A nucleus has mass number A₁ and volume V₁ . Another nucleus has mass number A₂ and volume V?

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13.Nuclei

hard

A nucleus has mass number $A_1$ and volume $V_1$.

Another nucleus has mass number $A_2$ and volume $V_2$. If relation between mass number is $A_2=4 A_1$, then $\frac{V_2}{V_1}=$_____.

A

$3$

B

$4$

C

$5$

D

$6$

(JEE MAIN-2024)

Solution

For a nucleus

Volume: $\mathrm{V}=\frac{4}{3} \pi \mathrm{R}^3$

$\mathrm{R}=\mathrm{R}_0(\mathrm{~A})^{1 / 3}$

$\mathrm{~V}=\frac{4}{3} \pi \mathrm{R}_0^3 \mathrm{~A}$

$\Rightarrow \frac{V_2}{V_1}=\frac{A_2}{A_1}=4$

Standard 12

Physics

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