Recoil shift) Since photons carry translational momentum (p = hk), when an atom in free space absorbs or emits a photon, the atom's momentum changes. Since the atom's kinetic energy also changes as a result, the transition energy for an atom in free space is slightly different than predicted by the Bohr model, as the change in the atom's kinetic energy also must be accounted for in the photon energy. Consider an initially-stationary hydrogen atom of mass mA me in the Bohr model that spontaneously emits a photon to go from the ni Bohr level to nf . Show that the ratio of recoil energy (i.e. the atom's final kinetic energy) to the photon's energy is given approximately by Er hni nf me mA 2 4 1 n2 f 1 n2 i . You should neglect the finite-nuclear-mass correction in the center of mass frame (which is to say take me me) and the recoil energy correction to the photon's energy to arrive at this estimate