If the ratio of mass number of two nuclei is 8 : 27, then the ratio of the volumes of their nuclei is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 8 : 27 \)
The radius of a nucleus is \( R = R_0 A^{1/3} \), so its volume is proportional to the mass number, because nuclear density is the same for all nuclei.
\( \displaystyle V = \frac{4}{3}\pi R^{3} = \frac{4}{3}\pi R_0^{3}\,A \;\Rightarrow\; V \propto A \)
\( \displaystyle \frac{V_1}{V_2} = \frac{A_1}{A_2} = \frac{8}{27} \)
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.”