The ratio of densities of nuclei with mass numbers \( A \) and \( 2A \), respectively is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1 : 1
The radius of a nucleus grows as \( R = R_0 A^{1/3} \), so its volume is proportional to the mass number \( A \). Its mass is also proportional to \( A \) (about \( A \) atomic mass units, \( m_u \)).
\( \displaystyle \rho = \frac{A\,m_u}{\frac{4}{3}\pi R_0^{3} A} = \frac{3\,m_u}{4\pi R_0^{3}} \)
\( A \) 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.”