Bohr-de Broglie Standing Waves
Bohr's allowed orbits look arbitrary until you treat the electron as a wave. This simulation wraps a de Broglie wave around each orbit, showing that only orbits fitting a whole number of wavelengths survive.
How to use this simulation
- Select the quantum number n
- Adjust the orbit radius to non-allowed values
- Display the wave wrapped around the orbit
What to look for
- Allowed orbits close the wave neatly onto itself
- Non-integer orbits leave a mismatch where the wave destroys itself
- Higher n fits more wavelengths around a larger circumference
The physics behind it
An electron has wavelength λ = h/mv. For the orbiting wave to reinforce itself rather than cancel, the circumference must hold a whole number of wavelengths: 2πr = nλ. Substituting the de Broglie relation gives Bohr's quantisation condition mvr = nh/2π, so the allowed orbits follow from wave interference rather than being postulated.