Q.Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the nucleus.

Step 1. Picture the electron's de Broglie wave, of wavelength $\lambda$, wrapped around a circular orbit of radius $r$. For the wave to reinforce itself consistently on every loop (rather than gradually falling out of phase with itself and cancelling out through destructive interference), the orbit's circumference must contain a WHOLE number of complete wavelengths - a "standing wave" condition:

Step 2. Substitute de Broglie's relation $\lambda=h/mv$ (eq. 2.9) into this condition:

Step 3. Rearrange to isolate $mvr$:

$mvr=\frac{nh}{2\pi}$ …

Start from the standing-wave closure condition (circumference = integer × wavelength) and subs …

• Starting from Bohr's formula and just restating it, rather than deriving it from the standing-wave condition as asked. …