The ratio of radii of the nuclei with the mass numbers given as 2, 16, 54 and 128, respectively, will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 1 : 2 : 3 : 4 \)
The radius of a nucleus grows as the cube root of its mass number.
\( \displaystyle R = R_0\,A^{1/3} \;\Rightarrow\; R \propto A^{1/3} \)
Each mass number is 2 times a perfect cube:
\( 2 = 2 \times 1 \)
\( 16 = 2 \times 8 \)
\( 54 = 2 \times 27 \)
\( 128 = 2 \times 64 \)
The common factor \( 2^{1/3} \) cancels in the ratio.
\( \displaystyle R_1 : R_2 : R_3 : R_4 = 1^{1/3} : 8^{1/3} : 27^{1/3} : 64^{1/3} = 1 : 2 : 3 : 4 \)
Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
