# Obtain Bohr’s quantisation condition for angular momentum of electron orbiting in nth orbit in hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.

Let $\lambda$ be the wavelength associated with the electrons orbiting in the nth orbit. and the electrons have speed 'V' and the orbit of radius be (r) in the hydrogen atom.

We know

$\lambda=\frac{h}{mv}$

Where, $\lambda$ is de-broglie wavelength

$h$ is Plank's constant

$mv$ is the momentum of the electrons revolving

and also.

$2\pi r=n\lambda$

On putting the value of $\lambda$ , we get

$2\pi r=\frac{nh}{mV}$

Hence, the angular momentum of the electron orbiting in 'the orbit in the hydrogen atom, will be-

$L=mvr=\frac{nh}{2\pi }$

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