The Photoelectric Effect in More Detail

Testing the wave-particle duality of light.

Light knocks electrons out of metal surfaces as if it were made of particles --- photons. For light of frequency f, each photon has energy hf.

In 1902, P.Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination.

To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current.

Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it V_stop. This means that there is a threshold kinetic energy that the electrons must have in order to reach the detector.

Contrary to intuition, Lenard found that V_stop did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons.

But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color --- the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion as his experimental apparatus lacked good the means to make a reliable measurement. Still this was a puzzling result at the time.

Let's examine some of the implications of Lenard's experiment in terms of whether light is a wave or a particle:

If its a wave, then Wave Theory: Light is an oscillating electric field would predict that only the electric field strength should affect electrons.

Prediction: Sufficiently intense light should eject electrons no matter what the frequency.

But this is not what was observed. The amount of current generated in the metal was not dependent on the intensity/power of the incoming light. A more powerful light source did not produce a stronger current.





If its a wave, then Wave Theory: The power in a light beam is spread out. The area near an electron intercepts very little of the energy initially.

Prediction: It should take some time for an electron to absorb enough energy to be ejected and the electron then flows through the material.

Again, this is not observed. When Lenard used his ultraviolet light, a current was immediately generated in the metal. No time delay was observed.



Hence, Lenard's experimental results are inconsistent with the Light as a Wave model. So what about considering light as a particle. Indeed this will turn out to provide a compelte explanation of why the photoelectric effect exists.



Under the particle model, all the energy in a light "wave" is contained in discrete particles (Photons) whose energy = hf; (h= constant; f = frequency; 1/f = w = wavelength).

Particle model works:

Particle theory: A photon with energy hf strikes an electron and ejects it from the metal.
hf = K.E. + w

w = work to remove electron from metal
K.E. = kinetic energy of ejected electron.



The particle model completely explains the observed threshold effect. In the wave theory, greater light intensity simply means more photons per unit time striking the metal. Each photon ejects electrons in the same way, so more intensity means more electrons. This was not observed.

However, for each metal, there is a threshold frequency. Light frequencies below the threshold eject no electrons, no matter how intense the light. Light frequencies above the threshold eject electrons, no matter how low the intensity. Ultraviolet light has much higher energy per photon than optical light since the frequency of ultraviolet light is about twice as high as optical light.



When the ultratiolet light source is turned on, the electrons begin to be ejected immediately. No matter how weak the light source, if the frequency is above the threshold, there is no time delay. These observations are therefore completely consistent with the light as a particle idea.



So now, by 1905 or so, we know that light interacting with certain metals can produce electricity. This is the basis for how PV cells work and how digital cameras work. However, at this time we still do not know how to control the direction of flow of electricty through a metal, we only know how to generate this flow.