The stable nucleus that has a radius $1 / 3$ that $O s^{189}$ is

_{3} {L i}^{7}

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_{2} {H e}^{4}

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_{5} B^{10}

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_{6} C^{12}

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Solution

The correct option is A $_{3} {L i}^{7}$
We know that radius $R = 1.2 \times 10^{- 15} A^{1 / 3} m$ , where $A$ is mass number which is $189$ for Os, suppose it is $A_{1}$ for stable nuclei then
$\frac{R_{0}}{R_{1}} = (\frac{189}{A_{1}})^{1 / 3}$
Given that $R_{1} = R_{0} / 3$ so we get $3^{3} = \frac{189}{A_{1}}$
So $A_{1} = \frac{189}{27} = 7$
Option A is correct.

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