A nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $\mathrm{R}_{\beta}$. If $\beta=8 \alpha$ then $R_{\alpha} / R_{\beta}$ is :

JEE Main · 2026 · 28 Jan 2026 · Shift 2 · Modern Physics

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 :

(A)2
(B)8
(C)1
(D)0.5✓ Correct

Answer: (D)

Solution

The nuclear radius obeys

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

, so

\frac{R _{α}}{R _{β}} = (\frac{α}{β})^{1/3}

. With

β = 8 α

\frac{R _{α}}{R _{β}} = (\frac{α}{8 α})^{1/3} = (\frac{1}{8})^{1/3} = \frac{1}{2} = 0.5

JEE Main · 2026 · 28 Jan 2026 · Shift 2 · Single correct option

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