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Question

In Bohr's atom, energy is absorbed or radiated when an electron makes a transition between two stationary states. If f is the frequency of emitted radiation and E1 and E2 are the energies of electron in two states, then practically which is correct for a hydrogen like atom for the transition as shown in the figure.

A
hf=|E1E2|
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B
hf<|E1E2|
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C
hf>|E1E2|
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D
|E1E2|hf|E1+E2|
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Solution

The correct option is B hf<|E1E2|
When an atom that is in excited state E emits a photon of energy hf, the photon also carries a momentum P=hfc=hλ. Conservation of momentum requires that atom must recoil with a momentum p and so, will have a kinetic energy P22m where, m= mass of atom.
So, conservation of energy gives.
ΔE=EE
=hf+ recoil KE of atom
hf=ΔE(P)22m
hf<ΔE

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