Two nuclei have their mass numbers in the ratio of 1:27. The ratio of their nuclear densities is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1:1
The nuclear radius grows as the cube root of the mass number, so the nuclear volume is proportional to A, just like the nuclear mass.
\( R = R_0 A^{1/3} \)
\( \displaystyle \rho = \frac{A\,m_u}{\frac{4}{3}\pi R_0^{3} A} = \frac{3m_u}{4\pi R_0^{3}} \)
A cancels, so the nuclear density is the same (about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \)) for all nuclei, and the ratio is 1:1.
Why the other options are incorrect
Option (1) 1:27 — Incorrect. 1:27 is the ratio of the masses (and of the volumes); the density is their quotient, which is the same for both nuclei.
Option (3) 1:9 — Incorrect. 1:9 is the ratio of the surface areas, proportional to \( A^{2/3} \).
Option (4) 1:3 — Incorrect. 1:3 is the ratio of the radii, proportional to \( A^{1/3} \).
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 \( R^{3} \) is proportional to \( A \). Thus the density of nucleus is a constant, independent of \( A \), for all nuclei.”