Question

If the ratio of radii of nuclei $\underset{13}{27}Al$ and $\underset{52}{A}X$ is 3 : 5, then the number of neutrons in the nuclei of X will be:

• A. 13
• B. 52
• C. 100
• D. 73

Answer 1

Answer: (D)

73

By using the relation,
$r\propto A^{1/3}$
$\frac{r_1}{r_2}=(\frac{A_1}{A_2}{)}^{1/3}$
$\frac{3}{5}=(\frac{27}{A}{)}^{1/3}$
$\frac{27}{125}=\frac{27}{A}\Rightarrow A=125$
So, number of neutrons in the nuclei
$N=A-52=125-52=73$