Question

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

Answer 1

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 $=\frac{2 \pi r \times m v}{h}$
$mvr =\frac{n h}{2 \pi}$
$mv =\frac{n h}{2 \pi r}$
No. of waves $=\frac{2 \pi r}{h} \times \frac{n h}{2 \pi r}= n$
For $3^{\text {rd }}$ orbit $n =3$.