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 varies as \( R = R_0A^{1/3} \), so its volume is proportional to \( A \). The mass is also proportional to \( A \) (A nucleons of nearly equal mass), so the two cancel in the density.

    \( \displaystyle \rho = \frac{\text{mass}}{\text{volume}} = \frac{A\,m_N}{\frac{4}{3}\pi R_0^{3}A} = \frac{3m_N}{4\pi R_0^{3}} \)

This does not contain A, so the density is the same for every nucleus, \( \rho \propto A^{0} \).

Note: A similar question was also asked in CUET (UG) 2023 on 12-06-2023 (Slot 2).

Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.

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

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

where \( R_0 = 1.2 \times 10^{-15} \) m (= 1.2 fm; 1 fm = \( 10^{-15} \) m). This means the volume of the nucleus, which is proportional to \( R^3 \) is proportional to A. Thus the density of nucleus is a constant, independent of A, for all nuclei.”