Question

The mass numbers of two nuclei A and B are 27 and 64 respectively. The ratio of their radii \( \left(\frac{r_A}{r_B}\right) \) will be:

• A. \( \frac{27}{64} \)
• B. \( \frac{9}{16} \)
• C. \( \frac{3\sqrt{3}}{8} \)
• D. \( \frac{3}{4} \)

Hint:

Nuclear radii follow \( R = R_0 A^{1/3} \), so use cube roots for radius ratio.

Answer 1

The Correct Option is D

\[R \propto A^{1/3} \Rightarrow \frac{R_A}{R_B} = \left(\frac{27}{64}\right)^{1/3} = \frac{3}{4}\]