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SU403RUNFAST

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## Homework Statement

A stationary atom releases a photon when it goes from excited state n to lower state n. Delta(E) is the energy difference between initial state En and final state En', consider kinetic energy of recoiling atom. Apply conservation of energy and momentum and solve for the energy of the photon hf.

## Homework Equations

Delta(E)=En-En'=hf=hc/lamda

E=pc for a photon due to no mass

E^2=(pc)^2+(mc^2)^2 pythagorean relation for momentum and energy

## The Attempt at a Solution

I know that the the conservation requires that the photon and the final atom have opposite momenta of the same magnitude p. P=p1+p2 is the conservation for momentum. P is the atom before, p1 is the atom after and p2 is the photon after. p1 is root of E^2-(mc^2)^2 all divided by c while p2 is E/c. so I put the momentum before as 0 for P and plugged in the other values, substituted E=hf in p2 and solved for hf alone to get

hf=-root of E^2-(mc^2)^2. So i was able to get the answer without using an energy conservation equation i am not sure if i did this right (didnt do E=E1+E2)