Question

The radius of germanium ( $Ge$ ) nuclide is measured to be twice the radius of ${ }_{4}^{9} Be$ . The number of nucleons in $Ge$ are

• A. $73$
• B. $74$
• C. $75$
• D. $72$

Answer 1

Answer: (D)

Let the radius of ${ }_{4}^{9} Be$ nucleus be $r$. Then, radius of germanium $(Ge)$ nucleus will be $2 r$.
Radius of nucleus is given by
$R=R_{0} A^{1 / 3}$
$\therefore \frac{R_{1}}{R_{2}}=\left(\frac{A_{1}}{A_{2}}\right)^{1 / 3}$
$\Rightarrow \frac{r}{2 r}=\left(\frac{9}{A_{2}}\right)^{1 / 3} \left(\because A_{1}=9\right) $
$\Rightarrow\left(\frac{1}{2}\right)^{3}=\frac{9}{A_{2}}$
Hence, $A_{2}=9 \times(2)^{3}=9 \times 8=72$
Thus, in germanium $(Ge)$ nucleus number of nucleons is $72 .$