Question

The ratio of the nuclear radius, of an atom with mass number $A$ and $_{2}^{4}He$ is $\left(14\right)^{\frac{1}{3}}$ . What is the value of $A$ ?

Answer 1

From the relation $r \propto A^{1 / 3}$ ,
we have, $\frac{r_{2}}{r_{1}}=\left(\frac{A_{2}}{A_{1}}\right)^{1 / 3}$
or $\left(\frac{A_{2}}{4}\right)^{1 / 3}=\left(14\right)^{1 / 3}$
Therefore, $A_{2}=56$