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  4. Two nuclei have mass numbers in the ratio 1:8 . The ratio of their nuclear radii would be:

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Q. Two nuclei have mass numbers in the ratio $1:8$ . The ratio of their nuclear radii would be:

NTA AbhyasNTA Abhyas 2022

Solution:

$A_{1}:A_{2}=1:8 \\ \Rightarrow \frac{A_{1}}{A_{2}}=\frac{1}{8}$
Since ,
$R = R_{0} A^{1 / 3}$
$\therefore \frac{R_{1}}{R_{2}}=\frac{A_{1}^{1 / 3}}{A_{2}^{1 / 3}} \\ \Rightarrow \left(\right. \frac{A_{1}}{A_{2}} \left.\right)^{1 / 3}=\left(\right. \frac{1}{8} \left.\right)^{1 / 3} \\ \, =\frac{1}{2}$
The ratio of their radii = $1:2$ .