JEE Advanced Previous Year Questions (2018 - 2024): Atoms and Nuclei | Physics for JEE Main & Advanced PDF Download

 Page 1


 
Q1: A particle of mass m is moving in a circular orbit under the inuence of the central force F(r)
= -kr, corresponding to the potential energy V(r) = (kr²)/2, where k is a positive force constant
and r is the radial distance from the origin. According to the Bohr's quantization rule, the
angular momentum of the particle is given by L = n h, where h = h/(2 p), h is Planck's constant,
and n a positive integer. If v and E are the speed and total energy of the particle, respectively,
then which of the following expression(s) is(are) correct?
(a) 
(b) 
(c) 
(d)    [JEE Advanced 2024 Paper 1]
Ans: (a), (b) & (c)
The central force will provide the necessary centripetal force
? kr = (mv²) / r
or, kr² = mv² ... (1)
Page 2


 
Q1: A particle of mass m is moving in a circular orbit under the inuence of the central force F(r)
= -kr, corresponding to the potential energy V(r) = (kr²)/2, where k is a positive force constant
and r is the radial distance from the origin. According to the Bohr's quantization rule, the
angular momentum of the particle is given by L = n h, where h = h/(2 p), h is Planck's constant,
and n a positive integer. If v and E are the speed and total energy of the particle, respectively,
then which of the following expression(s) is(are) correct?
(a) 
(b) 
(c) 
(d)    [JEE Advanced 2024 Paper 1]
Ans: (a), (b) & (c)
The central force will provide the necessary centripetal force
? kr = (mv²) / r
or, kr² = mv² ... (1)
By quantization rule n h = mvr
Page 3


 
Q1: A particle of mass m is moving in a circular orbit under the inuence of the central force F(r)
= -kr, corresponding to the potential energy V(r) = (kr²)/2, where k is a positive force constant
and r is the radial distance from the origin. According to the Bohr's quantization rule, the
angular momentum of the particle is given by L = n h, where h = h/(2 p), h is Planck's constant,
and n a positive integer. If v and E are the speed and total energy of the particle, respectively,
then which of the following expression(s) is(are) correct?
(a) 
(b) 
(c) 
(d)    [JEE Advanced 2024 Paper 1]
Ans: (a), (b) & (c)
The central force will provide the necessary centripetal force
? kr = (mv²) / r
or, kr² = mv² ... (1)
By quantization rule n h = mvr
  
 
Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. 
Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. 
List - I List - II 
(P)  
????
??????
?? ? 
????
??????
 ???? (1) one ?? particle and one ?? +
particle 
(Q)  
????
??????
 ???? ? 
????
??????
 ???? (2) three ?? -
particles and one ?? particle 
(R)  
????
??????
???? ? 
????
??????
 ???? (3) two ?? -
particles and one ?? particle 
(S)  
????
??????
 ???? ? 
????
??????
???? (4) one ?? particle and one ?? -
particle 
 (5) one ?? particle and two ?? +
particles 
 
(a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ??   [JEE Advanced 2023 Paper 1] 
Ans: (a) 
In the given nuclear reaction: 
 
?? 1
?? ?? 1
? 
?? 2
?? ?? 2
+ ?? 1
( 
2
?? 4
) + ?? 2
( 
1
?? 0
) + ?? 3
( 
-1
?? 0
) 
we have the conservation of charge expressed as : 
?? 1
= ?? 2
+ 2?? 1
+ ?? 2
- ?? 3
 
and the conservation of nucleons (mass number) is given by: 
?? 1
= ?? 2
+ 4?? 1
?? 1
=
?? 1
- ?? 2
4
… … …
 
Page 4


 
Q1: A particle of mass m is moving in a circular orbit under the inuence of the central force F(r)
= -kr, corresponding to the potential energy V(r) = (kr²)/2, where k is a positive force constant
and r is the radial distance from the origin. According to the Bohr's quantization rule, the
angular momentum of the particle is given by L = n h, where h = h/(2 p), h is Planck's constant,
and n a positive integer. If v and E are the speed and total energy of the particle, respectively,
then which of the following expression(s) is(are) correct?
(a) 
(b) 
(c) 
(d)    [JEE Advanced 2024 Paper 1]
Ans: (a), (b) & (c)
The central force will provide the necessary centripetal force
? kr = (mv²) / r
or, kr² = mv² ... (1)
By quantization rule n h = mvr
  
