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Lasers

The stimulated emission of light is the crucial quantum process necessary for the operation of a laser.

Population inversion Coherent light

Stimulated EmissionIf an electron is already in an excited state (an upper energy level, in contrast to its lowest possible level or "ground state"), then an incoming photon for which the quantum energy is equal to the energy difference between its present level and a lower level can "stimulate" a transition to that lower level, producing a second photon of the same energy.

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When a sizable population of electrons resides in upper levels, this condition is called a "population inversion", and it sets the stage for stimulated emission of multiple photons. This is the precondition for the light amplification which occurs in a laser, and since the emitted photons have a definite time and phase relation to each other, the light has a high degree of coherence.

Like absorption and emission, stimulated emission requires that the photon energy given by the Planck relationship be equal to the energy separation of the participating pair of quantum energy states.

Interaction of radiation with matterPopulation inversion Coherent light

Quantum ProcessesQuantum properties dominate the fields of atomic and molecular physics. Radiation is quantized such that for a given frequency of radiation, there can be only one value of quantum energy for the photons of that radiation. The energy levels of atoms and molecules can have only certain quantized values. Transitions between these quantized states occur by the photon processes absorption, emission, and stimulated emission. All of these processes require that the photon energy given by the Planck relationship is equal to the energy separation of the participating pair of quantum energy states.

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Interaction of radiation with matter Electromagnetic spectrum

Population InversionThe achievement of a significant population inversion in atomic or molecular energy states is a precondition for laser action. Electrons will normally reside in the lowest available energy state. They can be elevated to excited states by absorption, but no significant collection of electrons can be accumulated by absorption alone since both spontaneous emission and stimulated emission will bring them back down. A population inversion cannot be achieved with just two levels because the probabability for absorption and for spontaneous emission is exactly the same, as shown by Einstein and expressed in the Einstein A and B coefficients. The lifetime of a typical excited state is about 10-8 seconds, so in practical terms, the electrons drop back down by photon emission about as fast as you can pump them up to the upper level. The case of the helium-neon laser illustrates one of the ways of achieving the necessary population inversion.

Characteristics of Laser Light 1. Coherent. Different parts of the laser beam are related to each other inphase. These phase relationships are maintained over long enough time so that interference effects may be seen or recorded photographically. This coherence property is what makes holograms possible.

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2. Monochromatic. Laser light consists of essentially one wavelength,having its origin in stimulated emission from one set of atomic energy levels.

3. Collimated. Because of bouncing back between mirrored ends of a lasercavity, those paths which sustain amplification must pass between the mirrors many times and be very nearly perpendicular to the mirrors. As a result, laser beams are very narrow and do not spread very much.

Coherent LightCoherence is one of the unique properties of laser light. It arises from the stimulated emission process which provides the amplification. Since a common stimulus triggers the emission events which provide the amplified light, the emitted photons are "in step" and have a definite phase relation to each other. This coherence is described in terms of temporal coherence and spatial coherence, both of which are important in producing the interference which is used to produce holograms. Ordinary light is not coherent because it comes from independent atoms which emit on time scales of about 10^-8 seconds. There is a degree of coherence in sources like the mercury green line and some other useful spectral sources, but their coherence does not approach that of a laser.

Monochromatic Laser LightThe light from a laser typically comes from one atomic transition with a single precise wavelength. So the laser light has a single spectral color and is almost the purest monochromatic light available. That being said, however, the laser light is not exactly monochromatic. The spectral emission line from which it originates does have a finite width, if only from the Doppler effect of the moving atoms or molecules from which it comes. Since the wavelength of the light is extremely small compared to the size of the laser cavities used, then within that tiny spectral bandwidth of the emission lines are many resonant modes of the laser cavity.

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Parallel Light from a LaserThe light from a typical laser emerges in an extremely thin beam with very little divergence. Another way of saying this is that the beam is highly "collimated". An ordinary laboratory helium-neon laser can be swept around the room and the red spot on the back wall seems about the same size at that on a nearby wall.

