Derive Bohr's quantisation condition for angular momentum of orbiting electron in hydrogen atom using De Broglie's hypothesis.

Explanation

For an electron revolving in `n^(th)` circular orbit of radius `r_(n)`
total distance covered = circumference of the orbit
`:.` For permissible orbit,
`2 pi r_(n) = n lamda`
`:' n -1`
`rArr 2pi r_(1) = lamda`
Also, accordint to de Broglie, `lamda = (h)/(mv_(n))`
where `v_(n) =` speed of electron in `n^(th)` orbit
`rArr 2pi r_(1) = (h)/(mv_(1))`
or `mv_(1) r_(1) = (h)/(2pi)`