Show mathematically how Bohr's postulate of quantization of orbit… - Vidyadip

Question

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

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Answer

de Broglie wavelength, $\lambda = \frac{\text{h}}{\text{mv}}$
For electron moving in the n^th orbit, $2 \pi\text{r} = \text{n}\lambda$
$\therefore2\pi\text{r} = \frac{\text{nh}}{\text{mv}}$
$\therefore\text{mvr} = \frac{\text{nh}}{2\pi} = \text{L}$ (orbital angular momentum)
This is Bohr’s Postulate of quantization of orbital angular momentum.

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