Question

Show mathematically how Bohr’s postulate of quantization of orbital angular momentum in the hydrogen atom is explained by de Broglie's hypothesis.

Answer 1

According to de Broglie's hypothesis
$\lambda =\frac{h}{mv}$
According to de Broglie’s condition of stationary orbits, the stationary orbits are those which contain complete de Broglie wavelength.
$2\pi r=n\lambda$

Substituting the value of $\lambda$ from (ii) in (i), we get
$2\pi r=n\frac{h}{mv}$
$\Rightarrow mvr=n\frac{h}{2\pi }$
This is Bohr's postulate of quantization of energy levels.