The ratio of the radii of two Bohr's orbit of ${\mathrm{H}}^{-}$atom: is 4 : 1. What would be their nomenclature ?

we now that

Radii of Bohr's orbit $=0.529\times \frac{(n{)}^2}{2}$

For ${\mathrm{H}}^{-}$ atom $\mathrm{z}=1$

$\mathrm{r}=0.529\times (n{)}^2$

For K- shell  n=1,  $r=0.529\times (1{)}^2=0.529$.

 L- shell  n=2 ,  $$\begin{gathered} \mathrm{r}=0.529\times (2{)}^2 \\ =0.529\times 4 \end{gathered}$$

 M- shell  n=3, $\mathrm{r}=0.529\times (3{)}^2=0.529\times 9$

N- shell  n=4,  $\mathrm{r}=0.529\times (4{)}^2=0.529\times 16$

$\frac{L}{K}=\frac{0.529\times 4}{0.529}=\frac{4}{1}$

$\frac{N}{L}=\frac{0.529\times 16}{0.529\times 4}=\frac{4}{1}$