If r1 and r2 are the radii of the atomic nuclei of mass number 4 and 32, respectively, then the ratio \( \left(\displaystyle\frac{r_1}{r_2}\right) \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1:2
Nuclear matter has nearly constant density, so the volume of a nucleus is proportional to its mass number A, and the radius varies as the cube root of A:
\( \displaystyle R = R_0 A^{1/3} \)
\( \displaystyle \frac{r_1}{r_2} = \left(\frac{4}{32}\right)^{1/3} = \left(\frac{1}{8}\right)^{1/3} = \frac{1}{2} \)