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  4. The mass density of a nucleus varies with mass number A as

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Q. The mass density of a nucleus varies with mass number $A$ as

AIPMTAIPMT 1992Atoms

Solution:

The nuclear radius $r$ varies with mass number
A according to the relation
$r=r_{0} A^{1 / .3} \Rightarrow r \propto A^{1 / 3}$ or $A \propto r^{3}$
Now density $=\frac{\text { mass }}{\text { volume }}$
Further mass $\propto A$ and volume $\propto r^{3}$
$\therefore \frac{\text { mass }}{\text { volume }}=$ constant