The high degree of collimation arises from the fact that the cavity of the laser has very nearly parallel front and back mirrors which constrain the final laser beam to a path which is perpendicular to those mirrors. The back mirror is made almost perfectly reflecting while the front mirror is about 99% reflecting, letting out about 1% of the beam. This 1% is the output beam which you see. But the light has passed back and forth between the mirrors many times in order to gain intensity by the stimulated emission of more photons at the same wavelength. If the light is the slightest bit off axis, it will be lost from the beam. The highly collimated nature of the laser beam contributes both to its danger and to its usefulness. You should never look directly into a laser beam, because the highly parallel beams can focus to an almost microscopic dot on the retina of your eye, causing almost instant damage to the retina. On the other hand, this capacity for sharp focusing contributes to the both the medical applications and the industrial applications of the laser. In medicine it is used as a sharp scalpel and in industry as a fast, powerful and computer-controllable cutting tool.

Laser ApplicationsMedical applications Welding and Cutting Garment industry Laser printing Heat treatment Laser nuclear fusion Surveying Communication

CDs and optical discs Spectroscopy Barcode scanners Laser cooling

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Medical Uses of LasersThe highly collimated beam of a laser can be further focused to a microscopic dot of extremely high energy density. This makes it useful as a cutting and cauterizing instrument. Lasers are used for photocoagulation of the retina to halt retinal hemorrhaging and for the tacking of retinal tears. Higher power lasers are used after cataract surgery if the supportive membrane surrounding the implanted lens becomes milky. Photodisruption of the membrane often can cause it to draw back like a shade, almost instantly restoring vision. A focused laser can act as an extremely sharp scalpel for delicate surgery, cauterizing as it cuts. ("Cauterizing" refers to long-standing medical practices of using a hot instrument or a high frequency electrical probe to singe the tissue around an incision, sealing off tiny blood vessels to stop bleeding.) The cauterizing action is particularly important for surgical procedures in blood-rich tissue such as the liver. Lasers have been used to make incisions half a micron wide, compared to about 80 microns for the diameter of a human hair.

Welding and CuttingThe highly collimated beam of a laser can be further focused to a microscopic dot of extremely high energy density for welding and cutting. The automobile industry makes extensive use of carbon dioxide lasers with powers up to several kilowatts for computer controlled welding on auto assembly lines. Garmire points out an interesting application of CO2 lasers to the welding of stainless steel handles on copper cooking pots. A nearly impossible task for conventional welding because of the great difference in thermal conductivities between stainless steel and copper, it is done so quickly by the laser that the thermal conductivities are irrelevant.

Surveying and RangingHelium-neon and semiconductor lasers have become standard parts of the field surveyor's equipment. A fast laser pulse is sent to a corner reflector at the point to be measured and the time of reflection is measured to get the distance. Some such surveying is long distance! The Apollo 11 and Apollo 14 astronauts put corner reflectors on the surface of the Moon for determination of the Earth-Moon distance. A powerful laser pulse from the MacDonald Observatory in Texas had spread to about a 3 km radius by the time it got to the Moon, but the reflection was strong enough to be detected. We now know the range from the Moon to Texas within about 15 cm, a nine significant digit measurement. A pulsed ruby laser was used for this measurement.

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Lasers in the Garment IndustryLaser cutters are credited with keeping the U.S. garment industry competitive in the world market. Computer controlled laser garment cutters can be programmed to cut out 400 size 6 and then 700 size 9 garments - and that might involve just a few cuts. The programmed cutter can cut dozens to hundreds of thicknesses of cloth, and can cut out every piece of the garment in a single run. The usefulness of the laser for such cutting operations comes from the fact that the beam is highly collimated and can be further focused to a microscopic dot of extremely high energy density for cutting.

Laser FusionLaser fusion attempts to force nuclear fusion in tiny pellets or microballoons of a deuterium-tritium mixture by zapping them with such a high energy density that they will fuse before they have time to move away from each other. This is an example of inertial confinement. Two experimental laser fusion devices have been developed at Lawrence Livermore Laboratory, called Shiva and Nova. They deliver high power bursts of lase light from multiple lasers onto a small deuterium-tritium target. These lasers are neodynium glass lasers which are capable of extremely high power pulses.

