Question

Some statement regarding nucleus are given

$\text{(A) Volume is independent of}A$

$\text{(B) Volume is dependent on}{A}^{\frac{1}{3}}$

$\text{(C) Volume is dependent on}A$

$\text{(D) Density is dependent on}A$

$\text{(E) Density is independent of}A$

Here $A$ is atomic mass number, then choose correct option

Answer 1

If $r$ is the radius of an atom then,

$r=r_0{A}^{\frac{1}{3}}$

$\Rightarrow r^3\propto A$

Now,

$\text{Density}=\rho =\frac{M}{V}=\frac{A{m}_p}{A\times \frac{4}{3}\pi r_0^3}=\frac{m_p}{\frac{4}{3}\pi r_0^3}$

Hence, $\left(D\right)$ is the correct answer.