Nuclei

13 JEE Main questions · Physics

Nuclear structure

PhysicsJEE Main 22 Jan 2026, Shift 1·Q11·MCQ·Easy–moderate
Open
The minimum frequency of photon required to break a particle of mass 15.348 amu into $4\alpha$ particles is kHz. [mass of He nucleus $= 4.002$ amu, 1 amu $= 1.66\times10^{-27}$ kg, $h = 6.6\times10^{-34}$ J.s and $c = 3\times10^{8}$ m/s]
1. (1) $9\times10^{19}$
2. (2) $9\times10^{20}$
3. (3) $14.94\times10^{20}$
4. (4) $14.94\times10^{19}$
PhysicsJEE Main 23 Jan 2026, Shift 2·Q12·MCQ·Easy
Open
Which of the following pair of nuclei are isobars of the element?
1. (1) ${}^{2}_{1}\mathrm{H}$ and ${}^{3}_{1}\mathrm{H}$
2. (2) ${}^{236}_{92}\mathrm{U}$ and ${}^{238}_{92}\mathrm{U}$
3. (3) ${}^{198}_{80}\mathrm{Hg}$ and ${}^{197}_{79}\mathrm{Au}$
4. (4) ${}^{3}_{1}\mathrm{H}$ and ${}^{3}_{2}\mathrm{He}$
We corrected a printing error in the original paper
Source printed option (4) as “ ${}^{3}_{1}\mathrm{H}$ and ${}^{3}_{2}\mathrm{H}$ ”.
PhysicsJEE Main 24 Jan 2026, Shift 1·Q13·MCQ·Easy
Open
Given below are two statements:
Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II : For all elements, nuclei with less binding energy per nucleon transform to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below:
1. (1)Both Statement I and Statement II are true
2. (2)Statement I is true but Statement II is false
3. (3)Both Statement I and Statement II are false
4. (4)Statement I is false but Statement II is true
We corrected a printing error in the original paper
Source printed “nuclei with less binding energy per nucleon transforms”.
PhysicsJEE Main 24 Jan 2026, Shift 2·Q11·MCQ·Easy–moderate
Open
The binding energies for the following nuclear reactions are expressed in MeV. ${}_{2}\mathrm{He}^{3} + {}_{0}\mathrm{n}^{1} \rightarrow {}_{2}\mathrm{He}^{4} + 20\ \mathrm{MeV}$ ${}_{2}\mathrm{He}^{4} + {}_{0}\mathrm{n}^{1} \rightarrow {}_{2}\mathrm{He}^{5} - 0.9\ \mathrm{MeV}$ If $X_3$ , $X_4$ , $X_5$ denote the stability of ${}_{2}\mathrm{He}^{3}$ , ${}_{2}\mathrm{He}^{4}$ and ${}_{2}\mathrm{He}^{5}$ , respectively, then the correct order is:
1. (1) $X_4 > X_5 > X_3$
2. (2) $X_4 = X_5 = X_3$
3. (3) $X_4 > X_5 < X_3$
4. (4) $X_4 < X_5 < X_3$
We corrected a printing error in the original paper
Source printed “The binding energy for the following nuclear reactions are”.
PhysicsJEE Main 28 Jan 2026, Shift 1·Q6·MCQ·Easy–moderate
Open
An atom ${}_{3}X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by :
1. (1)250%
2. (2)150%
3. (3)225%
4. (4)900%
Flawed question. The mass number of ${}_{3}X$ is not printed, and with the evident $A = 8 \to 27$ the surface area grows by 125%, which is not an option (the key 225% is the final area as a percentage of the initial); Allen gives the question as BONUS. It is shown for completeness and is left out of practice tests.
PhysicsJEE Main 28 Jan 2026, Shift 2·Q1·MCQ·Easy–moderate
Open
A nucleus has mass number $\alpha$ and radius $R_\alpha$ . Another nucleus has mass number $\beta$ and radius $R_\beta$ . If $\beta = 8\alpha$ then $R_\alpha/R_\beta$ is:
1. (1)2
2. (2)8
3. (3)1
4. (4)0.5
PhysicsJEE Main 2 Apr 2026, Shift 2·Q19·MCQ·Easy–moderate
Open
The binding energy per nucleon of $^{209}_{\ 83}\mathrm{Bi}$ is MeV. [Take $m\left(^{209}_{\ 83}\mathrm{Bi}\right) = 208.980388$ u, $m_p = 1.007825$ u, $m_n = 1.008665$ u, $1\,\mathrm{u} = 931\ \mathrm{MeV}/c^2$ ]
1. (1)7.48
2. (2)7.84
3. (3)8.79
4. (4)6.94
PhysicsJEE Main 4 Apr 2026, Shift 1·Q4·MCQ·Easy–moderate
Open
Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass number 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, $\Delta Mc^2 =$ MeV.
1. (1)6.9
2. (2)7.9
3. (3)2.2
4. (4)4.3
PhysicsJEE Main 5 Apr 2026, Shift 2·Q19·MCQ·Easy–moderate
Open
Assuming the experimental mass of ${}^{12}_{6}\mathrm{C}$ nucleus as 12u, the mass defect of ${}^{12}_{6}\mathrm{C}$ nucleus is $\mathrm{MeV/c^2}$ . (Mass of proton $= 1.00727$ u. mass of neutron $= 1.00866$ u, 1 u $= 931.5\ \mathrm{MeV/c^2}$ and c is the speed of the light in vacuum.)
1. (1)127.5
2. (2)89.03
3. (3)272.0
4. (4)92.0
We corrected a printing error in the original paper
Source printed “experimental mass of ${}^{12}_{6}$ C as 12u, the mass defect of ${}^{12}_{6}$ C atom”; corrected to the intended “ ${}^{12}_{6}$ C nucleus” in both places (the data give proton, not hydrogen-atom, masses and no electron mass; the key 89.03 is the nuclear defect).
PhysicsJEE Main 6 Apr 2026, Shift 2·Q16·MCQ·Easy–moderate
Open
The energy released if hydrogen atoms are combined to form ${}^{4}_{2}\mathrm{He}$ is MeV.
(Take binding energies per nucleon of ${}^{2}_{1}\mathrm{H}$ and ${}^{4}_{2}\mathrm{He}$ as 1.1 MeV and 7.2 MeV, respectively).
1. (1)6.1
2. (2)24.4
3. (3)26.6
4. (4)5
We corrected a printing error in the original paper
Source printed helium as a fraction “ $\frac{4}{2}$ He”; “1.1 meV”; no unit after the blank (MeV added).

