84 Chapter 2. Interaction of Radiation with Matter
explained this effect by arguing that light is transferred to the material in packets
calledquanta, each of which carries an energy equal to
Eγ=hν=hc
λ, (2.3.1)
whereνandλare the frequency and wavelength of light respectively andcis the
velocity of light in vacuum. Now, since electrons in the material are bonded therefore
to set them free the energy delivered must be greater than their binding energy. For
metals, this energy is calledwork functionand generally represented by the symbol
φ. Hence, in order for an electron to be emitted from a metal surface, we must have
Eγ ≥ φ (2.3.2)or ν ≥φ
h(2.3.3)
or λ ≤hc
φ. (2.3.4)
If the photon energy is larger than the work function, the rest of the energy is
carried away by the emitted electron, that is
Ee=Eγ−φ. (2.3.5)Proving this theory is quite simple as one can design an experiment that measures
the electron energy as a function of the incident light frequency or wavelength and
see if it follows the above relation.
Since most metals have very low work functions, on the order of a few electron
volts, therefore even very low energy light can set them free. The work function
of metals is approximately half the binding energy offreemetallic atoms. In other
words, if there were no metallic bonds and the metallic atoms were free, the energy
needed for the photoelectric effect to occur would be twice.
The photoelectric effect can also occur in free atoms. During this process, a pho-
ton is completely absorbed by an atom making it unstable. To return to the stable
state, the atom emits an electron from one of its bound atomic shells. Naturally the
process requires that the incident photon has energy greater than or equal to the
binding energy of the most loosely bound electron in the atom. The energy carried
away by the emitted electron can be found by subtracting the binding energy from
the incident photon energy, that is
Ee=Eγ−Eb, (2.3.6)whereEbis the binding energy of the atom. Theatomicphotoelectric effect is
graphically depicted in Fig.2.3.2
Since the photon completely disappears during the process, the photoelectric
effect can be viewed as theconversionof a single photon into a single electron. It
should however be noted that this is just a convenient way of visualizing the process
and does not in any way represents an actual photon to electron conversion. Just
like nuclear reactions we visited in the first chapter, we can also write this reaction
as
γ+X−>X++e. (2.3.7)