4.5.2 The photoelectric effect

The photoelectric effect: when Heinrich Hertz shone UV radiation onto zinc in 1887 electrons were emitted from the surface of the metal. The emitted photons are known as photoelectrons.

We need to know a simple demonstration of the photoelectric effect - this can be done with a gold-leaf electroscope. If we briefly touch the top place with the negative electrode from a high voltage power supply we will charge the electroscope. Excess electrons are deposited onto the plate and stem of the electroscope. Any charge developed on the plate and stem of the electroscope spreads to the stem and the gold leaf - since the stem and gold leaf now both have the same charge they repel each other and the leaf lifts away from the stem. If a clean piece of zinc is placed on top of a negatively charged gold-leaf electroscope and UV radiation shines onto the zinc surface the gold leaf slowly falls back toward the stem because the electroscope gradually loses its negative charge. This is because the UV (incident radiation) has caused the free electrons to be emitted from the zinc. These are photoelectrons. Three key observations resulted:

1. Photoelectrons were only emitted if the incident radiation was above a certain frequency (the threshold frequency) - no matter how intense the radiation was.
2. If the incident radiation was above the threshold frequency emission of photoelectrons was instantaneous.
3. If the incident radiation was above threshold frequency, increasing the intensity of the radiation increased the number of electrons emitted (not the kinetic energy at which they were emitted). To increase maximum kinetic energy you increase the frequency of the incident radiation.

These observations cannot be explained with the wave model of light so Einstein published the photon model in 1905. He suggested that each electron in the metals surface requires a certain amount of energy in order to escape from the metal and that each photon could transfer its exact energy to one surface electron only in a one-to-one reaction. Remember, if threshold frequency is not met (this depends on the energy of the photon, E=hf) the photoelectron will not be released regardless of the intensity (number of photos per second).

Depending on their positions within the metal electrons would require different amounts of energy to free them. Einstein defined a constant for each metal - the work function. This is the minimum energy required to free an electron from the surface of the metal.

Provided threshold frequency is met, increasing the intensity of incident radiation means more photons hit the metal surface per second so more photoelectrons are emitted per second. The rate of emission of photoelectrons is directly proportional to the incident radiation intensity.

Using the principle of conservation of energy there must be some leftover energy after the electron was freed from the metal - this is the maximum value of kinetic energy that any emitted photoelectron can have. The only way to increase maximum kinetic energy is to increase the frequency of the incident radiation - each photon has more kinetic energy so each electron has more kinetic energy after it has been freed from the metal. From this, Einstein derived his photoelectric effect equation. The energy of each photon must be conserved - it frees a single electron (in a one-to-one reaction) then any remainder is transferred into the kinetic energy of the photoelectron. According to the principle of conservation of energy he produced this equation…

hf = ϕ + KEmax

NOTE: Since all terms are energies, they should all be in joules, or all be in electronvolts. 

It is important to realise that some electrons in the surface of the metal are much closer to the positive metal ions than others. Their relative positions affect how much energy is required to free them. The work function is the minimum energy required to free an electron from the metal - most electrons need a little more energy than the work function to free them. This means that only a few of the emitted photoelectrons have the maximum kinetic energy, most travel a little slower. Also, if a photon strikes the surface of the metal at the threshold frequency for the metal then no energy will be left over from the incident photon to be transferred into kinetic energy. The equation becomes hf₀ = ϕ.

Lastly….. so we already know that the only way to increase the maximum kinetic energy of photoelectrons is to increase the frequency of the incident radiation. A graph of maximum kinetic energy against frequency of radiation on the surface gives a gradient equal to Plancks constant and a y-intercept equal to the negative work function. It is important to realise that since energy metal has a different work function the threshold frequency for each metal is different.