As the electron travels round in one of its Bohr's circular orbits, the associated matter waves propogate along the circumference. A stationary wave pattern can form along the circumference if only an integral number of wavelengths fit into the orbit, otherwise the wave would be out of phase with itself after one orbit and after a large number of orbits, all possible phaseswould be obtained and wave would be annihilated by destructive interference.

Thus, the condition for formation of standing wave in an orbit is,
2 (pi) r = n (lamda), (where n= 1,2,3..............) .............(1)
But according to concept of matter waves,
(lamda) = h / (mv)
Putting this value of (lamda) in equation (1), we get
2 (pi) r = (n h) / (m v)

So, m v r = (n h) / [2 (pi)]

i.e. the angular momentum of electrons in Bohr's circular orbits is quantized.

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By :-   Dr. A. W. Pangantiwar