Obtains Bohr's quantisation condition for angular momentum of electron orbiting in $$n^{th}$$ hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.
According to De-brogile's wavelength associated with an electron ;
$$\lambda =\dfrac{h}{mv}$$......1
and the standing wave condition that circumference $$=$$ whole Number of wave length If 'n' is the nth orbit
$$\therefore 2\pi r=n\lambda n$$....2
$$\therefore $$ since angular momentum
$$L=mvr$$ from eqn (1)
$$L=\dfrac{hr}{\lambda}$$
$$=\dfrac{hr}{\left(\dfrac{2\pi r}{n}\right)}$$ from 1 and 2
$$\therefore L=\dfrac{nh}{2\pi}$$ Bohr's Quantization condition