Question

A nucleus X ${}^{235}$ splits into two nuclei having the mass numbers in the ratio $2:1.$ The ratio of the radii of those two nuclei is:

• A. $2:1$
• B. $1:2$
• C. $2^{1/3}:1$
• D. $1:2^{1/3}$

Answer 1

The correct option is C $2^{1/3}:1$

Ratio of the mass number is given as $\frac{A_2}{A_1}=\frac{2}{1}$

Radius of a nucleus $R=R_o{A}^{1/3}$

where $R_o=1.2$ fm

Thus we get the ratio of radii $\frac{R_2}{R_1}=(\frac{A_2}{A_1}{)}^{1/3}$

$⟹$ $\frac{R_2}{R_1}=\frac{2^{1/3}}{1}$