The ratio of the radii of two nuclei of mass numbers \( A_1 \) and \( A_2 \) respectively would be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( (A_1/A_2)^{1/3} \)
The radius of a nucleus grows as the cube root of its mass number, because the nuclear density is the same for all nuclei (volume proportional to \( A \)).
\( \displaystyle R = R_0\,A^{1/3} \)
\( \displaystyle \frac{R_1}{R_2} = \frac{R_0\,A_1^{1/3}}{R_0\,A_2^{1/3}} = \left(\frac{A_1}{A_2}\right)^{1/3} \)
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).”