Nuclei

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 numbers 3,4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, \(∆M{c}^{2}=____MeV\).

[04 April, 2026 (Shift-I)]

Choose the correct nuclear process from the below options
[p: proton, n : neutron, \({e}^{-}:\)electron, \({e}^{+}:\) positron, \(\nu\) : neutrino, \(\nu\): antineutrino]

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous \(\alpha\)-decay with same Q value of 1 Me V. The ratio of energies of \(\alpha\)-rays produced by A and B is __________

[JEE Main 2026, 8 Apr (Shift 2)]

Energy released when two deuterons \(({{}_{1}\mathrm{H}}^{2})\) fuse to form a helium nucleus \(({{}_{2}\mathrm{He}}^{4})\) is :
(Given : Binding energy per nucleon of \({{}_{1}\mathrm{H}}^{2}=1.1\mathrm{MeV}\) and binding energy per nucleon of \({{}_{2}\mathrm{He}}^{4}=7.0\mathrm{MeV}\) )

[JEE Main 2025, 2 Apr (Shift 2)]

A radioactive nucleus \(\mathrm{n}_2\) has 3 times the decay constant as compared to the decay constant of another radioactive nucleus \(n_1\). If initial number of both nuclei are the same, what is the ratio of number of nuclei of \(n_2\) to the number of nuclei of \(n_1\), after one half-life of \(n_1\) ?

[JEE Main 2025, 23 Jan (Shift 1)]

The energy released if hydrogen atoms are combined to form \({}_{2}^{4}\text{He}\) is _______ MeV.

(Take binding energies per nucleon of \({}_{1}^{2}\text{H}\) and \({}_{2}^{4}\text{He}\) as \(1.1\text{ MeV}\) and \(7.2\text{ MeV}\), respectively)

[JEE Main 2026, 6 Apr (Shift 2)]

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number (A), for nuclei with mass numbers between 30 and 170.
Reason (R) : Nuclear force is long range.
In the light of the above statements, choose the correct answer from the options given below :

[JEE Main 2025, 23 Jan (Shift 2)]

Which of following reaction is correct ? (Where symbols have their usual meanings)

(Shift - I Memory Based)

Energy released when two deuterons \(({{}_{1}H}^{2})\) fuse to form a helium nucleus \(({{}_{2}He}^{4})\) is :
(Given : Binding energy per nucleon of \({{}_{1}H}^{2}=1.1MeV\) and binding energy per nucleon of \({{}_{2}He}^{4}=7.0MeV\) )

The atomic mass of \({ }_6 C ^{12}\) is \(12.000000 u\) and that of \({ }_6 C ^{13}\) is \(13.003354 u\). The required energy to remove a neutron from \({ }_6 C ^{13}\), if mass of neutron is \(1.008665 u\), will be :

[JEE Main 2024, 27 Jan (Shift 2)]

The atomic mass of \({ }_6 C ^{12}\) is \(12.000000 u\) and that of \({ }_6 C ^{13}\) is \(13.003354 u\). The required energy to remove a neutron from \({ }_6 C ^{13}\), if mass of neutron is \(1.008665 u\), will be :

[JEE Main 2024, 27 Jan (Shift 2)]

Assuming the experimental mass of \({}_{6}^{12}C\) as 12u, the mass defect of \({}_{6}^{12}C\) atom is_____ \(\mathrm{MeV}/{\mathrm{c}}^{2}.\)
(Mass of proton = 1.00727u. mass of neutron = 1.00866u, \(1\mathrm{u}=931.5\mathrm{MeV}/{\mathrm{c}}^{2}\) and c is the speed of the light in vacuum).

[JEE Main 2026, 5 Apr (Shift 2)]

The energy equivalent of 1 g of substance is :

[JEE Main 2024, 9 Apr (Shift 1)]

The energy equivalent of 1 g of substance is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(\left({}_{29}^{64}\mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({}_{6}^{12}\mathrm{C}\right)\) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to \({\mathrm{A}}^{1/3}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

[JEE Main 2025, 7 Apr (Shift 2)]

A radioactive nucleus \(\mathrm{n}_2\) has 3 times the decay constant as compared to the decay constant of another radioactive nucleus \(n_1\). If initial number of both nuclei are the same, what is the ratio of number of nuclei of \(n_2\) to the number of nuclei of \(n_1\), after one half-life of \(n_1\) ?

