William Thomson, 1st Baron Kelvin (1824-1907) was one of the most famous scientists of his age. He was Professor of Natural Philosophy at the University from 1846 to 1899, Dean of Faculties from 1901 to 1903, and served as Chancellor from 1904 to 1907. He stood for Rector, unsuccessfully, in 1899.
Born in Belfast, Thomson moved to Glasgow in 1832 when his father James became Professor of Mathematics. He and his elder brother James (subsequently Professor of Civil and Mechanical Engineering) matriculated to study at the University in 1834, but did not graduate. He went on to study at Peterhouse, Cambridge, and abroad before becoming Professor of Natural Philosophy at the University at the age of twenty-two.
During his 53 years as a professor, Thomson taught some 7,000 students from all over the world, and established an advanced class in mathematical physics and a laboratory in which they could undertake experimental work. The laboratory students worked mainly on problems derived from Kelvin's own scientific and engineering research in electricity, establishing a "school of electrical engineering".
Thomson was as famous for his inventions as for his academic work. He published more than 600 scientific papers during his lifetime and earned international acclaim for proposing an absolute scale of temperature now known as the Kelvin Scale and for his pioneering research in the fields of mechanical energy and heat. He was equally well-known for his work on planning the Trans-Atlantic telegraph cable and his invention of the Kelvin Compass and sounding machine.
Knighted in 1866, Thomson became the first scientist to be elevated to the peerage when he was created Baron Kelvin of Largs in 1892. He is buried in Westminster Abbey.
Friday, August 19, 2011
Saturday, November 13, 2010
What is a Black Hole?
A black hole is what remains when a massive star dies.
If you have read How Stars Work, then you know that a star is a huge, amazing fusion reactor. Because stars are so massive and made out of gas, there is an intense gravitational field that is always trying to collapse the star. The fusion reactions happening in the core are like a giant fusion bomb that is trying to explode the star. The balance between the gravitational forces and the explosive forces is what defines the size of the star.
As the star dies, the nuclear fusion reactions stop because the fuel for these reactions gets burned up. At the same time, the star's gravity pulls material inward and compresses the core. As the core compresses, it heats up and eventually creates a supernova explosion in which the material and radiation blasts out into space. What remains is the highly compressed, and extremely massive,
core. The core's gravity is so strong that even light cannot escape.
Artist concept of a black hole: The arrows show the paths of objects in and around the opening of the black hole.
This object is now a black hole and literally disappears from view. Because the core's gravity is so strong, the core sinks through the fabric of space-time, creating a hole in space-time -- this is why the object is called a black hole.
The core becomes the central part of the black hole called the singularity. The opening of the hole is called the event horizon.
You can think of the event horizon as the mouth of the black hole. Once something passes the event horizon, it is gone for good. Once inside the event horizon, all "events" (points in space-time) stop, and nothing (even light) can escape. The radius of the event horizon is called the Schwarzschild radius, named after astronomer Karl Schwarzschild, whose work led to the theory of black holes
If you have read How Stars Work, then you know that a star is a huge, amazing fusion reactor. Because stars are so massive and made out of gas, there is an intense gravitational field that is always trying to collapse the star. The fusion reactions happening in the core are like a giant fusion bomb that is trying to explode the star. The balance between the gravitational forces and the explosive forces is what defines the size of the star.
As the star dies, the nuclear fusion reactions stop because the fuel for these reactions gets burned up. At the same time, the star's gravity pulls material inward and compresses the core. As the core compresses, it heats up and eventually creates a supernova explosion in which the material and radiation blasts out into space. What remains is the highly compressed, and extremely massive,
core. The core's gravity is so strong that even light cannot escape.
Artist concept of a black hole: The arrows show the paths of objects in and around the opening of the black hole.
This object is now a black hole and literally disappears from view. Because the core's gravity is so strong, the core sinks through the fabric of space-time, creating a hole in space-time -- this is why the object is called a black hole.
The core becomes the central part of the black hole called the singularity. The opening of the hole is called the event horizon.
