Special relativity and quantum mech

[bs vasanth]

An atom can exist in two states , ground state of M and excited state of mass M+Δ , it goes to excited state by absorption of an photon, what is the photon frequency in the in the lab frame of reference ( where the atom is initially at rest )?

A simple energy equation gives the answer:
E=( M+Δ -M)c^{2}=hγ
γ=Δc^{2}/h
But my intuition says that I am overlooking something and can't be that simple..

 

[PAllen]

An atom can exist in two states , ground state of M and excited state of mass M+Δ , it goes to excited state by absorption of an photon, what is the photon frequency in the in the lab frame of reference ( where the atom is initially at rest )?

A simple energy equation gives the answer:
E=( M+Δ -M)c^{2}=hγ
γ=Δc^{2}/h
But my intuition says that I am overlooking something and can't be that simple..

It is that simple.

 

[Meir Achuz]

You should include the recoil of the excited atom in the final state.
Use Energy^2=(M+K)^2=(M+Delta)^2+K^2, and solve for K (the photon energy). (with c=1)

 

[PAllen]

You should include the recoil of the excited atom in the final state.
Use Energy^2=(M+K)^2=(M+Delta)^2+K^2, and solve for K (the photon energy). (with c=1)

Yes, I ignored recoil because its contribution is small for common cases. I, of course, agree with the above formula. Note that even for as extreme a case as a 10 Mev delta for a hydrogen atom, including recoil only changes the required photon energy to about 10.05 Mev. For Sodium, to about 10.002 Mev. For delta of 1 Mev and hydrogen, including recoil would require a 1.0005 Mev photon.