Under the photon theory of light, a photon is a discrete bundle (or quantum) of electromagnetic (or light) energy. Photons are always in motion and, in a vacuum, have a constant speed of light to all observers, at the vacuum speed of light (more commonly just called the speed of light) of c = 2.998 x 108 m/s.
Basic Properties of Photons
According to the photon theory of light, photons . . .
move at a constant velocity, c = 2.9979 x 108 m/s (i.e. "the speed of light"), in free space
have zero mass and rest energy.
carry energy and momentum, which are also related to the frequency nu and wavelength lamdba of the electromagnetic wave by E = h nu and p = h / lambda.
can be destroyed/created when radiation is absorbed/emitted.
can have particle-like interactions (i.e. collisions) with electrons and other particles, such as in the Compton effect.
History of Photons
The term photon was coined by Gilbert Lewis in 1926, though the concept of light in the form of discrete particles had been around for centuries and had been formalized in Newton's construction of the science of optics.
In the 1800s, however, the wave properties of light (by which I mean electromagnetic radiation in general) became glaringly obvious and scientists had essentially thrown the particle theory of light out the window. It wasn't until Albert Einstein explained the photoelectric effect and realized that light energy had to be quantized that the particle theory returned.
Wave-Particle Duality in Brief
As mentioned above, light has properties of both a wave and a particle. This was an astounding discovery and is certainly outside the realm of how we normally perceive things. Billiard balls act as particles, while oceans act as waves. Photons act as both a wave and a particle all the time (even though it's common, but basically incorrect, to say that it's "sometimes a wave and sometimes a particle" depending upon which features are more obvious at a given time).
Just one of the effects of this wave-particle duality (or particle-wave duality) is that photons, though treated as particles, can be calculated to have frequency, wavelength, amplitude, and other properties inherent in wave mechanics.
Fun Photon Facts
The photon is an elementary particle, despite the fact that it has no mass. It cannot decay on its own, although the energy of the photon can transfer (or be created) upon interaction with other particles. Photons are electrically neutral and are one of the rare particles that are identical to their antiparticle, the antiphoton.
Photons are spin-1 particles (making them bosons), with a spin axis that is parallel to the direction of travel (either forward or backward, depending on whether it's a "left-hand" or "right-hand" photon). This feature is what allows for polarization of light.
Friday, September 3, 2010
What is the Photoelectric Effect?
Though originally observed in 1839, the photoelectric effect was documented by Heinrich Hertz in 1887 in a paper to the Annalen der Physik. It was originally called the Hertz effect, in fact, though this name fell out of use.
When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons). This is depicted in the image to the right.
Setting Up the Photoelectric Effect
To observe the photoelectric effect, you create a vacuum chamber with the photoconductive metal at one end and a collector at the other. When a light shines on the metal, the electrons are released and move through the vacuum toward the collector. This creates a current in the wires connecting the two ends, which can be measured with an ammeter. (A basic example of the experiment can be seen by clicking on the image to the right, and then advancing to the second image available.)
By administering a negative voltage potential (the black box in the picture) to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential Vs, and can be used to determine the maximum kinetic energy Kmax of the electrons (which have electronic charge e) by using the following equation:
Kmax = eVs
It is significant to note that not all of the electrons will have this energy, but will be emitted with a range of energies based upon the properties of the metal being used. The above equation allows us to calculate the maximum kinetic energy or, in other words, the energy of the particles knocked free of the metal surface with the greatest speed, which will be the trait that is most useful in the rest of this analysis.
The Classical Wave Explanation
In classical wave theory, the energy of electromagnetic radiation is carried within the wave itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal. The minimum energy needed to remove the electron is the work function phi of the material. (Phi is in the range of a few electron-volts for most common photoelectric materials.)
Three main predictions come from this classical explanation:
The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.
The photoelectric effect should occur for any light, regardless of frequency or wavelength.
There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.
The Experimental Result
By 1902, the properties of the photoelectric effect were well documented. Experiment showed that:
The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons.
Below a certain frequency, the photoelectric effect does not occur at all.
There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.
As you can tell, these three results are the exact opposite of the wave theory predictions. Not only that, but they are all three completely counter-intuitive. Why would low-frequency light not trigger the photoelectric effect, since it still carries energy? How do the photoelectrons release so quickly? And, perhaps most curiously, why does adding more intensity not result in more energetic electron releases? Why does the wave theory fail so utterly in this case, when it works so well in so many other situation Einstein's Wonderful Year
In 1905, Albert Einstein published four papers in the Annalen der Physik journal, each of which was significant enough to warrant a Nobel Prize in its own right. The first paper (and the only one to actually be recognized with a Nobel) was his explanation of the photoelectric effect.
