Simulation · Physics · Class 12
De Broglie's wave round an orbit
From the lesson De Broglie's explanation in Atoms. Change the values and watch what happens.
De Broglie's wave round an orbitPhysics · Class 12
The idea behind it
NCERT §12.6
- 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.