First slide

Size of nucleus

Question

A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8 : 1. The ratio of radii of the fragments is

Moderate

A

1 : 2
B

1 : 4
C

4 : 1
D

2 : 1

Solution

By conservation of momentum $m_{1} v_{1} = m_{2} v_{2}$
$\Rightarrow \frac{v_{1}}{v_{2}} = \frac{8}{1} = \frac{m_{2}}{m_{1}} . . . . . . . . (i)$
$Also from r \propto A^{1 / 3} \Rightarrow \frac{r_{1}}{r_{2}} = {(\frac{A_{1}}{A_{2}})}^{1 / 3} = {(\frac{1}{8})}^{1 / 3} = \frac{1}{2} .$

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