A nucleus has mass number α and radius R_ α . Another nucleus has mass number β and radius R_ β . If β=8 α then R_ α / R_ β is:

Correct answer: B. 0.5 Nuclear radius follows R = R_0 A^ 1/3 where A is mass number. Given β = 8α , we have R_α = R_0 α^ 1/3 and R_β = R_0 (8α)^ 1/3 = R_0 · 2 α^ 1/3 = 2R_α . Thus R_α/R_β = 1/2 = 0.5 .

JEE Main 202628 JanuaryEvening Shift

Exam: JEE Main
Year: 2026
Date: 28 January
Shift: Evening Shift
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2026 · 28 January · Evening Shift · Physics · Nuclear Physics

A nucleus has mass number α and radius R_ α . Another nucleus has...

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:

Options

A8
B0.5
C2
D1

Correct answer

B. 0.5

Step-by-step solution

Nuclear radius follows

R = R_0 A^{1/3}

where

A

is mass number.
Given

\beta = 8\alpha

, we have

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

and

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

.
Thus

R_\alpha/R_\beta = 1/2 = 0.5

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