Question

Give de-Broglie’s explanation of quantisation of angular momentum as proposed by Bohr. 

Answer 1

The condition for stationary wave formation is that the total distance travelled between the nodes(two) up and down or given path is integral multiple of ‘λ’ 

i.e ., 2πr_n = nλ where, n = 1,2,3,……. 

But λ = h/mv (from de-Broglie’s hypothesis) 

2πr_n = nh/mv_n 

mv_nr_n = n (h/2π) 

i.e. integral multiple of (h/2π) should be equal to the angular momentum of electron in the orbit.