Question

Two nuclei have mass numbers in the ratio $8:125$ . The ratio of their nuclear radii is:

• A. $5:3$
• B. $3:5$
• C. $5:2$
• D. $2:5$

Answer 1

Answer: (D)

Here ,
$R=R_0{A}^{1/3}$
Since, $R=R_0{A}^{1/3}$
$$\begin{gathered} \therefore \frac{R_1}{R_2}=\frac{A_1^{1/3}}{A_2^{1/3}}=(\frac{A_1}{A_2}{)}^{1/3} \\ =(\frac{8}{125}{)}^{1/3} \\ =\frac{2}{5} \end{gathered}$$
$\therefore$ The ratio of their radii = $2:5$