Lasers in CommunicationFiber optic cables are a major mode of communication partly because multiple signals can be sent with high quality and low loss by light propagating along the fibers. The light signals can be modulated with the information to be sent by either light emitting diodes or lasers. The lasers have significant advantages because they are more nearly monochromatic and this allows the pulse shape to be maintained better over long distances. If a better pulse shape can be maintained, then the communication can be sent at higher rates without overlap of the pulses. Ohanian quotes a factor of 10 advantage for the laser modulators. Telephone fiber drivers may be solid state lasers the size of a grain of sand and consume a power of only half a milliwatt. Yet they can sent 50 million pulses per second into an attached telephone fiber and encode over 600 simultaneous telephone conversations (Ohanian).

Laser Printers7

The laser printer has in a few years become the dominant mode of printing in offices. It employs a semiconductor laser and the xerography principle. The laser is focused and scanned across a photoactive selenium coated drum where it produces a charge pattern which mirrors the material to be printed. This drum then holds the particles of the toner to transfer to paper which is rolled over the drum in the presence of heat. The typical laser for this application is the aluminum-gallium-arsenide (AlGaAs) laser at 760 nm wavelength, just into the infrared.

Compact Disc AudioAnalog sound data is digitized by sampling at 44.1 kHz and coding as binary numbers in the pits on the compact disc. As the focused laser beam sweeps over the pits, it reproduces the binary numbers in the detection circuitry. The same function as the "pits" can be accomplished by magnetooptical recording. The digital signal is then reconverted to analog form by a D/A converter. The tracks on a compact disc are nominally spaced by 1.6 micrometers, close enough that they are able to separate reflected light into it's component colors like a diffraction grating. This is an active graphic. Click on any bold text for further details.

Laser SpectroscopyAbsorption spectroscopy usually implies having a tunable frequency source and producing a plot of absorption as a function of frequency. This was not feasible with

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lasers until the advent of the dye lasers which can be tuned over a nearly continuous range of frequencies. Laser spectroscopy has led to advances in the precision with which spectral line frequencies can be measured, and this has fundamental significance for our understanding of basic atomic processes. This precision has been obtained by passing two laser beams through the absorption sample in opposite directions, selectively triggering absorption only in those atoms that have a zero velocity component in the direction of the beams. This effectively eliminates the Doppler broading of spectral lines from the distribution of atomic velocities present in the sample.

Heat TreatmentHeat treatments for hardening or annealing have been long practiced in metallurgy. But lasers offer some new possibilities for selective heat treatments of metal parts. For example, lasers can provide localized heat treatments such as the hardening of the surfaces of automobile camshafts. These shafts are manufactured to high precision, and if the entire camshaft is heat treated, some warping will inevitably occur. But the working surfaces of the cams can be heated quickly with a carbon dioxide laser and hardened without appreciably affecting the remainder of the shaft, preserving the precision of manufacture.

Barcode ScannersSupermarket scanners typically use helium-neon lasers to scan the universal barcodes to identify products. The laser beam bounces off a rotating mirror and scans the code, sending a modulated beam to a light detector and then to a computer which has the product information stored. Semiconductor lasers can also be used for this purpose.

Helium-Neon Laser

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The most common and inexpensive gas laser, the helium-neon laser is usually constructed to operate in the red at 632.8 nm. It can also be constructed to produce laser action in the green at 543.5 nm and in the infrared at 1523 nm. One of the excited levels of helium at 20.61 eV is very close to a level in neon at 20.66 eV, so close in fact that upon collision of a helium and a neon atom, the energy can be transferred from the helium to the neon atom. Helium-neon lasers are common in the introductory physics laboratories, but they can still be dangerous! According to Garmire, an unfocused 1-mW HeNe laser has a brightness equal to sunshine on a clear day (0.1 watt/cm^2) and is just as dangerous to stare at directly. The helium gas in the laser tube provides the pumping medium to attain the necessary population inversion for laser action.

Helium-Neon LaserThe most common and inexpensive gas laser, the helium-neon laser is usually constructed to operate in the red at 632.8 nm. It can also be constructed to produce laser action in the green at 543.5 nm and in the infrared at 1523 nm.

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The collimation of the beam is accomplished by mirrors on each end of the evacuated glass tube which contains about 85% helium and 15% neon gas at 1/300 atmospheres pressure (Metrologic). These mirrors could be both flat, but this requires great precision in alignment, so the common laboratory He-Ne lasers are manufactured with the semiconfocal mirror arrangement shown.

The helium gas in the laser tube provides the pumping medium to attain the necessary population inversion for laser action.

