Question

A radioactive nucleus with mass number A splits in to two nuclei whose mass numbers are in the ratio of $3:2$. The ratio of radii of the nuclei is

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

Answer 1

Answer: (B)

$3$${}^{1/3}$$:2$${}^{1/3}$

${}^{A}X{\to }^{\frac{3A}{5}}Y{+}^{\frac{2A}{5}}Z$

$R\propto A^{1/3}$

$\frac{R_Y}{R_Z}={\left(\frac{3}{2}\right)}^{1/3}$