OBJECTIVES After you have finished this lesson you should understand and know about * emission and absorption of light by atoms and molecules. * reflection, absorption, transmission, and scattering of light. * PlanckÕs relationship between energy and frequency. * potential energy, kinetic energy, and total energy. * energy levels and bands. * emission, absorption, and incandescence and the measurement of spectra. * lifetimes of excited states, fluorescence, and phosphorescence. * stimulated and spontaneous emission of photons. * coherent light and lasers. * electronic, vibrational, and rotational energy levels. * microwave, infrared, visible, and ultraviolet spectra. * color. * measuring the size of the universe with spectra. Free atoms are spheres of constantly vibrating electron standing wave patterns with a very small core of dense material, a core that is constituted of constantly vibrating neutron and proton standing wave patterns. One can think of an atom as a musical instrument that is constantly playing. A musical instrument can only be heard when it interacts with its surroundings, causing sound waves to propagate outwards; analogously the effect of the vibrating electrons in the atoms can only be observed when they interact with their surroundings. Instead of interacting with air or other matter producing sound, the vibrations interact with electromagnetic fields (i.e., light), and instead of hearing the music atoms play, we see them! We saw in the last unit that objects could be forced to vibrate at their natural frequencies by resonating with an external vibration. The resonance condition was that the frequency of the external vibration must be equal to the difference of the natural frequency at which the object is vibrating and a higher natural frequency. If the object was not initially vibrating, we say that the initial natural frequency was zero. The electrons surrounding nuclei are always vibrating with a non-zero frequency. If a beam of light hits an atom or a molecule and satisfies the resonance condition, it will cause one of the electronic standing waves to form a standing wave pattern at a higher frequency. The probability that the incident light wave, in other words photon, hits the atom or molecule in just the right way to produce this excitation is related to the intensity of the light wave. This is directly proportional to the amplitude of the wave or the number of photons in the light beam. The high frequency natural electronic vibrations are at a higher energy than the lower ones. To produce new standing wave patterns, the photon does work (i.e., applies force), thus using up all of its energy. Hence, once the electrons are vibrating at a higher natural frequency, the photon no longer exists! It has been completely absorbed by the atom or molecule. Once an atom or molecule has been excited to a higher energy state, it will want to deexcite to a lower energy state; that is, the excited electron will want to reform a standing wave pattern at a lower frequency. When this occurs, it will emit a package of electromagnetic energy, a photon, with a frequency that equals the difference between the excited frequency and the frequency of the lower energy standing wave pattern. The direction in which this photon is emitted is often quite random. Invariably a light beam comes in contact with many atoms or molecules, not just one. If the atoms/molecules are densely packed, as in a solid or liquid, photons emitted towards to the bulk of the material, away from the surface, will be alternatively absorbed then remitted in a chaotic journey, continually being bounced around. This is called scattering of light and accounts for the attenuation of the light intensityÑin other words, the bulk absorption of the light in material. The light emitted backwards towards the light source is the reflected light. If the incident light does not match any of the natural frequencies of the electronic standing wave patterns of the material, it will pass through the material without interacting and the material is said to be transparent to that frequency of light, which is thus transmitted through the material. It is also possible that a small portion of the light absorbed by the material could be transmitted through the material, especially if the material is thin. But the probability of such transmission is low. In 1902 Max Planck postulated that energy was related to frequency in the following manner E = hu where E is the total energy of the object, u the frequency associated with that energy, and h is PlankÕs constant, which has the value 6.626x10-34 Js. The total energy of an object is made up of its potential energy, its kinetic energy, and its internal energy. We discussed potential energy in Lesson 3 and know that it depends on the object and external forces that the object is interacting with. The kinetic energy of an object depends on the mass of the object and its speed, while the internal energy depends on the internal structure of the object. These forms of energy can be converted into each other. For instance, consider a mass connected to a spring that is fixed to a wall as in the following diagram: The mass can move back and forth about the equilibrium position, X0. To start the motion one stretches the spring towards the point R and lets go. The spring exerts a force, pulling the mass back towards X0; the amount of the force depends on the stiffness of the spring. The mass will be pulled back with such force that it will go past X0 and end up at the point L compressing the spring, which now exerts a force in the opposite direction again towards X0. When the mass reaches the points L and R it stops, while when it is at the point X0 its speed is the fastest. Thus at the points R and