Neodynium-YAG LaserAn example of a solid-state laser, the neodynium-YAG uses the Nd3+ ion to dope the yttrium-aluminum-garnet (YAG) host crystal to produce the triplet geometry which makes population inversion possible. Neodynium-YAG lasers have become very important because they can be used to produce high powers. Such lasers have been constructed to produce over a kilowatt of continuous laser power at 1065 nm and can achieve extremely high powers in a pulsed mode. Neodynium-YAG lasers are used in pulse mode in laser oscillators for the production of a series of very short pulses for research with femtosecond time resolution.

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Carbon Dioxide LaserThe carbon dioxide gas laser is capable of continuous output powers above 10 kilowatts. It is also capable of extremely high power pulse operatin. It exhibits laser action at several infrared frequencies but none in the visible. Operating in a manner similar to the helium-neon laser, it employs an electric discharge for pumping, using a percentage of nitrogen gas as a pumping gas. The CO2 laser is the most efficient laser, capable of operating at more than 30% efficiency. That's a lot more efficient than an ordinary incandescent light bulb at producing visible light (about 90% of the output of a lightbulb filament is invisible). The carbon dioxide laser finds many applications in industry, particularly for welding and cutting.

Argon LaserThe argon ion laser can be operated as a continuous gas laser at about 25 different wavelengths in the visible between 408.9 and 686.1nm, but is best known for its most efficient transitions in the green at 488 nm and 514.5 nm. Operating at much higher powers than the helium-neon gas laser, it is not uncommon to achieve 30 to 100 watts of continuous power using several transitions. This output is produced in a hot plasma and takes extremely high power, typically 9 to 12 kW, so these are large and expensive devices.

Ruby LaserThe ruby laser is the first type of laser actually constructed, first demonstrated in 1960 by T. H. Maiman. The ruby mineral (corundum) is aluminum oxide with a small amount(about 0.05%) of chromium which gives it its characteristic pink or red color by absorbing green and blue light. The ruby laser is used as a pulsed laser, producing red light at 694.3 nm. After receiving a pumping flash from the flash tube, the laser light emerges for as long as the excited atoms persist in the ruby rod, which is typically about a millisecond.

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A pulsed ruby laser was used for the famous laser ranging experiment which was conducted with a corner reflector placed on the Moon by the Apollo astronauts. This determined the distance to the Moon with an accuracy of about 15 cm.

Laser DiodesLaser action (with the resultant monochromatic and coherent light output) can be achieved in a p-n junction formed by two doped gallium arsenide layers. The two ends of the structure need to be optically flat and parallel with one end mirrored and one partially reflective. The length of the junction must be precisely related to the wavelength of the light to be emitted. The junction is forward biased and the recombination process produces light as in the LED (incoherent). Above a certain current threshold the photons moving parallel to the junction can stimulate emission and initiate laser action. Type GaAs Peak Power Wavelength Application 5 mW 840 nm 760 nm 1300 nm CD Players Laser printers Fiber communications

AlGaAs 50 mW GaInAsP 20 mW

Eximer LasersEximer is a shortened form of "excited dimer", denoting the fact that the lasing medium in this type of laser is an excited diatomic molecule. These lasers typically produce ultraviolet pulses. They are under investigation for use in communicating with submarines by conversion to blue-green light and pulsing from overhead satellites through sea water to submarines below. The eximers used are typically those formed by rare gases and halogens in electronexcited gas discharges. Molecules like XeF are stable only in their excited states and quickly dissociate when they make the transition to their ground state. This makes 13

possible large population inversions because the ground state is depleted by this dissociation. However, the excited states are very short-lived compared to other laser metastable states, and lasers like the XeF eximer laser require high pumping rates. Eximer lasers typically produce high power pulse outputs in the blue or ultraviolet after excitation by fast electron-beam discharges.

Free-Electron LaserThe radiation from a free-electron laser is produced from free electrons which are forced to oscillate in a regular fashion by an applied field. They are therefore more like synchrotron light sources or microwave tubes than like other lasers. They are able to produce highly coherent, collimated radiation over a wide range of frequencies. The magnetic field arrangement which produces the alternating field is commonly called a "wiggler" magnet.