[JEE Main 2025, 23 Jan (Shift 1)]

Choose the correct nuclear process from the below options
[p: proton, n : neutron, \({e}^{-}:\)electron, \({e}^{+}:\) positron, \(\nu\) : neutrino, \(\nu\): antineutrino]

[JEE Main 2025, 28 Jan (Shift 1)]

Which of following reaction is correct ? (Where symbols have their usual meanings)

(Shift - I Memory Based)

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as:

[JEE Main 2021, 26 Aug (Shift 1)]

The binding energy per nucleon of \({}_{83}^{209}Bi\) is _______ MeV .
[Take \(m\left({}_{83}^{209}Bi\right)=208.980388u,{m}_{p}=1.007825u,{m}_{n}=1.008665u\) \(1u=931MeV/{c}^{2}\) ]

[02 April, 2026 (Shift-2)]

The half-life of \({}^{198}\mathrm{Au}\) is 3 days. If atomic weight of \({}^{198}\mathrm{Au}\) is \(198\mathrm{g}/\mathrm{mol}\) then the activity of \(2\mathrm{mg}\) of \({}^{198}\mathrm{Au}\) is [in disintegration/second]:

[JEE Main 2021, 25 Jul (Shift 1)]

A free neutron decays into a proton but a free proton does not decay into neutron. This is because:

[JEE Main 2023, 31 Jan (Shift 1)]

The ratio of the density of oxygen nucleus \(\left({}_{8}^{16}\mathrm{O}\right)\) and helium nucleus \(\left({}_{2}^{4}\mathrm{He}\right)\) is

[JEE Main 2023, 25 Jan (Shift 1)]

A free neutron decays into a proton but a free proton does not decay into neutron. This is because [JEE Main 2023, 31 Jan (Shift 1)]

The mass of proton, neutron and helium nucleus are respectively 1.0073 u, 1.0087 u and 4.0015 น. The binding energy of helium nucleus is:

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If \({\lambda }_{A}\) and \({\lambda }_{B}\) are decay constants of A and B respectively, then choose the correct relation from the given options.

[JEE Main 2023, 11 Apr (Shift 1)]

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number (A), for nuclei with mass numbers between 30 and 170.
Reason (R) : Nuclear force is long range.
In the light of the above statements, choose the correct answer from the options given below :

Consider the following statements:
(A) Atoms of each element emit spectrum.
(B) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
(C) The density of nuclear matter depends on the size of the nucleus.
(D) A free neutron is stable but a free proton decay is possible.
(E) Radioactivity is an indication of the instability of nuclei.

Choose the correct answer from the options given below:

[JEE Main 2024, 6 Apr (Shift 1)]

For a nucleus \({}_{Z}^{A}X\) having mass number A and atomic number Z
(A) The surface energy per nucleon (b) \(={a}_{1}{\mathrm{A}}^{2/3}\)
(B) The Coulomb contribution to the binding energy
\({b}_{c}=-{a}_{2}\frac{Z(Z-1)}{{A}^{4/3}}\)
(C) The volume energy \({\mathrm{b}}_{\mathrm{v}}={\mathrm{a}}_{3}\mathrm{A}\)
(D) Decrease in the binding energy is proportional to surface area.
(E) While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons, \(\left({a}_{1},{a}_{2}\right.\) and \({a}_{3}\) are constants)

Choose the most appropriate answer from the options given below:

[JEE Main 2023, 8 Apr (Shift 1)]

\({}_{92}^{238}A\to {}_{90}^{234}B+{}_{2}^{4}D+Q\)

In the given nuclear reaction, the approximate amount of energy released will be:
[Given, mass of \({}_{92}^{238}A=238.05079\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2}\), mass of \({}_{90}^{234}B=234.04363\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2},\) mass of \({}_{2}^{4}D=4.00260\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2}\) ]

[JEE Main 2023, 13 Apr (Shift 1)]

If a radioactive element having half-life of \(30\min\) is undergoing beta decay, the fraction of radioactive element that remains undecayed after \(90\min\) will be:

[JEE Main 2023, 29 Jan (Shift 1)]

Three specimens \(\mathrm{A},\mathrm{B},\mathrm{C}\) of same radioactive element has activities \(1\) microcurie, \(1\) rutherford and \(1\) becquerel respectively. Which specimen has maximum mass?

