A nucleus has mas nucleus has mass number

JEE MAIN 2024

31.01.24 S2

Question

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 $\frac{V_2}{V_1}=$

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Solution

Sol. For a nucleus $$ \begin{aligned} & \text { Volume: } \mathrm{V}=\frac{4}{3} \pi \mathrm{R}^3 \\ & \begin{array}{l} \mathrm{R}=\mathrm{R}_0(\mathrm{~A})^{1 / 3} \\ \mathrm{~V}=\frac{4}{3} \pi \mathrm{R}_0^3 \mathrm{~A} \\ \Rightarrow \frac{\mathrm{~V}_2}{\mathrm{~V}_1}=\frac{\mathrm{A}_2}{\mathrm{~A}_1}=4 \end{array} \end{aligned} $$

Question Tags

JEE Main

Physics

Easy

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