L its kinetic energy (motional energy) is zero while its potential energy is at a maximum (the maximum amount of force is being exerted on the mass). So potential energy is continually flowing into kinetic energy and vice-versa. If the mass is moving on a rough surface there will be some friction between the surface and the mass. This will cause the mass and the surface to heat up and the speed and amplitude of the back and forth motion to decrease; thus potential and kinetic energy both flow into internal energy of the mass and the surface. The frequency of a standing electronic wave corresponds through PlankÕs constant to the total energy of the electron (one electron in an atom or molecule is one electronic standing wave). If an electron absorbs energy it will form a more energetic standing wave pattern at a higher frequency. For a given molecule or atom these higher frequencies are fixed and depend on the nature of the atom or molecule, that is, the types of atoms making up the molecule and the nuclear charge of the atoms, as well as the total number of electrons present. This is exactly analogous to the thickness, tension, material, and geometry of a guitar string determining the natural frequencies of the string. As electrons are fermions, identical electrons cannot be at the same place at the same time due to the Pauli Exclusion Principle. However, it is found that there two types of electrons, an alpha one and a beta one. As they are not identical, they can be at the same place at the same time and they can form identical standing wave patterns. Most often there is only one combination of standing wave patterns that corresponds to the lowest energy state of the atom or molecule; this is called the Ground State. The various combinations of standing wave patterns that the fixed number of electrons in a particular molecule or atom can form are called electronic configurations. If any of these configurations have equal total energy, they are called degenerate. Sometimes there are several degenerate configurations that could be the ground state. The interaction of light with matter involves many interconnected phenomenaÑthe possible configurations of a system, the possible excitations and deexcitations, the various energies and frequencies of the standing wave patterns and the absorbed and emitted photons, and which electrons are alpha and which are beta. In order to describe in a succinct manner all these different facets, energy level diagrams were invented. These diagrams show the frequencies, thus the energies, of some standing wave patterns for the system, which standing wave patterns are actually being manifested, and which excitations and deexcitations are taking place. The following examples illustrate their use: In a. light is absorbed, causing an alpha electron, , to be excited to a higher frequency standing wave pattern,E2 ® E3. The frequency of the incoming light must thus be u3-u2, where E3 =hu3 and E2 =hu2. In b. a deexcitation takes place; the standing wave pattern with frequency u3 and energy E3 loses energy, emits a photon with frequency u3-u2, and forms the standing wave pattern with energy E2. In c. the b electron, ¯, with standing wave pattern energy of E2 is excited to E5 with a photon of frequency u5-u2 (much higher than before). In d. the standing wave pattern with energy E5 deexcites to form a standing wave pattern of energy E4, emitting a photon with frequency u5- u4. The number of energy levels found in a given system is equal to the sum of the number of energy levels of the individual atoms. The more atoms present the more energy levels. In a solid or dense material there are on the order of 1023 atoms present in a small region of space; thus the number of energy levels is huge, in fact so huge that many of the levels merge into bands, the energy difference being too small to be measured. Energy gaps between bands can still be found, and some bands can be partially filled; that is, not all the standing wave patterns in the energy range belonging to the band are actually manifested by the electrons present. As shown by the following diagram (a), there are two filled bands with energies of E1 to E2 and E3 to E4 and an empty band with energies between E5 to E6. The frequencies of absorbed photons can thus be any number belonging to the range u5-u4 to u6- u3. In (b) there is one filled band with energies of E1 to E2 and two partially filled bands with energies E3 to E4 and E5 to E6. The emitted photons can have frequencies in the range u5-u4 to u5-u3. The effects of absorption and emission are easily observed with lenses and prisms combined in a scientific instrument called a Spectrometer. If a dilute gas is initially excited (i.e., the electrons in the molecules of the gas are excited to higher energy standing wave patterns), the photons emitted during deexcitation can be observed using the following set up: The image on the screen or photographic plate of the slit that the emitted light passes through appears at different places due to the fact that different wavelengths of light are bent differently when passing through the prism. If we plot a graph of the intensity of light against observed frequency we obtain in general Intensity Frequency This is called a Discrete Emission Spectra. If a solid or dense material is excited and then allowed to deexcite, the resulting photons can be observed in the same manner; the resulting observed spectra looks like a rainbow (if the emitted light is in the visible range), and a plot of intensity against frequency looks like Intensity Frequency This is called an Incandescent Spectra. The form of the plot depends on the temperature, T, of the material. The higher the temperature, the higher the frequency of maximum intensity; in