Question

Which energy state of the triply ionized beryllium $\left( Be ^{+++}\right)$ has the same electron orbital radius as that of the ground state of hydrogen? Given $Z$ for beryllium $=4$.

Answer 1

As $r_{n} \propto \frac{n^{2}}{Z}$ we use
$\Rightarrow \frac{n_{ Be }^{2}}{Z_{ Be }}=\frac{n_{ H }^{2}}{Z_{ Be }}$
$ \Rightarrow n_{ Be }^{2}=\frac{(1)^{2}}{1} \times 4 $
$\Rightarrow n_{ Be }=2$