The ratio of the nuclear radii of elements with mass numbers $216$ and $125$ is

216 : 125

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216^{1 / 3} : 125^{1 / 3}

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36 : 25

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None of these

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Solution

The correct option is D $216^{1 / 3} : 125^{1 / 3}$
Nuclear radius of element $R = R_{o} A^{1 / 3}$
where $R_{o} = 1.2 f m$
$⟹$ $\frac{R_{1}}{R_{2}} = \frac{A_{1}^{1 / 3}}{A_{2}^{1 / 3}}$
Given : $A_{1} = 216$ and $A_{2} = 125$
$⟹$ $\frac{R_{1}}{R_{2}} = \frac{(216)^{1 / 3}}{(125)^{1 / 3}}$
We get $\frac{R_{1}}{R_{2}} = \frac{6}{5}$

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