Q65 / 75 · JEE Main 2026 (28 January Shift 2) · Physics
A nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $R_{\beta}$. If $\beta=8 \alpha$ then $R_{\alpha} / R_{\beta}$ is:
- A8
- Correct answerB0.5
- C2
- D1
Solution
Nuclear radius follows $R = R_0 A^{1/3}$ where $A$ is mass number.
Given $\beta = 8\alpha$, we have $R_\alpha = R_0 \alpha^{1/3}$ and $R_\beta = R_0 (8\alpha)^{1/3} = R_0 \cdot 2 \alpha^{1/3} = 2R_\alpha$.
Thus $R_\alpha/R_\beta = 1/2 = 0.5$.
Given $\beta = 8\alpha$, we have $R_\alpha = R_0 \alpha^{1/3}$ and $R_\beta = R_0 (8\alpha)^{1/3} = R_0 \cdot 2 \alpha^{1/3} = 2R_\alpha$.
Thus $R_\alpha/R_\beta = 1/2 = 0.5$.
Hence, the correct answer is option: 'B'.