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,

½mv^{2}. 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*
½mv^{2}_{max} = hf - φ

**The energy of the ejected electron may be found by determining what potential difference must be applied to stop its motion; then **½mv^{2} = V_{s}e. **For the most energetic electron**,

hf - φ = V_{s}e

**where** V_{s}**is 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.