$4.(12$ points$)$ The energy levels in a newly discovered isotope of Schneideronium $($atomic weight of $450\mathrm{.}4)$ are given by En $=8\mathrm{.}65$eV

n$3$

where n $=1$ is the ground state. What wavelengths must a photon have to ionize this atom when it is in the ground state? An atom of this element, at rest with respect to you, absorbs a photon that moves the electron from the ground state to the first excited state. Assuming that all the momentum of the photon is transformed into linear motion of the atom, what is the velocity of the atom after absorption$?$