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# Photoelectric effect

The photoelectric effect is the emission of electrons from a surface (usually metallic) upon exposure to, and absorption of, electromagnetic radiation (such as visible light and ultraviolet radiation) that is above the threshold frequency particular to each type of surface. No electrons are emitted for radiation below the threshold frequency, as they cannot gain sufficient energy to overcome their atomic bonding. The electrons that are emitted are often termed 'Photoelectrons' in many textbooks.

The photoelectric effect helped further wave-particle duality, whereby physical systems (such as photons in this case) can display both wave-like and particle-like properties and behaviours, a concept that was used by the creators of quantum mechanics. The photoelectric effect was explained mathematically by Albert Einstein extending the work on quanta developed by Max Planck.

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## History

### Hertz's observations on spark gaps

The first recorded observation of the photoelectric effect was by Heinrich Hertz in 1887 in the journal Annalen Der Physik when he was investigating the production and reception of electromagnetic (EM) waves. His receiver consisted of a coil with a spark gap, whereupon a spark would be seen upon detection of EM waves. He placed the apparatus in a darkened box in order to see the spark better; he observed, however, that the maximum spark length was reduced when in the box. The glass panel placed between the source of EM waves and the receiver absorbed ultraviolet radiation that assisted the electrons in jumping across the gap. When removed, the spark length would increase. He observed no decrease in spark length when he substituted quartz for glass, as quartz does not absorb UV radiation.

Hertz concluded his months of investigation and reported the results obtained. He did not further pursue investigation of this effect, nor did he make any attempt at explaining how the observed phenomenon was brought about.

### JJ Thomson: Electrons

In 1899, Joseph John Thomson investigated ultraviolet light in cathode ray tubes. Influenced by the work of James Clerk Maxwell, Thomson deduced that cathode rays consisted of negatively charged particles, which he called "corpuscles" (later called "electrons"). In the research, Thomson enclosed a metal plate (i.e., cathode), in a vacuum tube, and exposed it to high frequency radiation. The oscillating electromagnetic fields caused the atoms' field to be resonated and, after reaching a certain amplitude, caused by his model a subatomic "corpuscle" to be emitted, and current to be detected. The current and speed of this current varied with the intensity and color of the radiation. Larger increments of the radiation intensity or frequency of the field would produce more current.

### von Lenards observations

In 1902 Philipp von Lenard observed [1] the variation in electron energy with light intensity. He used a powerful electric arc lamp which enabled him to investigate large changes in intensity, and had sufficient power to enable him to investigate the variation of potential with light frequency. His experiment directly measured potentials, not electron kinetic energy: he found the electron energy by relating it to the maximum stopping potential (voltage) in a phototube. He found that the calculated maximum electron kinetic energy is determined by the frequency of the light. For example, an increase in frequency results in an increase in the maximum kinetic energy calculated for an electron upon liberation - ultraviolet radiation would require a higher applied stopping potential, to stop current in a phototube, than blue light. However Lenards results were qualitative rather than quantitative becuase of the difficulty in performing the experiments: the experiments need to be done on freshly cut metal so that the pure metal was observed, but it oxidised in tens of minutes even in the partial vacuums he used. The current emitted by the surface was determined by the light's intensity, or brightness. Doubling the intensity of the light doubled the number of electrons emitted from the surface. Lenard did not know of photons.

### Einstein: Light quanta

Albert Einstein's mathematical description in 1905 of how it was caused by absorption of photons, or quanta of light, in the interaction of light with the electrons in the substance, was contained in the paper named "On a Heuristic Viewpoint Concerning the Production and Transformation of Light". This paper proposed the simple description of "light quanta" (later called "photons") and showed how they could be used to explain such phenomena as the photoelectric effect. The simple explanation by Einstein in terms of absorption of single quanta of light explained the features of the phenomenon and helped explain the characteristic frequency. Einstein's explanation of the photoelectric effect won him the Nobel Prize of 1921.

The idea of light quanta was motivated by 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. Einstein, by assuming that light actually consisted of discrete energy packets, wrote an equation for the photoelectric effect that fit experiments. The idea of light quanta contradicted the wave theory of light that followed naturally from James Clerk Maxwell's equations for electromagnetic behavior 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, his explanation was not universally accepted.

Einsteins work predicted that the energy of the ejected electrons would increase linearly with the frequency of the light. Perhaps surprisingly, that had not yet been tested. In 1915 Robert Andrews Millikan showed that Einstein was correct [2].Albert Einstein's explanation of it helped him win the Nobel Prize.

### Effect on wave-particle question

The photoelectric effect helped propel the then-emerging concept of the dual nature of light (light exhibits characteristics of waves and particles at different times). It was impossible to understand in terms of the classical wave description of light, as the energy of the emitted electrons did not depend on the intensity of the incident radiation. Classical theory predicted that the electrons could 'gather up' energy over a period of time, and then be emitted. For such a classical theory to work a pre-loaded state would need to persist in matter. The idea of the pre-loaded state was discussed in Millikan's book Electrons (+ & -) and in Compton and Allison's book X-Rays in Theory and Experiment. These ideas were abandoned.

## Explanation

The photons of the light beam have a characteristic energy given by the wavelength of the light. In the photoemission process, if an electron absorbs the energy of one photon and has more energy than the work function, it is ejected from the material. If the photon energy is too low, however, the electron is unable to escape the surface of the material. Increasing the intensity of the light beam does not change the energy of the constituent photons, only their number, and thus the energy of the emitted electrons does not depend on the intensity of the incoming light.

Electrons can absorb energy from photons when irradiated, but they follow an "all or nothing" principle. All of the energy from one photon must be absorbed and used to liberate one electron from atomic binding, or the energy is re-emitted. If the photon is absorbed, some of the energy is used to liberate it from the atom, and the rest contributes to the electron's kinetic (moving) energy as a free particle.

### Equations

In analysing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations are used:

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

Algebraically:

$hf = hf_0 + {1 \over 2}{m}{v_m}^2$

Using physicists' symbols:

$hf = \phi + E_k\,$

where h is Planck's constant, f0 is threshold frequency for the photoelectric effect to occur, φ is the work function, or minimum energy require to remove electron from atomic binding, and Ek is maximum kinetic energy observed.

• Note: If the photon's energy (hf) is not greater than the work function (φ), no electron will be emitted.

When this equation is not observed to be true (that is, the electron is not emitted or it has less than the expected kinetic energy), it may be because when given an excess amount of energy to the body, some energy is absorbed as heat or emitted as radiation, as no system is perfectly efficient.

## Common uses

Solar cells (used in solar power) and light-sensitive diodes use the photoelectric effect. They absorb photons from light and put the energy into electrons, creating electric current.

### Electroscopes

Electroscopes are fork-shaped, hinged metallic leaves placed in a vacuum jar, partially exposed to the outside environment. When an electroscope is charged positively or negatively, the two leaves separate, as charge distributes evenly along the leaves causing repulsion between two like poles. When ultraviolet radiation (or any radiation above threshold frequency) is shone onto the metallic outside of the electroscope, the negatively charged one will discharge and collapse, while nothing will happen to the positively charged one. The reason is that electrons will be liberated from the negatively charged one, gradually making it neutral, while liberating electrons from the positively charged one will make it even more positive, keeping the leaves apart.