When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
`vecv=109677[(1)/(n_(i)^(2))-(1)/(n_(f)^(2))]`
What points of Bohr's model of an atom can be used to arrive at this formula? Based on these points derive the above formula giving description of each step and each term.

Explanation

The following two points of Bohr.s model can be used to derive the given formula :
(i) Electrons revolve around the nucleus in definite energy levels called orbits.
(ii) Energy is emitted or absorbed only when electron jumps from one orbit to another.
Derivation
(i) According to Bohr, energy of an electron in the `n^(th)` level is given as
`E_n = - (2 pi^2 m e^4)/(n^2 h^2)`
where m = mass of electron, e = charge of electron, h = Planck.s constant.
(ii) When electron jumps from outer orbit `(n_2)` to inner orbit `(n_1)`, then difference in energy `(Delta E)` is emitted as :
`Delta E = E_2 - E_1`
`= -(2 pi^2 m e^4)/(n_2^2 h^2) - (- (2pi^2 me^4)/(n_1^2 h^2))`
`= (2 pi^2 m e^4)/(h^2) (1/(n_1^2) -1/(n_2^2))`
Now, `Delta E = hv = h c/lambda = h c barv`
or `" " barv = (Delta E)/(hc) = (2 pi^2 m e^2)/(ch^3) (1/(n_1^2) - 1/(n_2^2))`
Substituting the values of `c, h, pi, m, e` in CGS units,
we get
`barv = 109677 cm^(-1)(1/(n_1^2) - 1/(n_2^2))`.