A nucleus has mass number and radius R. Another nucleus has mass number and radius R. If = 8, then R / R is:

A nucleus has mass number and radius R. Another nucleus has mass… — Solution | JEE Physics

MCQEasyJEE 2026Rutherford's Model of Atom

A nucleus has mass number $\alpha$ and radius $R_\alpha$ . Another nucleus has mass number $\beta$ and radius $R_\beta$ . If $\beta = 8\alpha$ , then $R_\alpha / R_\beta$ is:

A
$1$
B
$8$
C
$0.5$
D
$2$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: A nucleus has mass number $\alpha$ and radius $R_\alpha$ . Another nucleus has mass number $\beta$ and radius $R_\beta$ , with $\beta = 8\alpha$ .

Find: The ratio $R_\alpha / R_\beta$ .

Concept: The radius of a nucleus is related to its mass number $A$ by

R = R_0 A^{1/3}

Step 1: Write expressions for both radii

R_\alpha = R_0 \alpha^{1/3}, \quad R_\beta = R_0 \beta^{1/3}

Step 2: Use the given relation

\beta = 8\alpha

So,

R_\beta = R_0 (8\alpha)^{1/3} = 2R_0 \alpha^{1/3}

Step 3: Take the ratio

\frac{R_\alpha}{R_\beta} = \frac{R_0 \alpha^{1/3}}{2R_0 \alpha^{1/3}} = \frac{1}{2}

Therefore, $R_\alpha / R_\beta = 0.5$ and the correct option is C.

Common mistakes

Using a linear relation between radius and mass number. Nuclear radius varies as $A^{1/3}$ , not as $A$ . Use the cube-root dependence before comparing the two radii.
Inverting the ratio and calculating $R_\beta / R_\alpha$ instead of $R_\alpha / R_\beta$ . Read the asked ratio carefully before substituting values.
Substituting $\beta = 8\alpha$ but forgetting that $(8\alpha)^{1/3} = 2\alpha^{1/3}$ . Take the cube root of both the number and the variable correctly.

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Answer

Step-by-step solution

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