De Broglie Waves and the Bohr Model

One way of understanding the assumptions of Bohr that the orbits of the hydrogen atom are stationary, quantized states is to treat the states as standing electron waves. A standing wave exist whenever the circumference of the orbit is exactly equal to an integer number of wavelengths.

A schematic representation of a standing wave for the n = 4 orbit is shown to the right.

The de Broglie requirement can be written

2$\pi$rn = n$\lambda$

where rn is the radius of the nth state, $\lambda$ = h/mv is the de Broglie wavelength, and n is an integer. We can then rewrite

2$\pi$rn = n $\cdot$ h / (mv)

or

m v rn = L = n

which is the Bohr condition. Thus the angular momentum L is indeed an integer multiple of , just as Bohr postulated.

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