Building on Max Planck's blackbody radiation theory, Einstein proposed that radiation energy is not continuously distributed over the wavefront, but is instead localized in small bundles (later called photons). The photon's energy would be associated with its frequency (nu), through a proportionality constant known as Planck's constant (h), or alternately, using the wavelength (lambda) and the speed of light (c):
E = h nu = hc / lambda
or the momentum equation: p = h / lambda
In Einstein's theory, a photoelectron releases as a result of an interaction with a single photon, rather than an interaction with the wave as a whole. The energy from that photon transfers instantaneously to a single electron, knocking it free from the metal if the energy (which is, recall, proportional to the frequency nu) is high enough to overcome the work function (phi) of the metal. If the energy (or frequency) is too low, no electrons are knocked free.
If, however, there is excess energy, beyond phi, in the photon, the excess energy is converted into the kinetic energy of the electron:
Kmax = h nu - phi
Therefore, Einstein's theory predicts that the maximum kinetic energy is completely independent of the intensity of the light (because it doesn't show up in the equation anywhere). Shining twice as much light results in twice as many photons, and more electrons releasing, but the maximum kinetic energy of those individual electrons won't change unless the energy, not the intensity, of the light changes.
The maximum kinetic energy results when the least-tightly-bound electrons break free, but what about the most-tightly-bound ones; The ones in which there is just enough energy in the photon to knock it loose, but the kinetic energy that results in zero? Setting Kmax equal to zero for this cutoff frequency (nuc), we get:
nuc = phi / h
or the cutoff wavelength: lambdac = hc / phi
These equations indicate why a low-frequency light source would be unable to free electrons from the metal, and thus would produce no photoelectrons.
After Einstein
Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, and his work confirmed Einstein's theory. Einstein won a Nobel Prize for his photon theory (as applied to the photoelectric effect) in 1921, and Millikan won a Nobel in 1923 (in part due to his photoelectric experiments).
Most significantly, the photoelectric effect, and the photon theory it inspired, crushed the classical wave theory of light. Though no one could deny that light behaved as a wave, after Einstein's first paper, it was undeniable that it was also a particle.
When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons). This is depicted in the image to the right.
Setting Up the Photoelectric Effect
To observe the photoelectric effect, you create a vacuum chamber with the photoconductive metal at one end and a collector at the other. When a light shines on the metal, the electrons are released and move through the vacuum toward the collector. This creates a current in the wires connecting the two ends, which can be measured with an ammeter. (A basic example of the experiment can be seen by clicking on the image to the right, and then advancing to the second image available.)
By administering a negative voltage potential (the black box in the picture) to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential Vs, and can be used to determine the maximum kinetic energy Kmax of the electrons (which have electronic charge e) by using the following equation:
Kmax = eVs
It is significant to note that not all of the electrons will have this energy, but will be emitted with a range of energies based upon the properties of the metal being used. The above equation allows us to calculate the maximum kinetic energy or, in other words, the energy of the particles knocked free of the metal surface with the greatest speed, which will be the trait that is most useful in the rest of this analysis.
The Classical Wave Explanation
In classical wave theory, the energy of electromagnetic radiation is carried within the wave itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal. The minimum energy needed to remove the electron is the work function phi of the material. (Phi is in the range of a few electron-volts for most common photoelectric materials.)
Three main predictions come from this classical explanation:
The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.
The photoelectric effect should occur for any light, regardless of frequency or wavelength.
There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.
The Experimental Result
By 1902, the properties of the photoelectric effect were well documented. Experiment showed that:
The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons.
Below a certain frequency, the photoelectric effect does not occur at all.
There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.
As you can tell, these three results are the exact opposite of the wave theory predictions. Not only that, but they are all three completely counter-intuitive. Why would low-frequency light not trigger the photoelectric effect, since it still carries energy? How do the photoelectrons release so quickly? And, perhaps most curiously, why does adding more intensity not result in more energetic electron releases? Why does the wave theory fail so utterly in this case, when it works so well in so many other situation Einstein's Wonderful Year
In 1905, Albert Einstein published four papers in the Annalen der Physik journal, each of which was significant enough to warrant a Nobel Prize in its own right. The first paper (and the only one to actually be recognized with a Nobel) was his explanation of the photoelectric effect.
Building on Max Planck's blackbody radiation theory, Einstein proposed that radiation energy is not continuously distributed over the wavefront, but is instead localized in small bundles (later called photons). The photon's energy would be associated with its frequency (nu), through a proportionality constant known as Planck's constant (h), or alternately, using the wavelength (lambda) and the speed of light (c):
E = h nu = hc / lambda
or the momentum equation: p = h / lambda
In Einstein's theory, a photoelectron releases as a result of an interaction with a single photon, rather than an interaction with the wave as a whole. The energy from that photon transfers instantaneously to a single electron, knocking it free from the metal if the energy (which is, recall, proportional to the frequency nu) is high enough to overcome the work function (phi) of the metal. If the energy (or frequency) is too low, no electrons are knocked free.