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of \(\frac{1}{2}\) day. If both A and B simultaneously start undergo radioactivity at the same time with initial mass \(320\mathrm{g}\) each, how many total atoms of A and B combined would be left after 2 days.

[JEE Main 2023, 29 Jan (Shift 2)]

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If \({\lambda }_{A}\) and \({\lambda }_{B}\) are decay constants of A and B respectively, then choose the correct relation from the given options.

Two radioactive substances X and Y originally have \({N}_{\text{, }}\) and \({N}_{2}\) nuclei respectively. Half life of X is half of the life of Y. After three half lives of Y, number of nuclei of both are equal.The ratio \(\frac{{N}_{1}}{{N}_{2}}\) will be equal to:

[JEE Main 2021, 25 Feb (Shift 1)]

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170 .
Reason R : Nuclear force is short ranged.
In the light of the above statements, choose the correct answer from the options given below:

[JEE Main 2023, 24 Jan (Shift 1)]

Two radioactive substances X and Y originally have \({N}_{\text{1}}\) and \({N}_{2}\) nuclei respectively. Half life of X is half of the life of Y. After three half lives of Y, number of nuclei of both are equal.The ratio \(\frac{{N}_{1}}{{N}_{2}}\) will be equal to:

[JEE Main 2021, 25 Feb (Shift 1)]

A radioactive sample disintegrates via two independent decay processes having half lives \({\mathrm{T}}_{1/2}^{(1)}\) and \({\mathrm{T}}_{1/2}^{(2)}\) respectively. The effective half-life, \({\mathrm{T}}_{1/2}\) of the nuclei is:

[JEE Main 2021, 18 Mar (Shift 1)]

If a radioactive element having half-life of \(30\min\) is undergoing beta decay, the fraction of radioactive element that remains undecayed after \(90\min\) will be:

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

The half life of a radioactive nuclide is 100 hours . The fraction of original activity that will remain after 150 hours would be:

[NEET 2021]

\({}_{92}^{238}A\to {}_{90}^{234}B+{}_{2}^{4}D+Q\)

In the given nuclear reaction, the approximate amount of energy released will be:
[Given, mass of \({}_{92}^{238}A=238.05079\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2}\), mass of \({}_{90}^{234}B=234.04363\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2},\mathrm{m}\)ass of \({}_{2}^{4}D=4.00260\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2}\) ]

[JEE Main 2023, 13 Apr (Shift 1)]

The ratio of the density of oxygen nucleus \({(}_{8}^{16}\mathrm{O})\) and helium nucleus \({(}_{2}^{4}\mathrm{He})\) is:

The ratio of the density of oxygen nucleus \(\left({}_{8}^{16}\mathrm{O}\right)\) and helium nucleus \(\left({}_{2}^{4}\mathrm{He}\right)\) is:

[JEE Main 2023, 25 Jan (Shift 1)]

A radio-active material is reduced to \(1/8\) of its original amount in 3 days. If \(8\times {10}^{-3}\mathrm{kg}\) of the material is left after 5 days. The initial amount of the material is:

[JEE Main 2023, 8 Apr (Shift 2)]

A nucleus of mass \( M \) emits \( \gamma \)-ray photon of frequency \( v \) . The loss of internal energy by the nucleus is [Take \( c \) as the speed of electromagnetic wave]

A radioactive nucleus undergoes a series of decay according to the scheme

\(A \xrightarrow{\alpha} A_1 \xrightarrow{\beta} A_2 \xrightarrow{\alpha} A_3 \xrightarrow{\gamma} A_4\)

If the mass number and atomic number of \( A \) are 180 and 72 respectively, then what are these number for \( A_{3} \)

[JEE Main 2023, 24 Jan (Shift 1)]

The half-life of \(A{u}^{198}\) is 2.7 days. The activity of 1.50mg of \(A{u}^{198}\) if its atomic weight is 198\(gmo{l}^{-1}\) is, (\({N}_{A}=6\times {10}^{23}/mol\))

[JEE Main 2021, 16 Mar (Shift 2)]