑛𝑛 and 𝐹𝑛𝑝 are always attractive and 𝐹𝑝𝑝 is (b) Type of the particles detected can be
repulsive in this triplet spin state. identified.

(c)𝐹𝑝𝑝 and 𝐹𝑛𝑝 are always attractive and 𝐹𝑛𝑛 is (c)Energy of the particles detected can be
always repulsive. distinguished.

(d) All three forces are always attractive. (d) Operating voltage of the detector is few tens
of Volts.
4. Thermal neutrons may be detected most
efficiently by a 4. Deuteron has only one bound state : with spin
[NET June 2022] parity 1+ , isospin 0 and electric quadrupole
moment 0.286 efm2. These data suggest that the
(a) 6 Li loaded plastic scintillator
nuclear forces are having
[GATE 2012]
(b) Geiger-Müller counter (a) only spin and isospin dependence

49
 2. An electron enters a linear accelerator with a
(b) no spin dependence and no tensor speed 𝑣 = 10 m s−1. A vertical section of the
components accelerator tube is shown in the figure, where the
lengths of the successive sections are designed
(c)spin dependence but no tensor components such that the electron takes the same time 𝜏 =
20 ms to traverse each section.
(d) spin dependence along with tensor
components
If the momentum of the electron increases by 2%
5. The value of the magnetic field required to every time it crosses the narrow gap between two
maintain non-relativistic protons of energy 1 MeV sections, what is the length (in km ) of the collider
in a circular orbit of radius 100 mm is Tesla. which will be required to accelerate it to 100 km −
[GATE 2014] s −1 ?
(Given: 𝑚𝑝 = 1.67 × 10−27 kg, 𝑒 = 1.6 × 10−19 C [TIFR 2018]
3. In an experiment, a counting device is used to
6. Which of the following statements is NOT correct? record the number of charged particles passing
[GATE 2016] through it. Once this counter records a charged
(a) A deuteron can be disintegrated by irradiating particle, it does not respond for a short interval of
it with gamma rays of energy 4 MeV . time, called the 'dead time' of that counter.
This device is used to count the charged particles
(b) A deuteron has no excited states emitted by a particular radioactive source. It is
found that if the source emits 20,000
(c)A deuteron has no electric quadrupole counts/second at random intervals, the counter
moment records 19,000 particles per second on an average.
(d) The 1 S0 state of deuteron cannot be formed It follows that the counter dead time must be
[TIFR 2021]
7. An alpha particle is accelerated in a cyclotron. It (a) 2.63 seconds (b) 2.63 microseconds
leaves the cyclotron with a kinetic energy of 16
MeV . The potential difference between the D (c)2.63 nanoseconds (d) 50.0 milliseconds
electrodes is 50 kilovolts. The number of
revolutions the alpha particle makes in its spiral 4. The figure below shows on the right a sketch of an
path before it leaves the cyclotron is electron-positron collider experiment where the
[GATE 2016] innermost detector (shaded dark green) is a
tracking system which records the tracks of
❖ TIFR PYQ charged particles which pass through it. On the left
1. An atom is capable of existing in two states: a of the figure, a cross-sectional view of the same
ground state of mass 𝑀 and an excited state of tracking system is shown. The narrow (white)
mass 𝑀 + Δ. If the transtion from the ground state pipe in the centre is where electrons and positrons
to the excited state procceds by the absorption of are injected as shown and collide in the Centre.
a photon, the photon frquency in the laboratory (On the left it appears as a small central circle).
frame (where the atom is initially at rest) is Inside the tracking system there is a strong
[TIFR 2010] uniform magnetic field collinear with the
𝑒 + direction.
Δ𝑐 2 Δ𝑐 2 Δ [TIFR 2023]
(a) (b) (1 + )
ℎ ℎ 2𝑀

Mc 2 Δ𝑐 2 Δ
(c) (d) (1 − )
h ℎ 2𝑀

𝑀𝑐 2 Δ Mc 2 Δ
(𝑒) (1 + ) (f) (1 − )
ℎ 2𝑀 h 2M

50
 In one of the 𝑒 + 𝑒 −collisions, a high-energy 𝐾𝑆0
meson is produced that subsequently decays as (d) decreases due to (i), remains unchanged due
follows to (ii).
𝐾𝑆0 → 𝜋 + + 𝜋 −
A possible representation of the tracks (dotted 7. A cyclotron can accelerate deuteron to 16 MeV . If
lines) of the pions 𝜋 ± in the tracking systemwould the cyclotron is used to accelerate 𝛼-particles,
be what will be their energy? Take the mass of
deuteron to be twice the mass of proton and mass
of 𝛼-particles to be four times the mass of proton.
[JEST 2019]
(a) 8 MeV (b) 16MeV −

(c)32MeV − (d) 64 MeV

Answer Key
CSIR-NET PYQ
1. d 2. b 3. b 4. a
GATE PYQ
1. d 2. d 3. a 4. d 5. 1.44
6. c 7. 80
TIFR PYQ
1. b 2. 102 3. b 4. a 5. a
5. A beam of photons of 1 MeV energy each is shot at
6. b 7. c
a 10 mm thick lead brick (see figure).

Given that the density of lead is 11.29 g − cm−3 , its

atomic mass is 207.2 amu , and also that the
interaction crosssection for these photons with a
lead atom is 10−23 cm2, the fraction of the incident
photons that will cross the brick without losing
any energy is
[TIFR 2023]
(a) 72% (b) 28%

(c)67% (d) 33%

6. The binding energy of the k -shell electron in a

Uranium atom (Z = 92, A = 238) will be modified
due to ( i) screening caused by other electrons and
(ii) the finite extent of the nucleus as follows:
[JEST 2013]
(a) increases due to (i), remains unchanged due
to (ii):

(b) decreases due to (i), decreases due to (ii).

(c)increases due to (i), increases due to (ii).

51