The energy diagram for a Hydrogen like atom is shown in the figure. 

The radius of its first Bohr orbit is?

For the Hydrogen like atoms 

$\begin{array}{l}{\mathrm{E}}_{\mathrm{n}}=-13.6\frac{{\mathrm{Z}}^2}{{\mathrm{n}}^2}\mathrm{eV}\\ \mathrm{From}\mathrm{the}\mathrm{given}\mathrm{diagram}\\ -54.4=-13.6\frac{{\mathrm{Z}}^2}{1^2}\\ \Rightarrow \mathrm{Z}=2\\ \mathrm{Now} {\mathrm{r}}_1=0.53\frac{{\mathrm{n}}^2}{\mathrm{z}}=\frac{0.53}{2}=0.265\stackrel{0}{ \mathrm{A}}\end{array}$