 
Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. 
Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. 
List - I List - II 
(P)  
????
??????
?? ? 
????
??????
 ???? (1) one ?? particle and one ?? +
particle 
(Q)  
????
??????
 ???? ? 
????
??????
 ???? (2) three ?? -
particles and one ?? particle 
(R)  
????
??????
???? ? 
????
??????
 ???? (3) two ?? -
particles and one ?? particle 
(S)  
????
??????
 ???? ? 
????
??????
???? (4) one ?? particle and one ?? -
particle 
 (5) one ?? particle and two ?? +
particles 
 
(a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ??   [JEE Advanced 2023 Paper 1] 
Ans: (a) 
In the given nuclear reaction: 
 
?? 1
?? ?? 1
? 
?? 2
?? ?? 2
+ ?? 1
( 
2
?? 4
) + ?? 2
( 
1
?? 0
) + ?? 3
( 
-1
?? 0
) 
we have the conservation of charge expressed as : 
?? 1
= ?? 2
+ 2?? 1
+ ?? 2
- ?? 3
 
and the conservation of nucleons (mass number) is given by: 
?? 1
= ?? 2
+ 4?? 1
?? 1
=
?? 1
- ?? 2
4
… … …
 
From (i) and (ii), we get 
N
2
- N
3
= Z
1
- Z
2
- (
A
1
- A
2
2
) 
 (P)  
92
U
238
? 
91
 Pa
234
 N
1
=
238 - 234
4
= 1 ? 1?? N
2
- N
3
= (92 - 91) - (
4
2
) = -1 ? 1?? -
(Q)  
82
 Pb
214
? 
82
 Pb
210
 N
1
=
214 - 210
4
= 1 ? 1?? N
2
- N
3
= (82 - 82) - (
4
2
) = -2 ? 2?? -
(R)  
81
 Tl
210
? 
82
 Pb
206
 
N
1
=
210- 206
4
= 1 ? 1?? N
2
- N
3
= (81 - 83) -
4
2
= -3 ? 3?? -
 
(S)  
91
 Pa
228
?
88
Ra
224
 
N
1
=
228 - 224
4
= 1 ? 1?? 
N
2
- N
3
= (91 - 88) -
4
2
= 1?? +
 
2022 
Q1: The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. 
Assume that all nucleons are uniformly distributed inside the nucleus. Let th e binding energy of a 
proton be ?? ?? ?? and the binding energy of a neutron be ?? ?? ?? in the nucleus. 
Which of the following statement(s) is(are) correct? 
(a) ?? ?? ?? - ?? ?? ?? is proportional to ?? (?? - ?? ) where ?? is the atomic number of the nucleus. 
(b) ?? ?? ?? - ?? ?? ?? is proportional to ?? -
?? ?? where ?? is the mass number of the nucleus. 
(c) ?? ?? ?? - ?? ?? ?? is positive. 
(d) ?? ?? ?? increases if the nucleus undergoes a beta decay emitting a positron.   [JEE Advanced 2022 Paper 
1] 
Ans: (a), (b) & (d) 
Total binding energy (without considering repulsions), 
?? ?? = [?? ?? ?? + (?? - ?? )?? ?? - ?? ?? ]?? 2
 
Where,  
?? ?? ?? is the nuclei under consideration. 
Now, considering repulsion : 
Page 5


 
Q1: A particle of mass m is moving in a circular orbit under the inuence of the central force F(r)
= -kr, corresponding to the potential energy V(r) = (kr²)/2, where k is a positive force constant
and r is the radial distance from the origin. According to the Bohr's quantization rule, the
angular momentum of the particle is given by L = n h, where h = h/(2 p), h is Planck's constant,
and n a positive integer. If v and E are the speed and total energy of the particle, respectively,
then which of the following expression(s) is(are) correct?
(a) 
(b) 
(c) 
(d)    [JEE Advanced 2024 Paper 1]
Ans: (a), (b) & (c)
The central force will provide the necessary centripetal force
? kr = (mv²) / r
or, kr² = mv² ... (1)
By quantization rule n h = mvr
  
 
Q1: List-I shows different radioactive decay processes and List-II provides possible emitted particles. 
Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. 
List - I List - II 
(P)  
????
??????
?? ? 
????
??????
 ???? (1) one ?? particle and one ?? +
particle 
(Q)  
????
??????
 ???? ? 
????
??????
 ???? (2) three ?? -
particles and one ?? particle 
(R)  
????
??????
???? ? 
????
??????
 ???? (3) two ?? -
particles and one ?? particle 
(S)  
????
??????
 ???? ? 
????
??????
???? (4) one ?? particle and one ?? -
particle 
 (5) one ?? particle and two ?? +
particles 
 