If, however, there is excess energy, beyond phi, in the photon, the excess energy is converted into the kinetic energy of the electron:
Kmax = h nu - phi
Therefore, Einstein's theory predicts that the maximum kinetic energy is completely independent of the intensity of the light (because it doesn't show up in the equation anywhere). Shining twice as much light results in twice as many photons, and more electrons releasing, but the maximum kinetic energy of those individual electrons won't change unless the energy, not the intensity, of the light changes.
The maximum kinetic energy results when the least-tightly-bound electrons break free, but what about the most-tightly-bound ones; The ones in which there is just enough energy in the photon to knock it loose, but the kinetic energy that results in zero? Setting Kmax equal to zero for this cutoff frequency (nuc), we get:
nuc = phi / h
or the cutoff wavelength: lambdac = hc / phi
These equations indicate why a low-frequency light source would be unable to free electrons from the metal, and thus would produce no photoelectrons.
After Einstein
Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, and his work confirmed Einstein's theory. Einstein won a Nobel Prize for his photon theory (as applied to the photoelectric effect) in 1921, and Millikan won a Nobel in 1923 (in part due to his photoelectric experiments).
Most significantly, the photoelectric effect, and the photon theory it inspired, crushed the classical wave theory of light. Though no one could deny that light behaved as a wave, after Einstein's first paper, it was undeniable that it was also a particle.
Albert Einstein - Biography
Nationality: German
Born: March 14, 1879
Death: April 18, 1955
Spouse:
Mileva Maric (1903 - 1919)
Elsa Lowenthal (1919 - 1936)
1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" (from the official Nobel Prize announcement)
Albert Einstein - Early Work:
In 1901, Albert Einstein received his diploma as a teacher of physics and mathematics. Unable to find a teaching position, he went to work for the Swiss Patent Office. He obtained his doctoral degree in 1905, the same year he published four significant papers, introducing the concepts of special relativity and the photon theory of light.
Albert Einstein & Scientific Revolution:
Albert Einstein's work in 1905 shook the world of physics. In his explanation of the photoelectric effect he introduced the photon theory of light. In his paper "On the Electrodynamics of Moving Bodies," he introduced the concepts of special relativity.
Einstein spent the rest of his life and career dealing with the consequences of these concepts, both by developing general relativity and by questioning the field of quantum physics on the principle that it was "spooky action at a distance."
Albert Einstein Moves to America:
In 1933, Albert Einstein renounced his German citizenship and moved to America, where he took a post at the Institute for Advanced Study in Princeton, New Jersey, as a Professor of Theoretical Physics. He gained American citizenship in 1940.
He was offered the first presidency of Israel, but he declined it, though he did help found the Hebrew University of Jerusalem.
Misconceptions About Albert Einstein:
The rumor began circulating even while Albert Einstein was alive that he had failed mathematics courses as a child. While it is true that Einstein began to talk late - at about age 4 according to his own accounts - he never failed in mathematics, nor did he do poorly in school in general. He did fairly well in his mathematics courses throughout his education and briefly considered becoming a mathematician. He recognized early on that his gift was not in pure mathematics, a fact he lamented throughout his career as he sought out more accomplished mathematicians to assist in the formal descriptions of his theories.
Born: March 14, 1879
Death: April 18, 1955
Spouse:
Mileva Maric (1903 - 1919)
Elsa Lowenthal (1919 - 1936)
1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" (from the official Nobel Prize announcement)
Albert Einstein - Early Work:
In 1901, Albert Einstein received his diploma as a teacher of physics and mathematics. Unable to find a teaching position, he went to work for the Swiss Patent Office. He obtained his doctoral degree in 1905, the same year he published four significant papers, introducing the concepts of special relativity and the photon theory of light.
Albert Einstein & Scientific Revolution:
Albert Einstein's work in 1905 shook the world of physics. In his explanation of the photoelectric effect he introduced the photon theory of light. In his paper "On the Electrodynamics of Moving Bodies," he introduced the concepts of special relativity.
Einstein spent the rest of his life and career dealing with the consequences of these concepts, both by developing general relativity and by questioning the field of quantum physics on the principle that it was "spooky action at a distance."
Albert Einstein Moves to America:
In 1933, Albert Einstein renounced his German citizenship and moved to America, where he took a post at the Institute for Advanced Study in Princeton, New Jersey, as a Professor of Theoretical Physics. He gained American citizenship in 1940.
He was offered the first presidency of Israel, but he declined it, though he did help found the Hebrew University of Jerusalem.
Misconceptions About Albert Einstein:
The rumor began circulating even while Albert Einstein was alive that he had failed mathematics courses as a child. While it is true that Einstein began to talk late - at about age 4 according to his own accounts - he never failed in mathematics, nor did he do poorly in school in general. He did fairly well in his mathematics courses throughout his education and briefly considered becoming a mathematician. He recognized early on that his gift was not in pure mathematics, a fact he lamented throughout his career as he sought out more accomplished mathematicians to assist in the formal descriptions of his theories.
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