the preceding diagram T2>T1 and thus u2>u1. The temperature T is directly proportional to this frequency, thus the temperature of the material can be determined by spectroscopic means. The sun produces an incandescent spectrum with a maximum intensity in the yellow frequencies; other hotter stars have a maximum intensity in the blue range. Often incandescent spectra are not in the visible frequencies. All solids around us are actually emitting such spectra all the time, but in the infrared frequencies, which can be observed with an infrared camera. If one heats a metallic material such as an iron or tungsten bar, it will begin to glow dull red, showing that the maximum intensity frequency has moved from the infrared to the red frequencies. If one continues to heat it, it will glow white hot, showing that the red, yellow, and blue frequencies are being emitted with the maximum in the yellow range. If one could heat it still hotter then it would glow blue. However, before this occurs, the bar melts! Normal light bulbs have tungsten strips inside them, which are heated by passing an electric current through them, thus causing them to emit incandescent light. If one shines incandescent light through a non-dense material using a spectrometer, as in the following diagram, one observes a Discrete Absorption Spectra of the form When an electron assumes an excited state stationary wave pattern, it will naturally try to lose energy and deexcite to a lower energy state. The length of time it remains in the high energy standing wave pattern is called the life time of the state. The life time can be short, less than 10-6s, or long, greater than 10-6s or even many hours or days. If the life time is short, the emission of photons stops almost simultaneously with turning off of the source of light. This type of emission of light is called fluorescence. If the life time is long, the emission of photons will continue for some time after the source has been removed. This type of emission of light is called phosphorescence and can continue for days. Phosphorescence is observed, for example, in fire flies, clocks that glow in the dark, and TV screens. From the preceding discussion of excitation and deexcitation described by the energy level diagrams one can observe that the frequency of the emitted photon must be less than or equal to the frequency of the absorbed one. Thus it is possible to excite with ultraviolet light and produce visible light emission. This is the basis of fluorescent paints or dyes used in posters and clothing. A black light (ultraviolet light source) produces an excitation, which is followed by the emission of intense visible lightÑan effect often seen in discotheques. Another phenomena often seen in discotheques is the glowing of white shirts. This is because shirt manufacturers and detergent companies actually make white whiter than white. They do this by adding a dye that will absorb the ultraviolet and emit many visible colors that mix to form white; this white light formed from the ultraviolet combines with the reflection of visible frequencies to form extra intense white light, both in sunlight and in a disco. The type of deexcitation that produces fluorescence and phosphorescence is called spontaneous emission. When this occurs, the direction that the photon comes from the atom or molecule is often quite random. This should be contrasted to stimulated emission where an incident photon stimulates the emission of a photon that is of the same frequency, in phase, and travelling in the same direction with itself. Of course the frequency of the incoming photon must match the difference between the frequency of the excited state electron and a lower frequency electronic standing wave pattern. The light that is produced by stimulated emission is thus more intense than the incident light. (Constructive interference takes place as the two photons are in the same region of space and in phase.) This observation leads to the idea of enhancing this type of emission to produce very intense light beams. In order to optimize the use of input energy in the production of constructively interfering photons, the emitting material should (i) only produce photons of one frequency, called monochromatic light. Thus only one deexcitation channel or pathway should be available. (ii) only produce coherent photons propagating in the same direction. Thus emitted photons should be produced by stimulated emission. (iii) only produce a parallel beam of light. A beam of light that diverges (i.e., spreads out) attenuates much faster than a beam that stays narrow. A beam of such light is called Light Amplified by Stimulated Emmision of Radiation or LASER light. In order to produce light by stimulated emission, incident photons should collide with electrons in excited state standing wave patterns; in order to facilitate this, the excited state should be long lived, in fact so long lived that one talks about a meta stable state. Also incident photons should not be used up in producing such a state, which should be produced by some other means. The optimum situation for stimulated emission to occur is when most of the electrons are in these meta stable excited states. This occurs when we have a population inversion. The most common type of LASER is the Helium-Neon laser, which is described in some detail on page 553 of your textbook. The frequencies of the emitted and absorbed light are controlled by the environment in which the electronic standing waves exist. This environment is determined by the arrangement and type of nuclei and the total number of electrons present. Given a particular environment, electrons can form several harmonic series of patterns labelled s, p, d, f, g, h, and so on. Each series has