1. ## formula proof?

In the spectroscopic technique known as photoelectron spectroscopy (PES), ultra-
violet radiation is directed at an atom or a molecule. Electrons are ejected from the valence shell, and their kinetic energies are measured. Because the energy of
the incoming ultraviolet photon is known and the kinetic energy of the outgoing
electron is measured, the ionization energy, I, can be deduced from the fact that
the total energy is conserved.
(a) Show that the speed v of the ejected electron and the frequency v of the
$E = h v = I + \frac{1}{2}m_{e}v^{2}$
The kinetic energy of an eletron of mass $m_e$ and velocity v is, by definition, $\frac{1}{2}m_ev^2$.
"Conservation of energy" says that the total energy of the radiation, $hc$ must be equal to the total energy of the electron, $\frac{1}{2}m_ev^2$ plus the energy required to "knock" it off the atom, the "ionization energy", I.