First slide

Size of nucleus

Question

A nucleus disintegrates into two nuclear parts which have their velocities in ratio 2 : 1. The ratio of their nuclear sizes will be

Moderate

A

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

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

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

$1 : 2^{1 / 3}$

Solution

According to law of conservation of momentum, we get
$m_{1} v_{1} = m_{2} v_{2} or (m_{1} / m_{2}) = (v_{2} / v_{1}) But m = \frac{4}{3} {πr}^{3} ρ or m \propto r^{3} ∴ \frac{m_{1}}{m_{2}} = \frac{r_{1}^{3}}{r_{2}^{3}} Therefore, \frac{{r_{1}}^{3}}{{r_{2}}^{3}} = \frac{V_{2}}{V_{1}} = (\frac{1}{2}) or \frac{r_{1}}{r_{2}} = {(\frac{1}{2})}^{1 / 3} r_{1} : r_{2} = 1 : (2)^{1 / 3}$

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