The free-electron laser is a highly tunable device which has been used to generate coherent radiation from 10^-5 to 1 cm in wavelength. In some parts of this range, they are the highest power source. Particularly in the mm wave range, the FELs exceed all other sources in coherent power. FELs involve relativistic electron beams propagating in a vacuum and can be tuned continuously, filling in frequency ranges which are not reachable by other coherent sources. Applications of free-electron lasers are envisioned in isotope separation, plasma heating for nuclear fusion, long-range, high resolution radar, and particle acceleration in accelerators.

Laser SpectroscopyAbsorption spectroscopy usually implies having a tunable frequency source and producing a plot of absorption as a function of frequency. This was not feasible with lasers until the advent of the dye lasers which can be tuned over a nearly continuous range of frequencies. Laser spectroscopy has led to advances in the precision with which spectral line frequencies can be measured, and this has fundamental significance for our understanding 14

of basic atomic processes. This precision has been obtained by passing two laser beams through the absorption sample in opposite directions, selectively triggering absorption only in those atoms that have a zero velocity component in the direction of the beams. This effectively eliminates the Doppler broading of spectral lines from the distribution of atomic velocities present in the sample.

You may click on any of the types of radiation for more detail about its particular type of interaction with matter. The different parts of the electromagnetic spectrum have very different effects upon interaction with matter. Starting with low frequency radio waves, the human body is quite transparent. (You can listen to your portable radio inside your home since the waves pass freely through the walls of your house and even through the person beside you!) As you move upward through microwaves and infrared to visible light, you absorb more and more strongly. In the lower ultraviolet range, all the uv from the sun is absorbed in a thin outer layer of your skin. As you move further up into the xray region of the spectrum, you become transparent again, because most of the mechanisms for absorption are gone. You then absorb only a small fraction of the radiation, but that absorption involves the more violent ionization events. Each portion of the electromagnetic spectrum has quantum energies appropriate for the excitation of certain types of physical processes. The energy levels for all physical processes at the atomic and molecular levels are quantized, and if there are no available quantized energy levels with spacings which match the quantum energy of the incident radiation, then the material will be transparent to that radiation, and it will pass through.

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Microwaves, RadarWhile there are some radar bands from 1,300 to 1,600 MHz, most microwave applications fall in the range 3,000 to 30,000 MHz (3-30 GHz). Current microwave ovens operate at a nominal frequency of 2450 MHz, a band assigned by the FCC. There are also some amateur and radio navigation uses of the 3-30 GHz range. In interactions with matter, microwave radiation primarily acts to set produce molecular rotation and torsion, which manifests itself by heat. Molecular structure information can be obtained from the analysis of molecular rotational spectra, the most precise way to determine bond lengths and angles of molecules. Microwave radiation is also used in electron spin resonance spectroscopy. For microwave ovens and some radar applications, the microwaves are produced by magnetrons. Frequencies: 1.6-30 GHz Wavelengths: 187 - 10 mm Quantum energies: 0.66 x 10-5 - 0.12 x 10-3 eV

The Electromagnetic SpectrumClick on any part of the spectrum for further detail.

Speed of light

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InfraredThe term "infrared" refers to a broad range of frequencies, beginning at the top end of those frequencies used for communication and extending up the the low frequency (red) end of the visible spectrum. The wavelength range is from about 1 millimeter down to 750 nm. The range adjacent to the visible spectrum is called the "near infrared" and the longer wavelength part is called "far infrared". In interactions with matter, infrared primarily acts to set molecules into vibration. Infrared spectrometers are widely used to study the vibrational spectra of molecules. Frequencies: .003 - 4 x 1014 Hz Wavelengths: 1 mm - 750 nm Quantum energies: 0.0012 - 1.65 eV

Visible LightThe narrow visible part of the electromagnetic spectrum corresponds to the wavelengths near the maximum of the Sun's radiation curve. In interactions with matter, visible light primarily acts to set elevate electrons to higher energy levels. White light may be separated into its spectral colors by dispersion in a prism.

