The density of a nucleus of mass number A is proportional to:

The correct answer is Option (4) → \( A^0 \)

The radius of a nucleus of mass number A is \( R = R_0A^{1/3} \), so its volume \( \frac{4}{3}\pi R^{3} \) is proportional to A. The mass of the nucleus is also proportional to A, so the two cancel in the density.

    \( \displaystyle \rho = \frac{\text{mass}}{\text{volume}}\propto\frac{A}{A} = A^{0} \)

The density does not depend on the mass number; it is the same for all nuclei.

Note: A similar question was also asked in CUET (UG) 2023 on 13-06-2023 (Slot 1).

NCERT (2026-27):
Size of the Nucleus – “… It has been found that a nucleus of mass number A has a radius

    \( \displaystyle R = R_0 A^{1/3} \qquad (13.5) \)

… This means the volume of the nucleus, which is proportional to R³ is proportional to A. Thus the density of nucleus is a constant, independent of A, for all nuclei.”