Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1 : 1
The radius of a nucleus grows with mass number as \( R = R_0A^{1/3} \), so the nuclear volume is proportional to \( A \). The mass is also proportional to \( A \) (about \( m \) per nucleon), so \( A \) cancels in the density.
\( \displaystyle \rho = \frac{\text{mass}}{\text{volume}} = \frac{A\,m}{\frac{4}{3}\pi R_0^{3}A} = \frac{3m}{4\pi R_0^{3}} \)
The density does not depend on \( A \), so every nucleus has nearly the same density, about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \). The ratio is \( 1 : 1 \).
Note: A similar question was also asked in CUET (UG) 2026 on 19-05-2026 (Slot 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 – “… 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.”