Two spherical nuclei have mass numbers 216 and 64 with their radii R₁ and R ₂ respectively. rati

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13.Nuclei

easy

Two spherical nuclei have mass numbers $216$ and $64$ with their radii $R_1$ and $R _2$ respectively. The ratio, $\frac{R_1}{R_2}$ is equal to

A

$3:2$

B

$1:3$

C

$1:2$

D

$2:3$

(AIIMS-2015)

Solution

(a)

The relation between radius $(R)$ of nuclei and mass number $(A)$ is given by $R=$ $R_0 A^{1 / 3}$ where $R_0=$ empirical constant.

Thus, $\frac{R_1}{R_2}=\frac{A_1^{1 / 3}}{A_2^{1 / 3}}=\frac{(216)^{1 / 3}}{(64)^{1 / 3}}=6 / 4=3 / 2$

Standard 12

Physics

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