PhysicsLAB: Famous Discoveries: The Photoelectric Effect

Towards the end of the 19th century, it had been experimentally observed that when ultraviolet light was shone on a negatively-charged electroscope, the charged leaves fell closer together; the electroscope discharged. This was the beginnings of the path to understanding what we now call the photoelectric effect.

When light shines on any metal surface, the surface can release electrons. If light were composed of waves, then eventually any wavelength of light should be able to build up enough energy to knock an electron free. However, scientists had discovered that only certain wavelengths worked with each metal and that electrons were either emitted instantaneously, or never emitted. They had also noticed that shorter wavelengths worked better than longer wavelengths.

The equation for the photoelectric effect was first explained by Albert Einstein in 1905.

E_photon = Φ + KE_max

where

E_photon = hf is the energy present in the incident photon,
Φ is the work function of the metal surface off of which the photoelectrons are escaping (PE), and
KE_max is the maximum KE of the ejected photoelectrons .

Notice that this equation is actually just a restatement of conservation of energy. There are two other patterns that also occurred:

The intensity of the light source affected the number of photoelectrons ejected from the surface since higher intensities permit more photons to strike the surface.
The frequency of the light source affected the kinetic energy of each photoelectron.

Since each photon can be absorbed by only ONE photoelectron (that is, there is a one-to-one correspondence), the energy of the photons directly affects the kinetic energy of the released photoelectrons.

The Experiment

The electrons with the maximum KE can be stopped from completing their journey across the photoelectric tube if there is a stopping potential set-up to impede their progress. The formula that relates the KE of these photoelectrons to this stopping potential is

KE_max = qV_stopping

where

V_stopping is the stopping potential, and
q is the magnitude of the charge of an electron, 1.6 x 10^-19 coulombs.

This formula is based on the fact that work is done on charged particles when they cross through an electric field. The work done (qDV) equals the change in each electron's KE.

Often the photoelectric equation is illustrated on a graph of KE vs frequency. On this graph, the slope ALWAYS equals Planck's constant, 6.63 x 10^-34 J sec. It NEVER changes. All lines on this type of graph will be parallel, only differing in their y-axis intercept (-f) and their x-axis intercept (the threshold frequency).

The threshold frequency is the lowest frequency, or longest wavelength, that permits photoelectrons to be ejected from the surface. At this frequency the photoelectrons have no extra KE (KE = 0) resulting in

0 =	hf - Φ
hf =	Φ
E_photon =	Φ

Note that red light has such a low frequency (energy) that it will never eject photoelectrons - that is, the energy of a red photon is less than the work function of the metal.

Since KE = qV_s (the stopping potential), we often rearrange the equation KE = hf - Φ producing a second alternative presentation of the results of a photoelectric experiment in the form of the graph of V_s vs 1/λ

KE =	hf - Φ
qV_s =	hf - Φ
qV_s =	h(c/λ) - Φ
V_s =	hc/q (1/λ) - Φ/q

In this form,

the x-axis intercept would represent the reciprocal of the threshold wavelength,
the slope would equal the expression (hc/q), and
the y-axis intercept would represent the work function divided by the fundamental charge of an electron.

Albert Einstein received the Nobel Prize for Physics in 1921 for his discovery of the Law of the Photoelectric Effect, but he was unable to attend the Stockholm ceremonies. His work ended the controversy as to whether light had particle properties; that is, by invoking the quantum nature of light he was able to explain experimental results that his predecessors could not explain with just a wave model of light.