Find the number of waves made by a Bohr electron in one complete revolution in the $3^{r d}$ orbit.

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Solution

Velocity of the electron in $3^{r d} o r b i t = \frac{3 h}{2 π m r}$
where, $m =$ mass of electron and $r =$ radius of $3^{r d}$ orbit.
Applying de Broglie equation,
$λ = \frac{h}{m v} = \frac{h}{m} \times \frac{2 π m r}{3 h} = \frac{2 π r}{3}$
$Number of waves = \frac{2 π r}{λ} = \frac{2 π r}{2 π r} \times 3 = 3$

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