A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is [2022]

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Solution

Q.
A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is [2022]

1 1 : 1

2 4 : 5

3 5 : 4

4 25 : 16

Ans.
(3)

Nuclear radius, $R = R_{0} A^{1 / 3}$ ...(i)

where $R_{0}$ is a constant and $A$ is the mass number.

From eq. (i), $R \propto A^{1 / 3}$

$\frac{R_{1}}{R_{2}} = {(\frac{125}{64})}^{1 / 3}, \frac{R_{1}}{R_{2}} = \frac{5}{4}$

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