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Question
When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula
`bar(v) = 109677 1/n_1^2 - 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.
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Solution
The points of the Bohr’s model that can be considered are as follows:-
(i) Electrons revolve around the nucleus in a fixed orbit with fixed energy
(ii) The energy is absorbed or released when the electron moves from one energy level to another.
The energy for the nth stationary state is given by
`E_n = (- 2pi^2 me^4)/(n^2h^2)`
Where m = mass of the electron
e = charge of the electron
h = Planck’s constant
If an electron jumps from ni to nf then we have
ΔE = Ef – Ei = `(2pi^2 me^4)/(h^2) [(1/n_i^2) - (1/n_f^2)]`
`bar(v) = (ΔE)/(hc) = 109677 [(1/n_i^2) - (1/n_f^2)]`
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