Question

Show that the fractional change in the frequency of a photon absorbed or emitted by an atom initially at rest is $$ \frac{v-v_{0}}{v}=\pm \frac{h v}{2 M c^{2}} $$ where $M$ is the mass of the atom and $v_{0}$ is the frequency of the transition uncorrected for the recoil of the atom. In the above equation the plus sign corresponds to the absorption and the minus sign to the emission of a photon.

          Show that the fractional change in the frequency of a photon absorbed or emitted by an atom initially at rest is
$$
\frac{v-v_{0}}{v}=\pm \frac{h v}{2 M c^{2}}
$$
where $M$ is the mass of the atom and $v_{0}$ is the frequency of the transition uncorrected for the recoil of the atom. In the above equation the plus sign corresponds to the absorption and the minus sign to the emission of a photon.

Added by Wendy W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Timothy James

11/07/2022

Step 1

Step 1:** From the conservation of momentum, we have: Initial momentum = Final momentum 0 = M(v - v0) - h/c Mv - Mv0 = h/c v - v0 = h/(Mc) ** Show more…

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Show that the fractional change in the frequency of a photon absorbed or emitted by an atom initially at rest is $$ \frac{v-v_{0}}{v}=\pm \frac{h v}{2 M c^{2}} $$ where $M$ is the mass of the atom and $v_{0}$ is the frequency of the transition uncorrected for the recoil of the atom. In the above equation the plus sign corresponds to the absorption and the minus sign to the emission of a photon.