Which state of triply ionised Beryllium (Be⁺⁺⁺) has the same orbital radius as that of the ground state of hydrogen ?

H                             Be⁺³

${\mathrm{r}}_1=0.529\mathrm{X}\frac{{\mathrm{n}}^2}{\mathrm{Z}}$ ${\mathrm{r}}_2=0.529\mathrm{X}\frac{{\mathrm{n}}^2}{\mathrm{Z}}$

n=1, Z=1                 n=?, Z=4

${\mathrm{r}}_1=0.529\mathrm{X}\frac{1^2}{2}$${\mathrm{r}}_2=0.529\mathrm{X}\frac{{\mathrm{n}}^2}{4}$

                               r₁=r₂

$0.529=0.529\mathrm{X}\frac{{\mathrm{n}}^2}{4}$

${\mathrm{n}}^2=4\Rightarrow \mathrm{n}=2$