Using de-Broglie's hypothesis, explain Bohr's second postulate of quantisation of energy levels in a hydrogen atom.

Explanation

de-Broglie argued that the electron in its circular orbit must be seen as an electron wave. In terms of electron wave, he said that only those stationary Bohr orbits are possible in which total distance (i.e., the circumference of the orbit) contains a definite number of these electron waves, Mathematically,
total path length of orbit `n = (lambda_("electron wave"))`
`therefore " " 2pi r_(n) = n lambda`
where is an integer and may have values 1, 2, 3, 4,. .. etc.
From de-Broglie concept of matter waves, we know that wavelength of electron waves may be expressed as.
`lambda = (h)/(p_(n)) = (h)/(m v_(n))`
. where mass of electron and v. velocity of electron in state corresponding to it. Substituting the value of in de-Broglie.s quantum condition, we get
`2 pi r_(n) = n . (h)/(m v_(n)) rArr m v_(n) r_(n) = (h)/(2 pi)`
Which Bohr.s quantum condition on the second postulate for quantisation of angle momentum.