Photoelectric Effect: Definition, Equation & Experiment

Everything learned in classical physics was turned on its head as physicists explored ever smaller realms and discovered quantum effects. Among the first of these discoveries was the photoelectric effect. In the early 1900s, the results of this effect failed to match classical predictions and were only explainable with quantum theory, opening up a whole new world for physicists.

Today, the photoelectric effect has many practical applications as well. From medical imaging to the production of clean energy, the discovery and application of this effect now has implications that go well beyond simply understanding the science.

When light, or electromagnetic radiation, hits a material such as a metal surface, that material sometimes emits electrons, called ​photoelectrons​. This is essentially because the atoms in the material are absorbing the radiation as energy. Electrons in atoms absorb radiation by jumping to higher energy levels. If the energy absorbed is high enough, the electrons leave their home atom entirely.

This process is sometimes also called ​photoemission​ because incident photons (another name for particles of light) are the direct cause of the emission of electrons. Because electrons have a negative charge, the metal plate from which they were emitted is left ionized.

What was most special about the photoelectric effect, however, was that it did not follow classical predictions. The way in which the electrons were emitted, the number that were emitted and how this changed with intensity of light all left scientists scratching their heads initially.

The original predictions as to the results of the photoelectric effect made from classical physics included the following:

1. Energy transfers from incident radiation to the electrons. It was assumed that whatever energy is incident upon the material would be directly absorbed by the electrons in the atoms, regardless of wavelength. This makes sense in the classical mechanics paradigm: Whatever you pour into the bucket fills the bucket by that amount.
2. Changes in light intensity should yield changes in kinetic energy of electrons. If it is assumed that electrons are absorbing whatever radiation is incident upon them, then more of the same radiation should give them more energy accordingly. Once the electrons have left the bounds of their atoms, that energy is seen in the form of kinetic energy.
3. Very low-intensity light should yield a time lag between light absorption and emission of electrons. This would be because it was assumed that electrons must gain enough energy to leave their home atom, and low-intensity light is like adding energy to their energy "bucket" more slowly. It takes longer to fill, and hence it should take longer before the electrons have enough energy to be emitted.

The actual results were not at all consistent with the predictions. This included the following:

1. Electrons were released only when the incident light reached or exceeded a threshold frequency. No emission occurred below that frequency. It didn't matter if the intensity was high or low. For some reason, the frequency, or wavelength of the light itself, was much more important. 
2. Changes in intensity did not yield changes in kinetic energy of electrons. They changed only the number of electrons emitted. Once the threshold frequency was reached, increasing the intensity did not add more energy to each emitted electron at all. Instead, they all ended up with the same kinetic energy; there were just more of them.
3. There was no time lag at low intensities. There seemed to be no time required to "fill the energy bucket" of any given electron. If an electron was to be emitted, it was emitted immediately. Lower intensity had no effect on kinetic energy or lag time; it simply resulted in fewer electrons being emitted. 

The only way to explain this phenomenon was to invoke quantum mechanics. Think of a beam of light not as a wave, but as a collection of discrete wave packets called photons. The photons all have distinct energy values that correspond to the frequency and wavelength of the light, as explained by wave-particle duality.

In addition, consider that the electrons are only able to jump between discrete energy states. They can only have specific energy values, but never any values in between. Now the observed phenomena can be explained as follows:

1. Electrons are released only when they absorb very specific sufficient energy values. Any electron that gets the right energy packet (photon energy) will be released. None are released if the frequency of the incident light is too low regardless of intensity because none of the energy packets are individually big enough. 
2. Once the threshold frequency is exceeded, increasing intensity only increases the number of electrons released and not the energy of the electrons themselves because each emitted electron absorbs one discrete photon. Greater intensity means more photons, and hence more photoelectrons. 
3. There is no time delay even at low intensity as long as the frequency is high enough because as soon as an electron gets the right energy packet, it is released. Low intensity only results in fewer electrons.

One important concept related to the photoelectric effect is the work function. Also known as electron-binding energy, it is the minimum energy needed to remove an electron from a solid.

