Question

The radius $\mathrm{R}$ of a nucleus of mass number $\mathrm{A}$ can be estimated by the formula $\mathrm{R}=\left(1.3\times {10}^{-15}\right){\mathrm{A}}^{1/3}\mathrm{m}$. It follows that the mass density of n nucleus is of the order of: $\left(M_{prot}\cong M_{\text{neut }}\simeq 1.67\times {10}^{-27} \mathrm{kg}\right)$

JEE Main 2020 (03 Sep Shift 2)

Options

• A: ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$
• B: ${10}^{10 }\mathrm{kg} {\mathrm{m}}^{-3}$
• C: ${10}^{24} \mathrm{kg} {\mathrm{m}}^{-3}$
• D: ${10}^{17} \mathrm{kg} {\mathrm{m}}^{-3}$

Question

From the given data, the amount of energy required to break the nucleus of aluminium ${}_{13}{}^{27}\mathrm{Al}$ is __________$x\times {10}^{-3} \mathrm{J}$ 

Mass of neutron $=1.00866 \mathrm{u}$
Mass of proton $=1.00726 \mathrm{u}$
Mass of Aluminium nucleus $=27.18846 \mathrm{u}$
(Assume $1 \mathrm{u}$ corresponds to $x J$ of energy)
(Round off to the nearest integer)

JEE Main 2021 (25 Jul Shift 2)

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Question

Nucleus $A$ is having mass number $220$ and its binding energy per nucleon is $5.6 \mathrm{MeV}$. It splits in two fragments $B$ and $C$ of mass numbers $105$ and $115$. The binding energy of nucleons in $B$ and $C$ is $6.4 \mathrm{MeV}$ per nucleon. The energy $Q$ released per fission will be:

JEE Main 2022 (24 Jun Shift 1)

Options

• A: $0.8\mathrm{MeV}$
• B: $275\mathrm{MeV}$
• C: $220\mathrm{MeV}$
• D: $176\mathrm{MeV}$

Question

The $Q$-value of a nuclear reaction and kinetic energy of the projectile particle, $K_p$ are related as 

JEE Main 2022 (28 Jun Shift 1)

Options

• A: $Q=K_p$
• B: $\left(K_p+Q\right)<0$
• C: $Q<K_p$
• D: $\left(K_p+Q\right)>0$

Question

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:

 ${}_1{}^{2}X+{}_1{}^{2}X={}_2{}^{4}Y$

 The binding energies per nucleon ${}_1{}^{2}X$ and ${}_2{}^{4}Y$ are $1.1\mathrm{MeV}$ and $7.6\mathrm{MeV}$ respectively. The energy released in this process is_____ $\mathrm{MeV}$.

JEE Main 2022 (26 Jul Shift 2)

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Question

A common example of alpha decay is

${{}^{238}}_{92}\mathrm{U}{{\to }^{234}}_{90}\mathrm{Th}{+}_2{\mathrm{He}}^4+Q$

Given:

${{}^{238}}_{92}\mathrm{U}=238.05060 \mathrm{u}$

${{}^{234}}_{90}\mathrm{Th}=234.04360 \mathrm{u}$

${{}^4}_2\mathrm{He}=4.00260 \mathrm{u}$ and $1\mathrm{u}=931.5\frac{\mathrm{MeV}}{c^2}$

The energy released $\left(Q\right)$ during the alpha decay of ${{}^{238}}_{92}\mathrm{U}$ is _____ $\mathrm{MeV}$.

JEE Main 2023 (12 Apr Shift 1)

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Question

A star has $100 \%$ helium composition. It starts to convert three ${ }^4 \mathrm{He}$ into one ${ }^{12} \mathrm{C}$ via triple alpha process as ${ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}$. The mass of the star is $2.0 \times 10^{32} \mathrm{~kg}$ and it generates energy at the rate of $5.808 \times 10^{30} \mathrm{~W}$. The rate of converting these ${ }^4 \mathrm{He}$ to ${ }^{12} \mathrm{C}$ is $\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}$, where $\mathrm{n}$ is _________ [ Take, mass of ${ }^4 \mathrm{He}=4.0026 \mathrm{u}$, mass of ${ }^{12} \mathrm{C}=12 \mathrm{u}$ ]

JEE Main 2024 (09 Apr Shift 1)

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Question

The energy released in the fusion of $2 \mathrm{~kg}$ of hydrogen deep in the sun is $E_H$ and the energy released in the fission of $2 \mathrm{~kg}$ of ${ }^{235} \mathrm{U}$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately: (Consider the fusion reaction as $4 \mid H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{MeV}$, energy released in the fission reaction of ${ }^{235} \mathrm{U}$ is $200 \mathrm{MeV}$ per fission nucleus and $\mathrm{N}_{\mathrm{A}}=$ $\left.6.023 \times 10^{23}\right)$

JEE Main 2024 (09 Apr Shift 2)

Options

• A: 7.62
• B: 25.6
• C: 15.04
• D: 9.13

Question

From the statements given below :

(A) The angular momentum of an electron in $n^{th}$ orbit is an integral multiple of $h$.

(B) Nuclear forces do not obey inverse square law.

(C) Nuclear forces are spin dependent.

(D) Nuclear forces are central and charge independent.

(E) Stability of nucleus is inversely proportional to the value of packing fraction.

Choose the correct answer from the options given below :

JEE Main 2024 (01 Feb Shift 2)

Options

• A: (A), (B), (C), (D) only
• B: (A), (C), (D), (E) only
• C: (A), (B), (C), (E) only
• D: (B), (C), (D), (E) only

Question

The explosive in a Hydrogen bomb is a mixture of ${}_1\mathrm{H}^2,{}_1\mathrm{H}^3$ and ${}_3\mathrm{Li}^6$ in some condensed form. The chain reaction is given by ${}_3\mathrm{Li}^6+{}_0\mathrm{n}^1\to {}_2\mathrm{He}^4+{}_1\mathrm{H}^3$;  ${}_1\mathrm{H}^2+{}_1\mathrm{H}^3\to {}_2\mathrm{He}^4+{}_0\mathrm{n}^1$

During the explosion the energy released is approximately [Given : $M\left(\mathrm{Li}\right)=6.01690 \mathrm{amu}\mathit{,}\mathit{ }M\left({}_1\mathrm{H}^2\right)=2.01471 \mathrm{amu}, M\left({}_2\mathrm{He}^4\right)=4.00388 \mathrm{amu}$ and $1 \mathrm{amu}=931.5 \mathrm{MeV}$]

JEE Main 2024 (29 Jan Shift 1)

Options

• A: $28.12\mathrm{MeV}$
• B: $12.64\mathrm{MeV}$
• C: $16.48\mathrm{MeV}$
• D: $22.22\mathrm{MeV}$