The Photoelectric Effect
Qualitative description
Shining light on a metal surface causes electrons to be ejected from the surface. This is called the photoelectric effect. This effect was first observed in 1887 by the German physicist Heinrich Hertz.
At that time, the theory that light was a wave was well accepted. Light was well known to undergo such things as interference and diffraction, reinforcing this theory. Based on this, the favoured explanation for the photoelectric effect was that:
Light shining on a surface slowly heats up the particles making up that surface, causing them to emit electrons.
To the surprise of physicists at the time, the results of actual experiments contradicted this.
The behaviour observed was in fact very un-wavelike, and instead could be best explained if the light was considered to be a particle. The following table summarises the discrepancy between the expected and actual observations.
At that time, the theory that light was a wave was well accepted. Light was well known to undergo such things as interference and diffraction, reinforcing this theory. Based on this, the favoured explanation for the photoelectric effect was that:
Light shining on a surface slowly heats up the particles making up that surface, causing them to emit electrons.
To the surprise of physicists at the time, the results of actual experiments contradicted this.
The behaviour observed was in fact very un-wavelike, and instead could be best explained if the light was considered to be a particle. The following table summarises the discrepancy between the expected and actual observations.
Expected observation if light was a wave
Increasing the brightness of the light would increase the temperature of the metal and the kinetic energy of the emitted electrons. If the light used was sufficiently dim, it would take some time for the temperature of the metal to increase enough to emit electrons. The frequency (colour) of the light was not expected to have an effect on the energy of the emitted electrons. |
Actual observation showing particle-like behaviour
Increasing the brightness increased the number of electrons emitted. The kinetic energies of the emitted electrons were unchanged. When using UV light, electrons were emitted almost immediately. Increasing the frequency (colour) of the light increased the energy of the emitted electrons. Furthermore, below a certain frequency, electrons were no longer emitted. |
Quantitative description
The diagram to the right demonstrates an experiment set up to investigate the photoelectric effect.
A light source of a particular intensity and frequency is shone onto an emitting plate. If the right conditions are met, electrons are released from the emitting plate and are collected by the collecting plate.
The plates are connected through a battery. This allows a voltage to be applied between the plates. The effects of this are explored below.
A light source of a particular intensity and frequency is shone onto an emitting plate. If the right conditions are met, electrons are released from the emitting plate and are collected by the collecting plate.
The plates are connected through a battery. This allows a voltage to be applied between the plates. The effects of this are explored below.
Work function ɸ
It takes a certain amount of energy to release an electron from a metal. We call this amount of energy the work function, and give it the symbol ɸ.
The work function is a property of the material being used. It depends on the configurations of atoms at the surface of a material. Below are a few common examples:
The work function is a property of the material being used. It depends on the configurations of atoms at the surface of a material. Below are a few common examples:
MaterialGold
Aluminium
Copper
Carbon
|
Work function (J)8.17⨉10-19 to 8.76⨉10-19
6.51⨉10-19 to 6.83⨉10-19
7.26⨉10-19 to 8.17⨉10-19
~8.01⨉10-19
|
Work function (eV)5.1 to 5.47
4.06 to 4.26
4.53 to 5.10
~5
|
Hopefully the above table should give you some indication for why we will generally prefer to use eV over J when dealing with these kinds of energies!
Maximum kinetic energy of emitted electrons Ek
When light of energy Ek = hf (via the Planck relation) is shone onto a surface of work function ɸ, electrons will be emitted with a range of kinetic energies, due to some electrons in the metal being more bound than others. The maximum kinetic energy of the emitted electrons Ek can be written as...
Ek = hf - ɸ
Cutoff frequency fc
By definition, the work function is the minimum energy required to release an electron from a surface. Considering the Planck relation (E = hf), there must also be a corresponding minimum frequency. We call this frequency the cut-off frequency (or threshold frequency) and give it the symbol fc. It can be written as...
