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Question

If the radii of $_{13}^{27} A l$ and $_{30}^{64} Z n$ nucleus are $R_{1}$ & $R_{2}$ respectively, then $\frac{R_{1}}{R_{2}} =$ ____________.

A

\frac{27}{64}

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B

\frac{3}{4}

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C

\frac{9}{16}

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D

\frac{13}{30}

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Solution

The correct option is B $\frac{3}{4}$
The relation between the Atomic weighr (A) and nucleu radius(R) is given by $R = R_{0} A^{\frac{1}{3}}$
Here, $R_{1} = R_{0} A_{1}^{\frac{1}{3}}$
$\Rightarrow$ $R_{1} = 3 R_{0}$ $(∵ A_{1} = 27)$ ... $e q .1$
Using this relation again,
$R_{2} = R_{0} A_{2}^{\frac{1}{3}}$
$\Rightarrow$ $R_{2} = 4 R_{0}$ $(∵ A_{2} = 64)$ ... $e q .1$
Now,on dividing both equation, we get
$\frac{R_{1}}{R_{2}} = \frac{3}{4}$
Therefore option B is correct.

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