Lesson 10 of 12 · 7 min
De Broglie's explanation
NCERT §12.6
Bohr's rule L = nh/2π works, but Zoya asks the obvious question: why only whole multiples of h/2π? The answer came ten years later, from treating the electron as a wave.
The lesson in notes
In short
Bohr's second postulate, L = nh/2π, is the most puzzling one: why only whole multiples of h/2π? Louis de Broglie explained it in 1923, ten years after Bohr's model.
De Broglie treated the orbiting electron as a particle wave (λ = h/p). Davisson and Germer confirmed the wave nature of electrons experimentally in 1927.
On a plucked string only wavelengths with nodes at the ends survive, as standing waves; the others interfere with themselves on reflection and die away. In the same way, only an electron wave that fits the orbit exactly can persist.
The condition is that the circumference holds a whole number of wavelengths: 2πrn = nλ, n = 1, 2, 3 … (Eq. 12.12). Fig. 12.8 shows four wavelengths fitted round the orbit (n = 4).
For speeds much less than c, λ = h/mvn, so 2πrn = nh/mvn, which rearranges to mvnrn = nh/2π: exactly Bohr's quantum condition.
So the quantised orbits and energy levels come from the wave nature of the electron: only resonant standing waves survive.