Question

prove angular momentum equals to nh/2π

Answer 1

In H-atom the electron moves in orbits(not technically correct but we will use this for sake of this argument, as Bohr did) this electron has De Broglie wavelength : λ=h/mv

Only those electrons will be in orbit whose wavelength is : λ=2πr (r=radius of orbit) or an integral multiple of this ie. n.λ. This is because electron exists in particular orbits according to Bohr model.

So, n.λ=2πr

=> n.(h/mv)=2πr

=> mvr=nh/2π

Angular momentum of electron in H atom is quantised(it can have only particular values).