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Atoms and Nuclei Part 3

Section: Physics

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Question : 12 of 98

Marks: +1, -0

A nucleus has mass number

\alpha

R_{\alpha}

. Another nucleus has mass number

\beta

R_{\beta}

\beta = 8 \alpha

\frac{R_{\alpha}}{R_{\beta}}

[28 Jan 2026 Shift 2]

1
2
8
0.5

Solution:

Concept:

Nuclear radius is proportional to the cube root of the mass number:

R \propto A^{1/3}

.

Explanation:

For a nucleus,

R = R_0 A^{1/3}

, where

R_0

is a constant.

Given two nuclei with mass numbers

\alpha

and

\beta

, and

\beta = 8\alpha

.

Then

R_\alpha = R_0 \alpha^{1/3}

and

R_\beta = R_0 \beta^{1/3}

.

Ratio:

\frac{R_\alpha}{R_\beta} = \left(\frac{\alpha}{\beta}\right)^{1/3} = \left(\frac{\alpha}{8\alpha}\right)^{1/3} = \left(\frac{1}{8}\right)^{1/3} = \frac{1}{2} = 0.5

.

Answer:

\frac{R_\alpha}{R_\beta} = 0.5

. Hence, the correct option is D.

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