Consider an excited hydrogen atom in state n moving with a velocity v (v << c). It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency v of the emitted radiation. Compare this with the frequency v0 emitted if the atom were at rest.

As per the question is frequency of emitted radiation and


is frequency if atom is at rest and velocity of photon is u.


But as u << c so velocity of emitted photon is same as that of


Hydrogen atom =u.


Now applying Doppler’s effect formula



As u << c


Hence



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