ɸ = h fc
Cutoff voltage V0
A voltage can be applied to the plates such that the emitting plate is positively charged, and the collecting plate is negatively charged. If this voltage is sufficiently high, the electrons will be repelled back to the plate they were emitted from. No electrons would reach the collecting plate and the current would be zero. We call the voltage required to achieve this the cut-off voltage V0.
The amount of work W done on an electron with charge e travelling between two plates of voltage V, is given by the equation W = eV (this equation is derived in the Electrical Systems topic).
If the voltage applied to the plates is equal to the cut-off voltage, the kinetic energy of the electron must equal the work done on the electron by the plates. We can therefore write...
The amount of work W done on an electron with charge e travelling between two plates of voltage V, is given by the equation W = eV (this equation is derived in the Electrical Systems topic).
If the voltage applied to the plates is equal to the cut-off voltage, the kinetic energy of the electron must equal the work done on the electron by the plates. We can therefore write...
Ek = W
Ek = eV0
Ek = eV0
Graphs
Current vs Light intensity
As the amount of photons (light intensity) striking the emitting plate is increased, the amount of electrons being released from the emitting plate also increases.
Because current is by definition the rate of electron flow, more electrons flowing results in an increased current.
Because current is by definition the rate of electron flow, more electrons flowing results in an increased current.
Maximum kinetic energy of electron vs Light frequency
As discussed earlier, the frequency of a photon of light is proportional to its energy. Therefore the higher the frequency of the light, the greater the maximum kinetic energy of the released electrons.
Below the cutoff frequency, the photons of light will not have enough energy to release electrons. In this case, negative kinetic energy represents the energy debt that needs to be paid to release an electron.
The equation for the line is simply the equation Ek = hf - ɸ, introduced earlier. From this equation we see that the slope will be h and the y-intercept will be - ɸ (recall y=mx+c).
Below the cutoff frequency, the photons of light will not have enough energy to release electrons. In this case, negative kinetic energy represents the energy debt that needs to be paid to release an electron.
The equation for the line is simply the equation Ek = hf - ɸ, introduced earlier. From this equation we see that the slope will be h and the y-intercept will be - ɸ (recall y=mx+c).
Current vs Applied voltage
For a negative voltage, the emitting plate would become positive, and the collecting plate would become negative. Electrons would be attracted to the positive emitting plate and repelled from the negative collecting plate. The net effect is that electrons would tend to be drawn back towards emitting plate.
For a high enough voltage no electrons would reach the collecting plate and the current would be zero. As declared earlier, we call this voltage the cut-off voltage V0.
For a positive voltage, the emitting plate would become negative, and the collecting plate would become positive. Electrons would be repelled from the negative emitting plate and attracted to the positive collecting plate. The net effect is that electrons would be accelerated towards the collecting plate.
Although the speed of the electrons will increase for voltages above zero, the rate at which electrons are emitted and collected will remain the same. For this reason, increasing the applied voltage above zero will not change the overall electron flow rate (current).
For a high enough voltage no electrons would reach the collecting plate and the current would be zero. As declared earlier, we call this voltage the cut-off voltage V0.
For a positive voltage, the emitting plate would become negative, and the collecting plate would become positive. Electrons would be repelled from the negative emitting plate and attracted to the positive collecting plate. The net effect is that electrons would be accelerated towards the collecting plate.
Although the speed of the electrons will increase for voltages above zero, the rate at which electrons are emitted and collected will remain the same. For this reason, increasing the applied voltage above zero will not change the overall electron flow rate (current).
Further reading
Image: Light from the sun hitting lunar dust causes it to become charged through the photoelectric effect. The charged dust then repels itself and lifts off the surface of the Moon by electrostatic levitation. This manifests itself almost like an "atmosphere of dust", visible as a thin haze and blurring of distant features, and visible as a dim glow after the sun has set. It is thought that the smallest particles are repelled up to kilometres high, and that the particles move in "fountains" as they charge and discharge (from Wikipedia)