State Bohr’s postulate for the ‘permitted orbits’ for electrons in a hydrogen atom. How this postulate was explained by de Broglie?

Question

Philoid · Accepted Answer

According to Bohr’s postulate, electrons can revolve around the nucleus only in certain ‘permitted orbits’ called ‘stable orbits’, without any dissipation of energy. The angular momentum of the electrons in these orbits is given by , where n = number of orbit, h = Planck’s constant.

From De Broglie’s formula, we know that wavelength … (i), where h = Planck’s constant, p = momentum, m = mass, v = velocity.

Now, De Broglie imagined the circumference of the orbit as a string of length nλ, where λ = wavelength of the emitted radiation. Hence, this can be written as : … (ii), from (i).

From this, we get , which is Bohr’s postulate. (proved)