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  4. Two nuclei have mass numbers in the ratio 27:125 . The ratio of their nuclear radii would be:

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Q. Two nuclei have mass numbers in the ratio $27:125$ . The ratio of their nuclear radii would be:

NTA AbhyasNTA Abhyas 2020Nuclei

Solution:

Here ,
$A_{1}:A_{2}=27:125 \\ \Rightarrow \frac{A_{1}}{A_{2}}=\frac{27}{125}$
Since, $R = R_{0} A^{1 / 3}$
$\therefore \frac{R_{1}}{R_{2}}=\frac{A_{1}^{1/3}}{A_{2}^{1/3}}=\left(\right. \frac{A_{1}}{A_{2}} \left.\right)^{1/3} \\ \, =\left(\right. \frac{27}{125} \left.\right)^{1/3} \\ \, =\frac{3}{5}$
$\therefore $ The ratio of their radii = 3 : 5