Two nuclei have mass numbers in the ratio 8 : 125 . The ratio of their nuclear radii is:

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Two nuclei have mass numbers in the ratio

8 : 125

. The ratio of their nuclear radii is:

PhysicsNuclear PhysicsJEE Main

Options:

A $5 : 3$
B $3 : 5$
C $5 : 2$
D $2 : 5$

Solution:

1024 Upvotes Verified Answer

The correct answer is:

2 : 5

Here ,

R = R_{0} A^{1 / 3}

Since,

R = R_{0} A^{1 / 3}

\begin{array}{l} ∴ \frac{R_{1}}{R_{2}} = \frac{A_{1}^{\frac{1}{3}}}{A_{2}^{\frac{1}{3}}} = {(\frac{A_{1}}{A_{2}})}^{\frac{1}{3}} \\ = {(\frac{8}{125})}^{\frac{1}{3}} \\ = \frac{2}{5} \end{array}

∴

The ratio of their radii =

2 : 5

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