Question

A stationary nucleus disintegrates suddenly in two nuclei $X$ and $Y$ . The ratio of the kinetic energy of the two nuclei $X$ and $Y$ after the disintegration is $1:2$ , the ratio of the radii of the nuclei $X$ and $Y$ will be

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

Answer 1

Answer: (D)

$\frac{k_{x}}{k_{y}}=\frac{p_{x}^{2} / 2 m_{x}}{p_{y}^{2} / 2 m_{y}}=\frac{m_{y}}{m_{x}}=\frac{1}{2}$
$\frac{r_{x}}{r_{y}}=\left(\frac{A_{x}}{A_{y}}\right)^{1 / 3}=\left(\frac{m_{x}}{m_{y}}\right)^{1 / 3}=2^{1 / 3}$