The Photoelectric Effect
Wave theory of light vs. Ray Optics (one particle theory for light): all seems ok
At the end of the 1800’s light was understood to be a “wave” phenomena. Sometimes
light appears to behave like particles --- ray optics works for many purposes --- but this was
well understood as just a result of the fact that light wavelengths are very small compared to
λ
(and = 0 for
D
particles), are often practically negligible when D is the size of a mirror or camera lens. Said
otherwise, ray optics and wave optics predict exactly the same results whenever you can
ignore diffraction. And the thinking of physicists at the turn of the century (~1900) was that
light really is waves, but so far as the predictions of ray optics go, the waves usually behave
exactly like a stream of particles would.
lenses and mirrors and camera apertures. Thus diffraction effects, which go
But, no: the wave theory is not the end of the story: new particle-like results for light
In the early 1900’s several experiments were done which gave results that could not
be explained by the wave theory of light at all. The photoelectric effect is one of those
experiments.
The photoelectric effect occurs when light is shined on matter: under certain
circumstances electrons are freed (kicked) from the matter. In the experiment you will do, the
“matter” is a “metal plate” (cathode) in a tube and you will measure the freed electrons as a
current to a “collection electrode” (anode). You will also find the energy of the fastest (most
energetic) electrons that are kicked out of the metal by the light.
Now according to the wave theory of light the energy of a wave is proportional to the
intensity of the wave which in turn is proportional to the electric field squared. The wave
theory predicts that waves of any frequency should be able to kick electrons out of matter --you just need to get the intensity high enough. In addition, the wave theory predicts that you
will get more energetic electrons from the metal by increasing the intensity of the light. This
is NOT what is observed, experimentally. What is found (and you will see) is that the
frequency of light determines whether or the light can free electrons from the metal and
also determines the energy of the most energetic (fastest) electrons that are kicked out (if any
electrons are kicked out). It is exactly as if the light was a stream of particles: the energy of a
light particle being proportional to the frequency of the light wave, with proportionality
constant, h. Nowadays, we call these light particles “photons” and write E photon = hf . Where
h is the (very important) Planck’s constant. The minimum amount of energy to free an
electron from the metal plate is called the “work function,” W0 , of the metal and if the energy
of the photons, that is, the frequency of the waves in a light beam are too low no electrons are
kicked out of the metal, no matter how intense the light beam is. If there are photons in the
beam with more energy that the work function then those photons can use part of their energy
to free electrons from the metal and give the rest of their energy to the electrons as kinetic
energy. In lab you will find the kinetic energy of the most energetic electrons kicked out of
the metal by applying a “stopping voltage” that takes away the kinetic energy given to the
electrons by the photons ---or, in other words --- slows down the electrons to where they
cannot make it to the “collection electrode.” By measuring the energy of the fastest/most
energetic electrons for different colors/frequencies of light (or actually, in lab, “cutoff
wavelengths”) , you will be able the measure both Planck’s constant, h, and the metal’s work
function, W0 .