Find out the number of waves made by a Bohr electron in one complete revolution in its 3rd orbit.

${\text{r}}_{\text{n}}{\text{ for H= r}}_{\text{n}}{\text{×n}}^{\text{2}}$

 $\begin{array}{l}{\text{r}}_{\text{3}}{\text{ for H= 0.529×9×10}}^{-8}\text{cm}\\ {\text{=0.529×9×10}}^{-10}\text{m(}\because {\text{r}}_1=0.529{\text{A}}^0)\\ {\text{Also u}}_{\text{n}}\text{=Z}\frac{{\text{u}}_{\text{1}}}{\text{n}}\\ \therefore u_3=\frac{2.19\times {10}^8}{3}\text{cm }{\sec }^{-1}\frac{2.19\times {10}^6}{3}m{\sec }^{-1}\\ (\because u_1=2.19\times {10}^8{\text{cm sec}}^{\text{-1}})\\ \therefore \text{No. of waves in one round =}\frac{{\text{2πr}}_{\text{3}}}{\text{λ}}=\frac{{\text{2πr}}_{\text{3}}}{{\text{h/mu}}_3}=\frac{{\text{2πr}}_{\text{3}}{\text{×u}}_{\text{3}}\text{×m}}{\text{h}}\\ \frac{2\times 22\times 0.529\times 9\times {10}^{-10}\times 2.19\times {10}^6\times 9.108\times {10}^{-31}}{7\times 3\times 6.62\times {10}^{-34}}=3\end{array}$