Question

The radius of the nucleus is proportional to $\left(A\text{is the mass number}\right)$

• A. $A^{\frac{2}{3}}$
• B. $A^{\frac{1}{3}}$
• C. $A^3$
• D. $A$

Answer 1

The correct option is B $A^{\frac{1}{3}}$

Mass of the nucleus $m=m_{p}A$

Where, $m_p$ is the mass of the proton $(\text{we consider}{m}_p\approx m_n)$

We know that,

$Volume\times density=mass=m_{p}A$

$\Rightarrow \frac{4}{3}\pi R^3\times \rho =m_{p}A$

$\Rightarrow R^3\propto A$

$\Rightarrow R\propto A^{\frac{1}{3}}$

Hence, option $\left(B\right)$ is correct.