Time taken for an electron to complete one revolution in the Bohr orbit of hydrogen atom is      

velocity of electron = V cm/s, Circumference = 2πr

Distance travelled in one second = V cm

v cm ... 1sec

2πr cm ... ?

Time taken for one revolution =$\frac{2\mathrm{\pi r}}{\mathrm{v}}$

                                             $\mathrm{r}=\frac{{\mathrm{n}}^2}{\mathrm{z}}{\mathrm{r}}_0$

We know  $\mathrm{v}=\frac{\mathrm{z}}{\mathrm{n}}{\mathrm{v}}_1$

Time taken for one revolution =$\frac{2\mathrm{\pi }\left(\frac{{\mathrm{n}}^2}{\mathrm{z}}{\mathrm{r}}_0\right)}{\left(\frac{\mathrm{z}}{\mathrm{n}}{\mathrm{v}}_1\right)}$

                                             $=\frac{{\mathrm{n}}^3}{{\mathrm{z}}^2}\frac{2{\mathrm{\pi r}}_{\mathrm{o}}}{{\mathrm{v}}_1}$

       n=1; z=1                             

Time taken for one revolution    $=\frac{2{\mathrm{\pi r}}_{\mathrm{o}}}{{\mathrm{V}}_1}$   

                                                   $=\frac{2\mathrm{\pi r}}{\frac{\mathrm{nh}}{2\mathrm{\pi mr}}}$

                                                  $=\frac{4{\mathrm{\pi }}^2{\mathrm{mr}}^2}{\mathrm{nh}}$