Question

Consider an excited hydrogen atom in state n moving with a velocity υ(ν<

Answer 1

Ratio of frequencies of the Emitted Radiation, $\frac {\nu}{\nu_0} = (1+ \frac {u}{c})$

Explanation:

• Let the frequency emitted by the atom at rest be $v_0$

• 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,$\nu = \nu_0 (1+ \frac {u}{c})/(1 - \frac {u}{c})$

Since, u <<< c,

$\nu = \nu_0 (1+ \frac {u}{c})/1$

$\nu = \nu_0 (1+ \frac {u}{c})$

Ratio of frequencies of the emitted radiation, $\frac {\nu}{\nu_0} = (1+ \frac {u}{c})$