a fundamental and overtones; the higher overtones are distinguished from the lower ones by the number of nodal surfaces. (Remember, the standing electronic wave patterns are three dimensional in contrast to the one dimensional standing wave patterns of a string where the nodes are points.) At these nodal surfaces no electric charge exists. The higher overtones in each harmonic series of electron standing waves also spread further out; thus, in lithium an electron in a 2s standing wave pattern is on the average further away from the lithium nucleus than a 1s electron. As we noted, absorption can occur when an incoming photon has a frequency that equals the difference between an unoccupied electronic standing wave frequency (i.e., a frequency of an electronic standing wave pattern that is not present) and an occupied one. The smallest such frequencies that produce such excitations are generally in the visible or ultraviolet region of the spectrum. Photons emitted when such standing waves deexcite are also in these regions. Nuclei, however, are not stationary; thus the environment in which electrons exist is constantly changing. The motion of the nuclei can be decomposed into three parts: (a) a translational motion of all the nuclei in the same direction; (b) a rotational motion of all the nuclei about a central axis; and (c) a vibrational motion of the nuclei with respect to each other. This vibrational motion is similar to the motion of two masses connected by a spring, where the distance between the masses gets larger as the spring stretches and smaller as the spring compresses. The masses vibrate about equilibrium positions or average positions at the ends of the spring. The distance between these average positions is the length of the chemical bond between these two nuclei. It turns out that this nuclear vibrational motion can occur at various frequencies that form harmonic families, with the higher harmonics producing longer bond lengths (i.e., average distances between nuclei). It is the environment produced by the average positions of the vibrating nuclei that determines the frequencies of the electronic standing waves. Thus a 1s electronic standing wave pattern in the environment of a fundamental nuclear vibrational frequency will vibrate at a different frequency and will be of a different size than a 1s electron at an overtone nuclear vibrational frequency. The frequency of the 1s electron in the environment of the overtone nuclear vibration will be higher and its size bigger than that of an electron in the environment of a fundamental nuclear vibration. (Note that we are talking about two types of frequencies; one is the frequency of nuclei moving closer and further from each each other and the other is the frequency of the electronic standing wave pattern.) An incident photon that equals the difference between these two different 1s frequencies can cause an excitation between the lower frequency and the higher one, and hence cause the nuclear vibrational mode to change to a higher frequency. Exactly the same process can occur for 2s, 3s, 2p, 3p, 3d, 4d, and so on, and, in fact, any electronic standing wave. The frequencies of photons that produce such excitations belong in the infrared region of the spectrum, and the spectra produced by absorption and emission of such photons is called molecular vibrational spectra. The spectra produced by absorption or emission of photons that produce excitation between different harmonics of electron standing wave patterns is called an electronic spectra. The nuclei also perform rotational motions, which are at lower frequencies than nuclear vibrations. These also change the environment for the electronic standing wave patterns. The difference between the frequencies of the same electronic standing wave pattern in the environment of a rotating nuclear framework at two successive different natural frequencies lies in the microwave region of the spectra. Thus photons with microwave frequencies cause excitation between such electronic standing wave patterns, causing the rotational motion to increase its frequency. When infrared radiation shines onto our skins we feel it as heat. What microscopic processes does this feeling correspond to? We see from above that infrared photons cause an increase in the vibrational frequency of nuclei and the bond distances between them. It is this change in structure that we perceive as heat. If the vibrational motion of the nuclei increases more and more, the structure of the material on which the radiation is incident will begin to shatter and chemical bonds will begin to break, leading to all the well-known effects of continual heating (i.e., charring, melting, burning, etc.). The transitions associated with photons that cause purely electronic excitations (i.e., leaving unchanged the vibrational and rotational states of the nuclei) are called cold transitions, while transitions that are associated with photons that change the nuclear vibrational and rotational states are called hot transitions. Clearly an ultraviolet photon can cause a hot transition between two different electronic standing wave patterns if it equals the frequency difference between the electronic levels plus the difference between two vibrational levels or equals the frequency difference between the electronic levels plus the difference between two rotational levels as shown in the following diagrams. Also a deexcitation can occur between a hot level and cold level as shown in the following diagram It is also possible for a molecule to absorb several microwave photons sequentially, gradually increasing the level of rotational excitation until one reaches the level of the first vibrational level as shown in the following diagram. Other excited