Circular Waves and the Bohr Model
Now, if the wave has to fit into a circular "orbit" of radius r, the
circumference of that circle must be exactly as long as a whole number of
wavelengths:
where n is a positive integer. Plugging in the wavelength from
equation (1), we get
or
But we know that for a circular orbit,
Thus, if we assume the electron is a wave with its wavelength given by de
Broglie's formula, then we automatically get Bohr's constraint on its angular
momentum:
The integer n, as we've noted earlier, corresponds to the energy level;
thus, for example, an electron in the third energy level would have three
wavelengths around its orbit, and so on.

