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 $2r$.
Radius of nucleus is given by
$R=R_0{A}^{1/3}$
$\therefore \frac{R_1}{R_2}={\left(\frac{A_1}{A_2}\right)}^{1/3}$
$\Rightarrow \frac{r}{2r}={\left(\frac{9}{A_2}\right)}^{1/3}\left(\because A_1=9\right)$
$\Rightarrow {\left(\frac{1}{2}\right)}^3=\frac{9}{A_2}$
Hence, $A_2=9\times (2{)}^3=9\times 8=72$
Thus, in germanium $(Ge)$ nucleus number of nucleons is $72.$