MC²

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are emitted from matter (metals and non-metallic solids, liquids, or gases) after the absorption of energy from electromagnetic radiation such as X-rays or visible light. The emitted electrons can be referred to as photoelectrons in this context. The effect is also termed the Hertz Effect, due to its discovery by Heinrich Rudolf Hertz, although the term has generally fallen out of use. Hertz observed and then showed that electrodes illuminated with ultraviolet light create electric sparks more easily. Photo Electric Effect

The photoelectric effect takes place with photons with energies from about a few electronvolts to, in some cases, over 1 MeV. At the high photon energies comparable to the electron rest energy of 511 keV, Compton scattering, another process, may take place, and above twice this (1.022 MeV) pair production may take place.

Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave–particle duality.

The term may also refer to the photoconductive effect (also known as photoconductivity or photoresistivitity), the photovoltaic effect, or the photoelectrochemical effect.

When a surface is exposed to electromagnetic radiation above a certain threshold frequency (typically visible light for alkali metals, near ultraviolet for other metals, and vacuum or extreme ultraviolet for non-metals), the light is absorbed and electrons are emitted. In 1902, Philipp Eduard Anton von Lenard observed that the energy of individual emitted electrons increased with the frequency, or color, of the light. This appeared to be at odds with James Clerk Maxwell’s wave theory of light, which was thought to predict that the electron energy would be proportional to the intensity of the radiation. In 1905, Einstein solved this apparent paradox by describing light as composed of discrete quanta, now called photons, rather than continuous waves. Based upon Max Planck’s theory of black-body radiation, Einstein theorized that the energy in each quantum of light was equal to the frequency multiplied by a constant, later called Planck’s constant. A photon above a threshold frequency has the required energy to eject a single electron, creating the observed effect. This discovery led to the quantum revolution in physics and earned Einstein the Nobel Prize in 1921.

Modern view

It has now been shown that it is not necessary for light to be quantized to explain the photoelectric effect. The most common way physicists calculate the probability of ejecting an electron uses what is known as Fermi’s golden rule based upon quantum mechanics. This method does not actually treat light as a particle phenomenon, but rather as an electromagnetic wave passing from one eigenstate to another. Nonetheless, the notion that the photoelectric effect demonstrates the so-called particle nature of light persists in many introductory textbooks. Additionally, the treatment of light as being made of particles like tiny billiard balls cannot explain the polarization dependence of the direction electrons are emitted. The latter effect is being considered as a possible way of gathering polarization information in astronomy.

Experimental results of the photoelectric emission

1. For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.
2. For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency.
3. Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light but depends on the frequency of the incident light.
4. The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10–9 second.
5. The direction distribution of emitted electrons peaks in the direction of polarization (the direction of the electric field) of the incident light, if it is linearly polarized.

Three-step model

In the X-ray regime, the photoelectric effect in crystalline material is often decomposed into three steps:

1. Inner photoelectric effect (see photodiode below). The hole left behind can give rise to auger effect, which is visible even when the electron does not leave the material. In molecular solids phonons are excited in this step and may be visible as lines in the final electron energy. The inner photoeffect has to be dipole allowed. The transition rules for atoms translate via the tight-binding model onto the crystal. They are similar in geometry to plasma oscillations in that they have to be transversal.
2. Ballistic transport of half of the electrons to the surface. Some electrons are scattered.
3. Electrons escape from the material at the surface.

In the three-step model, an electron can take multiple paths through these three steps. All paths can interfere in the sense of the path integral formulation. For surface states and molecules the three-step model does still make some sense as even most atoms have multiple electrons which can scatter the one electron leaving.

Einstein: light quanta

Albert Einstein’s mathematical description in 1905 of how the photoelectric effect was caused by absorption of quanta of light (now called photons), was in the paper named “On a Heuristic Viewpoint Concerning the Production and Transformation of Light”. This paper proposed the simple description of “light quanta”, or photons, and showed how they explained such phenomena as the photoelectric effect. His simple explanation in terms of absorption of discrete quanta of light explained the features of the phenomenon and the characteristic frequency. Einstein’s explanation of the photoelectric effect won him the Nobel Prize in Physics in 1921.

The idea of light quanta began with Max Planck’s published law of black-body radiation (”On the Law of Distribution of Energy in the Normal Spectrum”. Annalen der Physik 4 (1901)) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck’s constant. By assuming that light actually consisted of discrete energy packets, Einstein wrote an equation for the photoelectric effect that fitted experiments. It explained why the energy of photoelectrons were dependent only on the frequency of the incident light and not on its intensity: a low-intensity, high-frequency source could supply a few high energy photons, whereas a high-intensity, low-frequency source would supply no photons of sufficient individual energy to dislodge any electrons. This was an enormous theoretical leap, but the concept was strongly resisted at first because it contradicted the wave theory of light that followed naturally from James Clerk Maxwell’s equations for electromagnetic behaviour, and more generally, the assumption of infinite divisibility of energy in physical systems. Even after experiments showed that Einstein’s equations for the photoelectric effect were accurate, resistance to the idea of photons continued, since it appeared to contradict Maxwell’s equations, which were well-understood and verified.

Einstein’s work predicted that the energy of individual ejected electrons increases linearly with the frequency of the light. Perhaps surprisingly, the precise relationship had not at that time been tested. By 1905 it was known that the energy of photoelectrons increases with increasing frequency of incident light and is independent of the intensity of the light. However, the manner of the increase was not experimentally determined until 1915 when Robert Andrews Millikan showed that Einstein’s prediction was correct.

Simple photoelectric effect demonstration

Resources needed
Gold leaf electroscope or coulomb meter
Zinc plate attachment (sand-papered clean to remove oxidation)
Laser (class 2)
Mains lamp (a desk lamp is ideal)
Ultra violet lamp with clear quartz envelope

Safety
A class 2 laser requires a warning: Do not stare down the beam.
A short-wave UV lamp must be shielded so that the UV emerges through a hole. The hole is always directed away from eyes. The presence of UV can be demonstrated by showing fluorescence of paper.

Technique
Attach the zinc plate to the top of the electroscope. (A coulomb meter can be used instead of the electroscope.)

Photoelectric Effect Demonstration
Charge the plate negatively.
Shine red laser light onto the cleaned zinc plate – no effect.
Use a mains light bulb emitting white light – no effect.
Use an ultra violet lamp – the leaf falls immediately.