How does one explain, using de Broglie hypothesis, Bohr's second postulate of quantization of orbital angular momentum?

Solution

According to de-Broglie hypothesis, a stationary orbit is the one that contains an integral number of de-Broglie waves associated with the revolving electron.

Total distance covered by electron = Circumference of the orbit =

For the permissible orbit,
$2 pi r subscript n italic space italic equals italic space n italic space lambda$ ... (1)

Now, according to De-Broglie wavelength,

$lambda equals fraction numerator h over denominator m v end fraction$

Now, putting this in equation (1), we have

$2 pi r subscript n$ = $nh over mv$
$rightwards double arrow$ mv_n r_n = $fraction numerator nh over denominator 2 straight pi end fraction$ ; which is the required Bohr’s second postulate of quantization of orbital angular momentum.

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Wave Optics

How does one explain, using de Broglie hypothesis, Bohr's second postulate of quantization of orbital angular momentum?

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