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

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) 22 / 3 (C) (1/21 / 3) (D) 21 / 3

Tardigrade Admin · Accepted Answer

(kx/ky)=(px2 / 2 mx/py2 / 2 my)=(my/mx)=(1/2) (rx/ry)=((Ax/Ay))1 / 3=((mx/my))1 / 3=21 / 3

Q. 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

$2$

$2^{2/3}$

$\frac{1}{2 ^{1/3}}$

$2^{1/3}$

$\frac{k _{x}}{k _{y}} = \frac{p _{x}^{2} /2 m _{x}}{p _{y}^{2} /2 m _{y}} = \frac{m _{y}}{m _{x}} = \frac{1}{2}$
$\frac{r _{x}}{r _{y}} = (\frac{A _{x}}{A _{y}})^{1/3} = (\frac{m _{x}}{m _{y}})^{1/3} = 2^{1/3}$

Q. 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

2

22/3

21/31​

21/3

ky​kx​​=py2​/2my​px2​/2mx​​=mx​my​​=21​ ry​rx​​=(Ay​Ax​​)1/3=(my​mx​​)1/3=21/3

Q. 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

$2$

$2^{2/3}$

$\frac{1}{2 ^{1/3}}$

$2^{1/3}$

$\frac{k _{x}}{k _{y}} = \frac{p _{x}^{2} /2 m _{x}}{p _{y}^{2} /2 m _{y}} = \frac{m _{y}}{m _{x}} = \frac{1}{2}$
$\frac{r _{x}}{r _{y}} = (\frac{A _{x}}{A _{y}})^{1/3} = (\frac{m _{x}}{m _{y}})^{1/3} = 2^{1/3}$