Question

Find out the number of waves made by a Bohr electron in one complete revolution in its $3^{rd}$ orbit?

Answer 1

Answer: 3

Number of waves in an orbit $=$ circumference of orbit per unit wavelength
$\frac{2\pi r}{\lambda }$
$\lambda =\frac{h}{mv}$ [by de-Broglie's equation]
No. of waves $=\frac{2\pi r\times mv}{h}$
$mvr=\frac{nh}{2\pi }$
$mv=\frac{nh}{2\pi r}$
No. of waves $=\frac{2\pi r}{h}\times \frac{nh}{2\pi r}=n$
For $3^{\text{rd }}$ orbit $n=3$.