The ratio of nuclear densities of two nuclei having mass numbers A an…

The correct answer is Option (2) → 1 : 1

The radius of a nucleus grows as the cube root of its mass number, \( R = R_0 A^{1/3} \), so its volume is proportional to \( A \), just like its mass.

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

Here \( m \) is the mass of a nucleon. \( A \) cancels, so the nuclear density is the same for all nuclei, and the ratio is \( 1 : 1 \).

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 R₀ = 1.2 × 10^–15 m (=1.2 fm; 1 fm = 10^–15 m). 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.”