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.
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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