An atom of mass M is initially at rest, in its ground state. A moving (nonrelativistic) electron of mass m_e collides with the atom. The atom+electron system can exist in an excited state in which the electron is absorbed into the atom. The excited state has an extra, "internal," energy E relative to the atom's ground state.
Find the kinetic energy K_e that the electron must have in order to excite the atom.
What is the least possible initial kinetic energy the oxygen atom could have and still excite the cesium atom?