CK-12-Physics - Intermediate

23.2. Photons and the Photoelectric Effect http://www.ck12.org

• If the intensity of the light wave was increased, not only would more electrons be ejected, but those ejected
  would have a greater kinetic energy.


• The photoelectric effect should occur for any light, regardless of frequency. Lower frequency or intensity will
  have less energy, and will take more time to transfer enough energy for electrons to escape.

Experimental Results

The actual results contradicted the classical prediction markedly.

• Increasing the intensity of the light increased the number of electrons (the current), but had no effect on the
  kinetic energy of the electrons released.


• Increasing the frequency of the light increased the kinetic energy of the electrons released, but not the current.
  For some materials, a low-intensity blue light would eject electrons, whereas the red or orange light, no matter
  how bright, would cause no photoelectric effect at all.

Einstein’s Explanation

In 1905, Albert Einstein proposed that Planck’s blackbody equation could be explained in terms of the particle,

orphoton, model of light, rather than the wave model. The particle model suggests that light can be thought

of as particles called photons, rather than as waves. Einstein suggested an explanation for Planck’s equation

based upon a phenomenon called the photoelectric effect, which had been observed but never properly explained.

Physicists had known since the late 19th century that when light was incident upon a metal surface, under certain

conditions, electrons were ejected from the surface. However, until Einstein’s proposed model, there was no adequate

explanation for that mysterious phenomenon, which is known asthe photoelectric effect.

Einstein’s assumption was that photons of light were responsible for ejecting electrons and creating the observed

current. Furthermore, he claimed that the energy carried by each photon was given in terms of Planck’s equation:

E=h f

Therefore, the greater the frequency of the photon, the greater the kinetic energy of the ejected photon would be.

Blue light, for example, should emit electrons with a greater kinetic energy then red light.

Einstein went a step further and said that the photons must have a minimum frequencyfoin order to eject electrons

from the metal. This minimum frequency is known as the threshold frequency.

The threshold frequency corresponds to the minimum energy(Eo)E 0 =h f 0 needed to overcome the electrical forces

which bind the electron within the metal. We now call this minimum energy thework functionof the metal(Wo),

orWo=h fo.

Einsten gave the maximum kinetic energy of an ejected electron as:

KEmax=h f−h foorKEmax=h f−Wo

This equation is known as Einstein’s equation for photoelectric effect and is, essentially, a statement of the law of

conservation of energy applied to photoelectric effect.

Interestingly, the maximum kinetic energy of the electrons could be relatively easily determined by gradually

reversing the potential differenceVof the source shown inFigure23.6. As the reversed potential is slowly increased,

the current in the circuit eventually decreases to zero. The work done in stopping the ejected electrons (also known

as “photoelectrons”) would equal their maximum kinetic energy.

W=eVo=∆KE→ 0 −KEmax=eVo→−KEmax=eVo

But since the potential difference is reversed,