When an atom emits a photon in a transition from a state of energy E1 to a state of energy E2, the photon energy is not precisely equal to E1-E2. Conservation of momentum requires that the atom must recoil, and so some energy must go into recoil kinetic energy KR. Show that KR is roughly equal to (E1-E2)2/2Mc2, where M is the mass of the atom. Evaluate this recoil energy for the n=2 to n=1 transition of hydrogen.

When an atom emits a photon in a transition from a state of energy E1 to a state of energy E2, the photon energy is not precisely equal to E1-E2. Conservation of momentum requires that the atom must recoil, and so some energy must go into recoil kinetic energy KR. Show that KR is roughly equal to (E1-E2)2/2Mc2, where M is the mass of the atom. Evaluate this recoil energy for the n=2 to n=1 transition of hydrogen.