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

The nuclear radius empirical formula is $$R = r_0 A^{1/3}$$, where
$$R$$ = radius of the nucleus,
$$A$$ = mass number,
$$r_0$$ ≈ $$1.2 \times 10^{-15}\,$$m (a constant).

Hence the nuclear volume is
$$V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi\left(r_0 A^{1/3}\right)^{3} = \frac{4}{3}\pi r_0^{3} A$$.

The mass of a nucleus is roughly $$A m_n$$, where $$m_n$$ is the nucleon mass (proton/neutron mass).
Therefore nuclear density is

$$\rho = \frac{\text{mass}}{\text{volume}} = \frac{A m_n}{\frac{4}{3}\pi r_0^{3} A} = \frac{m_n}{\tfrac{4}{3}\pi r_0^{3}}$$.

The factor $$A$$ cancels out, so $$\rho$$ is the same constant for all nuclei, independent of their mass numbers.

Assertion (A): “The density of the copper $$\left(^{64}_{29}Cu\right)$$ nucleus is greater than that of the carbon $$\left(^{12}_{6}C\right)$$ nucleus.”
We just showed that densities are practically identical for all nuclei, so Assertion (A) is incorrect.

Reason (R): “The nucleus of mass number $$A$$ has a radius proportional to $$A^{1/3}$$.”
This is exactly the empirical formula stated above, so Reason (R) is correct.

Thus, Assertion (A) is not correct but Reason (R) is correct. The appropriate choice is Option B.