A moving hydrogen atom emits a photon perpendicular to the direction of its motion, corresponding
to the first member of the Lyman series. If $f_{0}$ is the frequency of the first member of the Lyman series and $f$ is the frequency of the emitted photon, then:

Question

A moving hydrogen atom emits a photon perpendicular to the direction of its motion, corresponding

to the first member of the Lyman series. If $f_{0}$ is the frequency of the first member of the Lyman series and $f$ is the frequency of the emitted photon, then:

TestHub · Accepted Answer

The problem involves the relativistic Doppler effect. Since the photon is emitted perpendicular to the direction of motion, we use the transverse Doppler effect formula:

$f = f_{0} 1 - \frac{v ^{2}}{c ^{2}}$

where $f_{0}$ is the frequency in the rest frame, $f$ is the observed frequency, $v$ is the velocity of the hydrogen atom, and $c$ is the speed of light. Therefore, the correct answer is C.

Physics - Modern Physics Question with Solution | TestHub

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