When
electromagnetic radiation is incident on the surface of certain metals
electrons may be
ejected. A
photon of energy
hf penetrates the
material and is absorbed by an electron. If enough energy is available, the electron will be raised to the
surface and ejected with some
kinetic energy,
½mv2. Depending on how deep in the material they are, electrons have a
range of valuesof
KE will be
emitted. Let
φ be the
energy required for an electron to break free of the surface, the so-called
work function. For electrons up near the surface to begin with, an amount of energy (hf -
φ) will be available and this is the
maximum kinetic energy that can be imparted to any electron.
Accordingly, Einstein's photoelectric equation is
½mv2max = hf - φ
The energy of the ejected electron may be found by determining what potential difference must be applied to stop its motion; then ½mv2 = Vse. For the most energetic electron,
hf - φ = Vse
where Vsis called the stopping potential.
For any surface, the radiation must be of short enough wavelength so that the photon energy hf is large enough to eject the electron. At the threshold wavelength (or the well-known frequency), the photon's energy just equals the work function. For ordinary metals the treshhold wavelength lies in the visible or ultraviolet range. X-rays will eject photoelectrons readily; far-infrared photons will not.