vibrational levels can also be reached in such a manner, as can excited electronic levels. As the frequency of an emitted photon must be less than or equal to the frequency of an absorbed one, an ultraviolet photon absorbed producing an electronic excitation can be followed by the emission of visible, infrared, or microwave photons, leaving behind hot or cold electronic standing wave patterns. Fluorescent lights utilize cold emission between electronic levels to produce light. (The fluorescent material is first electrically excited.) Cooking might not seem a particularly related subject, except for the word microwave; however, even this process can be described on a microscopic level. Why do we cook food? Usually it is to make it more tender (i.e., easier to break apart). Thus the object of cooking is to disrupt the structure of the food. This is achieved by heating, causing vibrational or rotational excitations, thus stretching chemical bonds until some break. (One can produce vibrational or rotational excitations by letting hot molecules collide with the cold substance as well as with collisions with infrared or microwave photons.) The microwave oven radiates food directly with microwave photons, causing rotational excitation and possible disruption of the structure of the food. This method is more efficient, as many of the microwave photons pass through the surface of the food and rotationally excite the inside of the food directly. Also microwave photons are of a lower energy than most other heating processes and are thus less expensive to use. What produces the color of cooked food or raw food or any object for that matter? We know the only way we can see an object is when the object is a source of, reflects, or transmits light towards our eyes. The color of the object is then determined by the frequencies of the photons entering our eyes. If monochromatic photons flow into our eyes, we see just one color, which depends on their frequency. This is also true if photons of various mixed frequencies stimulate our optic nerve, but this time the color we see depends on the mixture. The color we see can be analyzed by dividing the spectrum into three primary colorsÑred, green, and blue. The actual hue (i.e., frequency) can be taken to be in the middle of the frequency ranges in the spectrum that produce these colors. It is found that Red + Green = Yellow Red + Blue = Magenta Green + Blue = Cyan If two beams of primary colored light are mixed together, they form the colors shown on the right hand side of the above table. If three beams of primary colored light, all different, are focused together we see white light. If one of the primary colored beams is turned off, then the color of the mixture changes from white to one of the colors on the right hand side of the above table, depending on the color that is turned off. This observation leads to an analysis of reflected colors in terms of pigments. If one shines white light (i.e., a mixture of all visible frequencies) on a material, either all the frequencies are reflected (i.e., first absorbed then spontaneously emitted in the backward direction) or some of the frequencies are absorbed for a longer time and not reflected, producing a reflected color that is a mixture of the remaining frequencies. The color of the material is thus seen to be determined by the frequencies taken away from the white light. If blue light is absorbed by the material and red and green are reflected, then the material appears yellow and we say that the material contains a yellow pigment; if green light is absorbed, we see magenta and say that the material contains a magenta pigment; if red light is absorbed, we see cyan and say that the material contains a cyan pigment. If all the pigments are present, then all the light is absorbed and the material appears black. One can then form a table analogous to the one above for mixtures of pigments. Yellow + Cyan = Green Magenta + Cyan = Blue Magenta + Yellow = Red This is a table based on the subtraction of primary colors. If magenta is present, then green has been subtracted and the others reflected, while if cyan is present, then red has been subtracted, and if yellow is present, then blue has been subtracted. When one forms colors for dyes or paints, one concentrates on the addition of pigments. If colors are absorbed, then so is the energy associated with the photons that make up that color. In general the excited electronic standing wave patterns produced by these photons deexcite, producing hot electronic states. Thus every material that is not colored white heats up, with objects colored black heating up the most. Stars have a range of visible colors from red to blue, depending on their temperature. These colors come from the dense plasma on the surface. Above this violently boiling plasma is an atmosphere of atomic gases. The plasma radiates a continuous incandescent light that passes through these gases and produces an absorption spectra. This absorption spectra can be seen on earth or by the Hubble space telescope, informing us of (a) the elements that can be found on the star and (b) the Doppler shift of the light coming from the star. Each atom has its own unique, characteristic absorption spectral pattern made up of discrete lines. By matching the positions of these lines found in the spectra observed from the star with lines in spectra observed from atoms in an earth laboratory, one can determine whether the frequency of the lines has been increased or decreased with respect to the ones measured in the laboratory. If the frequency has been decreased, then the star is red shifted, while if the frequency has increased, it has been blue shifted. Using HubbleÕs Law, one can then deduce how far away the star is.