Nuclei - Result Question 12
12. The stable nucleus that has a radius half that of $Fe^{56}$ is
(a) $Li^{7}$
(b) $Na^{21}$
(c) $S^{16}$
(d) $Ca^{40}$
[1997]
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Answer:
Correct Answer: 12. (a)
Solution:
- (a) The nuclear radius $R=R_0 A^{1 / 3}$
or $R \propto A^{1 / 3}$
$ \begin{aligned} & \text{ or, } R^{3} \propto A \Rightarrow A \propto R^{3} \\ & \therefore \frac{A_2}{A_1}=(\frac{R_2}{R_1})^{3}=(\frac{R_1 / 2}{R_1})^{3}=\frac{1}{8} \\ & A_2=\frac{A_1}{8}=\frac{56}{8}=7 \end{aligned} $