You can think of the event horizon as the mouth of the black hole. Once something passes the event horizon, it is gone for good. Once inside the event horizon, all "events" (points in space-time) stop, and nothing (even light) can escape. The radius of the event horizon is called the Schwarzschild radius, named after astronomer Karl Schwarzschild, whose work led to the theory of black holes
Sunday, September 5, 2010
What Does General Relativity Mean?
or an analogy to general relativity, consider that you stretched out a bedsheet or piece of elastic flat, attaching the corners firmly to some secured posts. Now you begin placing things of various weights on the sheet. Where you place something very light, the sheet will curve downward under the weight of it a little bit. If you put something heavy, however, the curvature would be even greater.
Assume there's a heavy object sitting on the sheet and you place a second, lighter, object on the sheet. The curvature created by the heavier object will cause the lighter object to "slip" along the curve toward it, trying to reach a point of equilibrium where it no longer moves. (In this case, of course, there are other considerations -- a ball will roll further than a cube would slide, due to frictional effects and such.)
This is similar to how general relativity explains gravity. The curvature of a light object doesn't affect the heavy object much, but the curvature created by the heavy object is what keeps us from floating off into space. The curvature created by the Earth keeps the moon in orbit, but at the same time the curvature created by the moon is enough to affect the tides.
Assume there's a heavy object sitting on the sheet and you place a second, lighter, object on the sheet. The curvature created by the heavier object will cause the lighter object to "slip" along the curve toward it, trying to reach a point of equilibrium where it no longer moves. (In this case, of course, there are other considerations -- a ball will roll further than a cube would slide, due to frictional effects and such.)
This is similar to how general relativity explains gravity. The curvature of a light object doesn't affect the heavy object much, but the curvature created by the heavy object is what keeps us from floating off into space. The curvature created by the Earth keeps the moon in orbit, but at the same time the curvature created by the moon is enough to affect the tides.
Why Do Stars Twinkle?
Stars twinkle because of turbulence in the Earth's atmosphere. You can think as the atmosphere being made up of several "layers." Each layer has a different temperature and density. As the light from a star passes through the atmosphere, it is bent by each layer, and we perceive the twinkling.
The bending of the light when it passes from one medium to another, like water to air, or one layer of air to another, is called refraction. Refraction is what makes a straw look bent when you put it in a glass of water. Refraction also makes the stars and the Sun near the horizon look higher in the sky than they really are. In fact, when the Sun is setting, we are seeing the sun's disk when the Sun is already below the horizon
You will notice that stars closer to the horizon twinkle more; this is because there is a lot more atmosphere between you and a star near the horizon than between you and a star in the zenith (the point directly overhead) . You will also notice that planets do not twinkle. Stars are so far away that they appear as points of light, but planets are much closer and their disks can seen through telescopes. The fluctuations in the atmosphere are not large enough to affect the light coming from the planets, the Moon or the Sun.
The bending of the light when it passes from one medium to another, like water to air, or one layer of air to another, is called refraction. Refraction is what makes a straw look bent when you put it in a glass of water. Refraction also makes the stars and the Sun near the horizon look higher in the sky than they really are. In fact, when the Sun is setting, we are seeing the sun's disk when the Sun is already below the horizon
You will notice that stars closer to the horizon twinkle more; this is because there is a lot more atmosphere between you and a star near the horizon than between you and a star in the zenith (the point directly overhead) . You will also notice that planets do not twinkle. Stars are so far away that they appear as points of light, but planets are much closer and their disks can seen through telescopes. The fluctuations in the atmosphere are not large enough to affect the light coming from the planets, the Moon or the Sun.
Saturday, September 4, 2010
What Does the Large Hadron Collider Do?
What Does the Large Hadron Collider Do?
The LHC circulates a beam of charged particles (specifically hadrons, probably either protons or lead ions) through a tube which maintains a continuous vacuum. The particles are guided through the continuous vacuum within the circular tube using a series of magnetic superconductors which accelerate and guide the charged particles. In order to maintain the superconducting properties of the magnets, they remain supercooled near absolute zero by a massive cryogenic system.
Once the beam reaches its highest energy levels, obtained by steadily increasing the energy as the beam circles repeatedly through the magnets, it will be maintained in a storage ring. This is a loop of tunnel where the magnets will keep circulating the beam so that it retains its kinetic energy, sometimes for hours on end. The beam can then be routed out of the storage ring to be sent into the various testing areas of the LHC.
