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MHT CET 202624 AprilMorning Shift

Exam: MHT CET
Year: 2026
Date: 24 April
Shift: Morning Shift
Subject: Physics
Chapter: Nuclear Physics

MHT CET 2026 · 24 April · Morning Shift · Physics · Nuclear Physics

Two spherical nuclei have mass numbers 216 and 64 with their radii...

Two spherical nuclei have mass numbers 216 and 64 with their radii

R_1

and

R_2

respectively. The ratio

\dfrac{R_1}{R_2}

is

Options

A $1:2$
B $1:3$
C $2:3$
D $3:2$

Correct answer

D. $3:2$

Step-by-step solution

The radius of a nucleus is related to its mass number

A

by the empirical formula:

R = R_0 A^{1/3}

For the first nucleus with mass number

A_1 = 216

:

R_1 = R_0 (216)^{1/3} = 6 R_0

For the second nucleus with mass number

A_2 = 64

:

R_2 = R_0 (64)^{1/3} = 4 R_0

The ratio of their radii is:

\dfrac{R_1}{R_2} = \dfrac{6 R_0}{4 R_0} = \dfrac{3}{2}

Thus, the ratio is

3:2

.

Answer:

3:2

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