The formula for the work function is given by:

\(W = -e\phi – E\)

Where ​-e​ is the electron charge, ​ϕ​ is the electrostatic potential in the vacuum nearby the surface and ​E​ is the Fermi level of electrons in the material.

Electrostatic potential is measured in volts and is a measure of the electric potential energy per unit charge. Hence the first term in the expression, ​-eϕ​, is the electric potential energy of an electron near the surface of the material.

The Fermi level can be thought of as the energy of the outermost electron when the atom is in its ground state.

Closely related to the work function is the threshold frequency. This is the minimum frequency at which incident photons will cause the emission of electrons. Frequency is directly related to energy (higher frequency corresponds to higher energy), hence why a minimum frequency must be reached.

Above the threshold frequency, the kinetic energy of the electrons depends on the frequency and not the intensity of the light. Basically the energy of a single photon will be transferred entirely to a single electron. A certain amount of that energy is used to eject the electron, and the remainder is its kinetic energy. Again, a greater intensity just means more electrons will be emitted, not that those emitted will have any more energy.

The maximum kinetic energy of emitted electrons can be found via the following equation:

\(K_{max} = h(f – f_0)\)

Where ​_K_max​ is the maximum kinetic energy of the photoelectron, ​h_​ is Planck's constant = 6.62607004 ×10^-34 m²kg/s, ​f​ is the frequency of the light and ​_f₀_​ is the threshold frequency.

You can think of the discovery of the photoelectric effect as happening in two stages. First, the discovery of the emission of photoelectrons from certain materials as a result of incident light, and second, the determination that this effect does not obey classical physics at all, which led to many important underpinnings of our understanding of quantum mechanics.

Heinrich Hertz first observed the photoelectric effect in 1887 while performing experiments with a spark gap generator. The setup involved two pairs of metal spheres. Sparks generated between the first set of spheres would induce sparks to jump between the second set, thus acting as transducer and receiver. Hertz was able to increase the sensitivity of the setup by shining light on it. Years later, J.J. Thompson discovered that the increased sensitivity resulted from the light causing the electrons to be ejected.

While Hertz's assistant Phillip Lenard determined that the intensity did not affect the kinetic energy of the photoelectrons, it was Robert Millikan who discovered the threshold frequency. Later, Einstein was able to explain the strange phenomenon by assuming the quantization of energy.

Albert Einstein was awarded the Nobel Prize in 1921 for his discovery of the law of the photoelectric effect, and Millikan won the Nobel Prize in 1923 also for work related to understanding the photoelectric effect.

The photoelectric effect has many uses. One of those is that it allows scientists to probe the electron energy levels in matter by determining the threshold frequency at which incident light causes emission. Photomultiplier tubes making use of this effect were also used in older television cameras.

A very useful application of the photoelectric effect is in the construction of solar panels. Solar panels are arrays of photovoltaic cells, which are cells that make use of electrons ejected from metals by solar radiation to generate current. As of 2018, nearly 3 percent of the world's energy is generated by solar panels, but this number is expected to grow considerably over the next several years, especially as the efficiency of such panels increases.

But most important of all, the discovery and understanding of the photoelectric effect laid the groundwork for the field of quantum mechanics and a better understanding of the nature of light.

There are many experiments that can be performed in an introductory physics lab to demonstrate the photoelectric effect. Some of these are more complicated than others.

A simple experiment demonstrates the photoelectric effect with an electroscope and a UV-C lamp providing ultraviolet light. Place negative charge on the electroscope so that the needle deflects. Then, shine the UV-C lamp. Light from the lamp will release electrons from the electroscope and discharge it. You can tell this happens by seeing the needle's deflection reducing. Note, however, that if you tried the same experiment with a positively charged electroscope, it wouldn't work.

There are many other possible ways to experiment with the photoelectric effect. Several setups involve a photocell consisting of a large anode that, when hit with incident light, will release electrons that are picked up by a cathode. If this setup is connected to a voltmeter, for example, the photoelectric effect will become apparent when shining the light creates a voltage.

More complex setups allow for more accurate measurement and even allow you to determine the work function and threshold frequencies for different materials. See the Resources section for links.