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 :

(B) (A) is not correct but (R) is correct

(A) (A) is correct but (R) is not 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)

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Modern Physics

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 :

Answer: (B)

Writing the nuclear radius as

R = R_{0} A^{1/3}

, the nuclear volume

\frac{4}{3} π R_{0}^{3} A

grows in proportion to the mass number

A

. The nuclear mass is also proportional to

A

, so the density

ρ = \frac{m _{n} A}{\frac{4}{3} π R _{0}^{3} A} = \frac{m _{n}}{\frac{4}{3} π R _{0}^{3}}

is the same for every nucleus. Copper and carbon nuclei therefore have essentially equal densities, so the assertion fails, while the relation

R \propto A^{1/3}

in the reason holds. The reason is correct but the assertion is not.

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option