Two nuclei have mass numbers in the ratio 3 : 5. The ratio of their n…

The correct answer is Option (4) → 1 : 1

The radius of a nucleus of mass number A is \( R = R_0A^{1/3} \), so its volume is proportional to A, \( V = \frac{4}{3}\pi R_0^{3}A \). Its mass is also proportional to A (about A atomic mass units), so the density is the same for every nucleus.

    \( \displaystyle \rho = \frac{A\,m_{\mathrm{u}}}{\frac{4}{3}\pi R_0^{3}A} = \frac{3m_{\mathrm{u}}}{4\pi R_0^{3}} \)

The mass number cancels, so the ratio of the densities 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

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

… 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.”