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Question
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.
For an electron revolving in nth circular orbit of radius rn,
Total distance covered by electron = Circumference of the orbit = 2πrn
For the permissible orbit, we have
2πrn=nλ, where λ is the wavelength.
According to de-Broglie, wavelength of matter waves is given by
λ=h/mvn
where
h=Planck's constant
m=mass of electron
vn=speed of electron in nth orbit
∴2πrn=nh/mvn
⇒mvnrn=nh/2π
This is Bohr's second postulate of quantisation of orbital angular momentum.
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