The beams are expected to obtain energy levels up to 7 TeV (7 x 1012 electronvolts). Since two beams will collide with each other, the energy of the collisions are therefore anticipated to reach 14 TeV from protons.
In addition, by accelerating heavier lead ions, they anticipate collisions with energies in the range of 1,250 TeV ... energy levels on the order of those obtained only moments after the Big Bang. (Not the energies obtained during the Big Bang. The TeV energy scale is about 1016 times smaller than the Planck mass energy scale, for example, which Lee Smolin uses as the top of his particle energy scale in The Trouble with Physics. Presumably, the Big Bang energy levels would have been somewhere on this Planck energy scale or higher, where the quantum physics and general relativity aspects of reality both begin to break down.)
What Is the Large Hadron Collider Looking For?
Since the Large Hadron Collider will be having collisions of such high energy, the hope is that it will release exotic particles which are normally not observed. Any results from the Large Hadron Collider collisions should have a major impact on our understanding of physics, either confirming or refuting the projections from the Standard Model of particle physics.
One major product which is being looked for is the Higgs boson, the last particle from the Standard Model of particle physics that hasn't been observed.
It's also possible that the LHC will create some indicators of the exotic dark matter, which makes up nearly 95% of the universe but cannot be directly observed!
Similarly, there might be some evidence of the extra dimensions predicted by string theory. The fact is that we just don't know until we perform the experiments!
LHC Experiments
There are a variety of ongoing experimental systems built into CERN:
ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid) - these two large, general purpose detectors will be capable of analyzing the particle produced in LHC collisions. Having two such detectors, designed and operated on different principles, allows independent confirmation of the results.
ALICE (A Large Ion Collider Experiment) - this experiment will collide lead ions, creating energies similar to those just after the Big Bang. The hope is to create the quark-gluon plasma believed to have existed at these energy levels.
LHCb (LHC beauty) - this detector specifically looks for the beauty quark, which will allow it to study the differences between matter and antimatter, including why our universe appears to have so much matter and so little antimatter!
TOTEM (TOTal Elastic and diffractive cross section Measurement) - this smaller detector will analyze "forward particles" which only brush past each other instead of having head-on collisions. It will be able to measure the size of the proton, for example, and the luminosity within the LHC.
LHCf (LHC forward) - this small detector also studies forward particles, but analyzes how the cascades of charged particles within the LHC relates to the cosmic rays that bombard the Earth from outer space, helping interpret and calibrate studies of the cosmic rays.
Who Runs the Large Hadron Collider?
The Large Hadron Collider was built by the European Organization for Nuclear Research (CERN). It is staffed by physicists and engineers from around the world. Nations participating in the construction and experiments consist of:
Armenia, Australia, Austria, Azerbaijan Republic, Belarus, Belgium, Brazil, Bulgaria, Canada, China, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Georgia, Germany, Greece, Hungary, India, Israel, Italy, Japan, Korea, Morocco, Netherlands, Norway, Pakistan, Poland, Portugal, Romania, Russia, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, United Kingdom, United States, Uzbekistan
How Much Did It Cost?
The building of the accelerator, including manpower and materials, is 3.03 billion euros - roughly 4 billion U.S. dollars (using conversion from Sept. 4, 2008). On top of this, of course, is the cost of the various experiments and computing power.
How Is It Going?
The Large Hadron Collider originally went online in September of 2008 and, within about a week, had to shut down due to a leak in one of the seals that insulated the supercooled vacuum from the outside world. After about a year of repairs, the LHC went online once again, this time with much more success. In December 2009 it produced beams with an energy of 1.18 TeV each, resulting in collisions of 2.36 TeV - the most powerful experiment ever conducted on Earth. At present, physicists are still analyzing the results of these collisions to discover what the results mean.
The LHC circulates a beam of charged particles (specifically hadrons, probably either protons or lead ions) through a tube which maintains a continuous vacuum. The particles are guided through the continuous vacuum within the circular tube using a series of magnetic superconductors which accelerate and guide the charged particles. In order to maintain the superconducting properties of the magnets, they remain supercooled near absolute zero by a massive cryogenic system.