Frequencies: 4 - 7.5 x 1014 Hz

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Wavelengths: 750 - 400 nm Quantum energies: 1.65 - 3.1 eV

Electromagnetic spectrum

UltravioletThe region just below the visible in wavelength is called the near ultraviolet. It is absorbed very strongly by most solid substances, and even absorbed appreciably by air. The shorter wavelengths reach the ionization energy for many molecules, so the far ultraviolet has some of the dangers attendent to other ionizing radiation. The tissue effects of ultraviolet include sunburn, but can have some therapeutic effects as well. The sun is a strong source of ultraviolet radiation, but atmospheric absorption eliminates most of the shorter wavelengths. The eyes are quite susceptible to damage from ultraviolet radiation. Welders must wear protective eye shields because of the uv content of welding arcs can inflame the eyes. Snow-blindness is another example of uv inflamation; the snow reflects uv while most other substances absorb it strongly. Frequencies: 7.5 x 1014 - 3 x 1016 Hz Wavelengths: 400 nm - 10 nm Quantum energies: 3.1 - 124 eV

X-RaysX-ray was the name given to the highly penetrating rays which emanated when high energy electrons struck a metal target. Within a short time of their discovery, they were being used in medical facilities to image broken bones. We now know that they are high frequency electromagnetic rays which are produced when the electrons are suddenly decelerated - these rays are called bremsstrahlung radiation, or "braking radiation". Xrays are also produced when electrons make transitions between lower atomic energy levels in heavy elements. X-rays produced in this way have have definite energies just like other line spectra from atomic electrons. They are called characteristic x-rays since they have energies determined by the atomic energy levels. In interactions with matter, x-rays are ionizing radiation and produce physiological effects which are not observed with any exposure of non-ionizing radiation, such as the risk of mutations or cancer in tissue.

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X-rays are part of the

Frequencies: 3 x 1016 Hz upward Wavelengths: 10 nm - > downward Quantum energies: 124 eV -> upward

Electromagnetic spectrum

Absorption and EmissionTaking the electron transitions associated with visible and ultraviolet interactions with matter as an example, absorption of a photon will occur only when the quantum energy of the photon precisely matches the energy gap between the initial and final states. In the interaction of radiation with matter, if there is no pair of energy states such that the photon energy can elevate the system from the lower to the upper state, then the matter will be transparent to that radiation.

Photons: The Quanta of LightAccording to the Planck hypothesis, all electromagnetic radiation is quantized and occurs in finite "bundles" of energy which we call photons. The quantum of energy for a photon is not Planck's constant h itself, but the product of h and the frequency. The quantization implies that a photon of blue light of given frequency or wavelength will always have the same size quantum of energy. For example, a photon of blue light of wavelength 450 nm will always have 2.76 eV of energy. It occurs in quantized chunks of 2.76 eV, and you can't have half a photon of blue light - it always occurs in precisely the same sized energy chunks. But the frequency available is continuous and has no upper or lower bound, so there is no finite lower limit or upper limit on the possible energy of a photon. On the upper side, there are practical limits because you have limited mechanisms for creating really high energy photons. Low energy photons abound, but when you get below radio frequencies, the photon energies are so tiny compared to room temperature thermal energy that you really never see them as distinct quantized entities - they are swamped in the background.

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Another way to say it is that in the low frequency limits, things just blend in with the classical treatment of things and a quantum treatment is not necessary.

The Photoelectric EffectThe remarkable aspects of the photoelectric effect when it was first observed were: 1. The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

The details of the photoelectric effect were in direct contradiction to the expectations of very well developed classical physics. The explanation marked one of the major steps toward quantum theory.

Photoelectric Effect

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Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light. This showed that whatever was knocking the electrons out had an energy proportional to light frequency. The remarkable fact that the ejection energy was independent of the total energy of illumination showed that the interaction must be like that of a particle which gave all of its energy to the electron! This fit in well with Planck's hypothesis that light in the blackbody radiation experiment could exist only in discrete bundles with energy

E = hExperiment

Photoelectric Effect

Most commonly observed phenomena with light can be explained by waves. But the photoelectric effect suggested a particle nature for light.

Spectral ColorsIn a rainbow or the separation of colors by a prism we see the continuous range of spectral colors (the visible spectrum). A spectral color is composed of a single 21

wavelength and can be correlated with wavelength as shown in the chart below ( a general guide and not a precise statement about color). It is safe enough to say that monochromatic light like the helium-neon laser is red (632 nm) or that the 3-2 transition from the hydrogen spectrum is red ( 656 nm) because they fall in the appropriate wavelength range. But most colored objects give off a range of wavelengths and the characterization of color is much more than the statement of wavelength. Perceived colors can be mapped on a chromaticity diagram.

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