Radioactivity and nuclear energy

PhysicsJEE Main 23 Jan 2026, Shift 2·Q21·Numerical·Easy–moderate
Open
The average energy released per fission for the nucleus of ${}^{235}_{92}\mathrm{U}$ is 190 MeV. When all the atoms of 47 g pure ${}^{235}_{92}\mathrm{U}$ undergo fission process, the energy released is $\alpha\times10^{23}$ MeV. The value of $\alpha$ is .
(Avogadro Number $= 6\times10^{23}$ per mole)
PhysicsJEE Main 6 Apr 2026, Shift 1·Q23·Numerical·Moderate
Open
The energy released when $\dfrac{7}{17.13}$ kg of ${}^{7}_{3}\mathrm{Li}$ is converted into ${}^{4}_{2}\mathrm{He}$ by proton bombardment is $\alpha\times10^{32}$ eV. The value of $\alpha$ is . (Nearest integer)
(Mass of ${}^{7}_{3}\mathrm{Li} = 7.0183$ u, mass of ${}^{4}_{2}\mathrm{He} = 4.004$ u, mass of proton $= 1.008$ u and 1 u $= 931\ \mathrm{MeV/c^2}$ and Avogadro number $= 6.0\times10^{23}$ )
PhysicsJEE Main 8 Apr 2026, Shift 2·Q19·MCQ·Moderate
Open
Two radioactive substances A and B of mass numbers 200 and 212 respectively, show spontaneous $\alpha$ -decay with same Q value of 1 MeV. The ratio of energies of $\alpha$ -rays produced by A and B is .
1. (1) $\dfrac{2548}{2650}$
2. (2) $\dfrac{2706}{2646}$
3. (3) $\dfrac{2597}{2600}$
4. (4) $\dfrac{2862}{2499}$
We corrected a printing error in the original paper
Source printed “Two radioactive substances … shows”.