JEE Main 2025 Apr 7 Shift 2, Physics Q2: Mass-Energy and Nuclear Binding Energy

JEE Main2025Apr 7, Shift 2Physics

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 $(_{29}^{64} Cu)$ nucleus is greater than that of the carbon $(_{6}^{12} C)$ nucleus.

Reason (R) : The nucleus of mass number A has a radius proportional to $A^{1/3}$ .

In the light of the above statements, choose the most appropriate answer from the options given below :

A
(A) is correct but (R) is not correct
B
(A) is not correct but (R) is correct
C
Both (A) and (R) are correct and (R) is the correct explanation of (A)
D
Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Solution

Empirically the nuclear radius follows $R = R_{0} A^{1/3}$ , so the volume of a nucleus is proportional to $A$ : $V = \frac{4}{3} π R_{0}^{3} A$ . Reason (R) is therefore correct.

The mass of a nucleus is approximately $A$ times a nucleon mass $m_{n}$ , so density $ρ = \frac{m _{n} A}{\frac{4}{3} π R _{0}^{3} A} = \frac{m _{n}}{\frac{4}{3} π R _{0}^{3}}$ , independent of $A$ .

Since nuclear density is essentially the same for all nuclei, the density of $^{64}$ Cu is not greater than that of $^{12}$ C, they are equal. Hence Assertion (A) is incorrect while Reason (R) is correct.

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JEE Main 2025 Apr 7 Shift 2, Physics Q2: Mass-Energy and Nuclear Binding Energy

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