# Thread: formula proof?

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
incoming radiation are related by

$E = h v = I + \frac{1}{2}m_{e}v^{2}$

Any help appreciated,
Thank you.

2. What you have written makes no sense. If "v" is the "speed of the ejected electron", it cannot also be the "frequencey of the incoming radiation". I suspect you mean that "h" is the frequency of the incoming radiation. But then the energy of the incoming radiation is given by hc, where c is the speed of light, not hv.

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.