Think of an hydrogen atom with an electron at n=1. What happens when a low energy photon(not enough to excite electron to even to n=2) collides with the electron at the first energy level? Does photon scatter without losing its energy and momentum?
Scattering in a different direction means that the photon momentum changes. Both energy and momentum of the system are conserved. The scattered photon would transfer some momentum to the atom. So an atom that was initially at rest would also gain some kinetic energy. The photon experiences a recoil shift.