Once the beam reaches its highest energy levels, obtained by steadily increasing the energy as the beam circles repeatedly through the magnets, it will be maintained in a storage ring. This is a loop of tunnel where the magnets will keep circulating the beam so that it retains its kinetic energy, sometimes for hours on end. The beam can then be routed out of the storage ring to be sent into the various testing areas of the LHC.
The beams are expected to obtain energy levels up to 7 TeV (7 x 1012 electronvolts). Since two beams will collide with each other, the energy of the collisions are therefore anticipated to reach 14 TeV from protons.
In addition, by accelerating heavier lead ions, they anticipate collisions with energies in the range of 1,250 TeV ... energy levels on the order of those obtained only moments after the Big Bang. (Not the energies obtained during the Big Bang. The TeV energy scale is about 1016 times smaller than the Planck mass energy scale, for example, which Lee Smolin uses as the top of his particle energy scale in The Trouble with Physics. Presumably, the Big Bang energy levels would have been somewhere on this Planck energy scale or higher, where the quantum physics and general relativity aspects of reality both begin to break down.)
What Is the Large Hadron Collider Looking For?
Since the Large Hadron Collider will be having collisions of such high energy, the hope is that it will release exotic particles which are normally not observed. Any results from the Large Hadron Collider collisions should have a major impact on our understanding of physics, either confirming or refuting the projections from the Standard Model of particle physics.
One major product which is being looked for is the Higgs boson, the last particle from the Standard Model of particle physics that hasn't been observed.
It's also possible that the LHC will create some indicators of the exotic dark matter, which makes up nearly 95% of the universe but cannot be directly observed!
Similarly, there might be some evidence of the extra dimensions predicted by string theory. The fact is that we just don't know until we perform the experiments!
LHC Experiments
There are a variety of ongoing experimental systems built into CERN:
ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid) - these two large, general purpose detectors will be capable of analyzing the particle produced in LHC collisions. Having two such detectors, designed and operated on different principles, allows independent confirmation of the results.
ALICE (A Large Ion Collider Experiment) - this experiment will collide lead ions, creating energies similar to those just after the Big Bang. The hope is to create the quark-gluon plasma believed to have existed at these energy levels.
LHCb (LHC beauty) - this detector specifically looks for the beauty quark, which will allow it to study the differences between matter and antimatter, including why our universe appears to have so much matter and so little antimatter!
TOTEM (TOTal Elastic and diffractive cross section Measurement) - this smaller detector will analyze "forward particles" which only brush past each other instead of having head-on collisions. It will be able to measure the size of the proton, for example, and the luminosity within the LHC.
LHCf (LHC forward) - this small detector also studies forward particles, but analyzes how the cascades of charged particles within the LHC relates to the cosmic rays that bombard the Earth from outer space, helping interpret and calibrate studies of the cosmic rays.
Who Runs the Large Hadron Collider?
The Large Hadron Collider was built by the European Organization for Nuclear Research (CERN). It is staffed by physicists and engineers from around the world. Nations participating in the construction and experiments consist of:
Armenia, Australia, Austria, Azerbaijan Republic, Belarus, Belgium, Brazil, Bulgaria, Canada, China, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Georgia, Germany, Greece, Hungary, India, Israel, Italy, Japan, Korea, Morocco, Netherlands, Norway, Pakistan, Poland, Portugal, Romania, Russia, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine, United Kingdom, United States, Uzbekistan
How Much Did It Cost?
The building of the accelerator, including manpower and materials, is 3.03 billion euros - roughly 4 billion U.S. dollars (using conversion from Sept. 4, 2008). On top of this, of course, is the cost of the various experiments and computing power.
How Is It Going?
The Large Hadron Collider originally went online in September of 2008 and, within about a week, had to shut down due to a leak in one of the seals that insulated the supercooled vacuum from the outside world. After about a year of repairs, the LHC went online once again, this time with much more success. In December 2009 it produced beams with an energy of 1.18 TeV each, resulting in collisions of 2.36 TeV - the most powerful experiment ever conducted on Earth. At present, physicists are still analyzing the results of these collisions to discover what the results mean.
Friday, September 3, 2010
Photon
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.
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.
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.
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