(a) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(b) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(c) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ?? 
(d) ?? ? ?? , ?? ? ?? , ?? ? ?? , ?? ? ??   [JEE Advanced 2023 Paper 1] 
Ans: (a) 
In the given nuclear reaction: 
 
?? 1
?? ?? 1
? 
?? 2
?? ?? 2
+ ?? 1
( 
2
?? 4
) + ?? 2
( 
1
?? 0
) + ?? 3
( 
-1
?? 0
) 
we have the conservation of charge expressed as : 
?? 1
= ?? 2
+ 2?? 1
+ ?? 2
- ?? 3
 
and the conservation of nucleons (mass number) is given by: 
?? 1
= ?? 2
+ 4?? 1
?? 1
=
?? 1
- ?? 2
4
… … …
 
From (i) and (ii), we get 
N
2
- N
3
= Z
1
- Z
2
- (
A
1
- A
2
2
) 
 (P)  
92
U
238
? 
91
 Pa
234
 N
1
=
238 - 234
4
= 1 ? 1?? N
2
- N
3
= (92 - 91) - (
4
2
) = -1 ? 1?? -
(Q)  
82
 Pb
214
? 
82
 Pb
210
 N
1
=
214 - 210
4
= 1 ? 1?? N
2
- N
3
= (82 - 82) - (
4
2
) = -2 ? 2?? -
(R)  
81
 Tl
210
? 
82
 Pb
206
 
N
1
=
210- 206
4
= 1 ? 1?? N
2
- N
3
= (81 - 83) -
4
2
= -3 ? 3?? -
 
(S)  
91
 Pa
228
?
88
Ra
224
 
N
1
=
228 - 224
4
= 1 ? 1?? 
N
2
- N
3
= (91 - 88) -
4
2
= 1?? +
 
2022 
Q1: The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. 
Assume that all nucleons are uniformly distributed inside the nucleus. Let th e binding energy of a 
proton be ?? ?? ?? and the binding energy of a neutron be ?? ?? ?? in the nucleus. 
Which of the following statement(s) is(are) correct? 
(a) ?? ?? ?? - ?? ?? ?? is proportional to ?? (?? - ?? ) where ?? is the atomic number of the nucleus. 
(b) ?? ?? ?? - ?? ?? ?? is proportional to ?? -
?? ?? where ?? is the mass number of the nucleus. 
(c) ?? ?? ?? - ?? ?? ?? is positive. 
(d) ?? ?? ?? increases if the nucleus undergoes a beta decay emitting a positron.   [JEE Advanced 2022 Paper 
1] 
Ans: (a), (b) & (d) 
Total binding energy (without considering repulsions), 
?? ?? = [?? ?? ?? + (?? - ?? )?? ?? - ?? ?? ]?? 2
 
Where,  
?? ?? ?? is the nuclei under consideration. 
Now, considering repulsion : 
Number of proton pairs = 
?? ?? 2
 
? This repulsion energy ?
?? (?? -1)
2
×
1
4?? ?
0
?? 2
?? 
Where R is the radius of the nucleus 
? ?? ?? ?? - ?? ?? ?? ? ?? (?? - 1) ? there will be no repulsion term for neutrons. 
Also, since ?? = ?? 0
?? 1/3
 
? ?? ?? ?? - ?? ?? ?? ? ?? -1/3
 
Because of repulsion among protons, 
?? ?? ?? < ?? ?? ?? 
Since in ?? +
decay, number of protons decrease ? repulsion would decrease 
? ?? ?? ?? increases 
Q2: In a radioactive decay chain reaction,  
????
??????
???? nucleus decays into  
????
??????
???? nucleus. The ratio of the 
number of ?? to number of ?? -
particles emitted in this process is     [JEE Advanced 2022 Paper 2] 
Ans: 2 
Let the number of ?? -particles be ?? ?? Let the number of ?? -particles be ?? ?? 
Hence, 4?? ?? = 230- 214 
 ? ?? ?? = 4
?? ?? = 84 - (90 - 2?? ?? )
 = 84 - 90 + 2(4)
 = 2
 
So, 
?? ?? ?? ?? =
4
2
= 2: 1 
2021 
Q1: A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of ???? % and 
beta-decay with probability of ???? %. Initially, the number of Q nuclei is 1000 . The number of alpha-
decays of ?? in the first one hour is 
(a) 50 
(b) 75 
(c) 350 
(d) 525    [JEE Advanced 2021 Paper 1] 
Ans: (d) 
Out of 1000 nuclei of Q, 60% may go ?? -decay 
? 600 nuclei may have ?? -decay