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If the radius of a nucleus with a mass number 7 is 2 fermi then the radius of the nucleus with mass number 189 is

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27 fm

25 fm

6 fm

3 fm

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{R_{2}}{R_{1}} = \frac{{(A_{2})}^{1 / 3}}{{(A_{1})}^{1 / 3}} = {(\frac{189}{7})}^{1 / 3} \\ \Rightarrow \frac{R_{2}}{2} = (27)^{1 / 3} = 3 \Rightarrow R_{2} = 6 fm \end{array}$

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