Question

If $V$ is the volume of a nucleus, $A$ is its mass number and $\rho$ its density, then which of the following is a constant:

• A. $AV$
• B. $\rho V$
• C. $\frac{V^3}{A^2}$
• D. $\frac{V}{A}$

Answer 1

The correct option is D $\frac{V}{A}$

The expression for radius of the nucleus is given by,

$R=R_0{\left(A\right)}^{\frac{1}{3}}$

$\Rightarrow V=\frac{4}{3}\pi R^3$

$\Rightarrow V\propto R^3\Rightarrow V\propto A....\left(1\right)$

$\Rightarrow \frac{V}{A}=\text{constant}$

Using equation $\left(1\right)$,

$AV\propto A^2$

$\frac{V^3}{A^2}\propto A$

Also, as $\rho$ is independent of $A$ and is a constant.

$\rho V\propto A$
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Hence, option $\left(D\right)$ is correct.