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Consider an Excited Hydrogen Atom in State N Moving with a Velocity υ(ν<<C). It Emits a Photon in the Direction of Its - Physics


Consider an excited hydrogen atom in state n moving with a velocity υ(ν<<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 ν of the emitted radiation. Compare this with the frequency ν0 emitted if the atom were at rest.

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Let the frequency emitted by the atom at rest be ν0.

Let the velocity of hydrogen atom in state 'n' be u.

But u << c

Here, the velocity of the emitted photon must be u.

According to the Doppler's effect,

The frequency of the emitted radiation, ν is given by

Frequency of the emitted radiation,  `v = v_0 ((1 + u/c)/(1 - u/c))`

since u <<< c ,

`v = v_0 ((1+u/c)/1)`

`v = v_0 (1 + u/c)`

Ratio of frequencies of the emitted radiation,

`v/v_0 = (1 + u/e)`

Concept: The Line Spectra of the Hydrogen Atom
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HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 21 Bohr’s Model and Physics of Atom
Q 46 | Page 386
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