PHOTOCHEMICAL REACTIONS, Lecture notes of Physical Chemistry

Download PHOTOCHEMICAL REACTIONS and more Lecture notes Physical Chemistry in PDF only on Docsity! PHOTOCHEMICAL REACTIONS Ordinary reactions occur by absorption of heat energy from outside. The reacting molecules are energized and molecular collisions become effective. These bring about the reaction. The reactions which are caused by heat and in absence of light are called thermal or dark reactions. On the other hand, some reactions proceed by absorption of light radiations. These belong to the visible and ultraviolet regions of the electromagnetic spectrum (2000 to 8000 Å). The reactant molecules absorb photons of light and get excited. These excited molecules then produce the reactions. A reaction which takes place by absorption of the visible and ultraviolet radiations is called a photochemical reaction. The branch of chemistry which deals with the study of photochemical reactions is called photochemistry. When a photon from high energy electromagnetic radiations such as X- and - ray is used, the chemical processes are then called radiolytic reactions. Demonstration of a Photochemical reaction A mixture of hydrogen and chlorine remains unchanged with lapse of time. But when exposed to light, the reaction occurs with a loud explosion. A bottle is filled with equimolar amounts of hydrogen and chlorine (Fig.1). It is tightly stoppered with a handball. When the lamp is turned on, a beam of light falls on the mixture through the bottom of the bottle. The reaction occurs with an explosion. The ball is expelled with high velocity so that it strikes the opposite wall of the lecture theatre. 1 Figure.1 The 'HCl-cannon' experiment. DIFFERENCE BETWEEN PHOTOCHEMICAL AND THERMOCHEMICAL REACTIONS 2 In some literature accounts, the term wave number is used. This is the number of wavelengths per centimeter, and consequently wave number has units of reciprocal centimeters (cm -1 ). The energy of N photons "Einstein" We know that the energy of a photon (or quantum), ∈ , is given by the equation. (1) Where, h = Planck’s constant (6.624 × 10– 34 J-sec) v = frequency of radiation = wavelength of radiation c = velocity of light (3 × 1010 cm sec– 1) 5 The energy, E, of an Avogadro number (N) of photons is referred to as one einstein. That is, (2) N = 6.02 × 1023, It is evident from (2) that the numerical value of Einstein varies inversely as the wavelength of radiation. The higher the wavelength, the smaller will be the energy per Einstein. _______________________________________________________________ The production of the electronically - excited state by photon absorption is the feature that characterizes photochemistry and separates it from other branches of chemistry. ________________________________________________________________ Table 1.1 shows the properties of visible and ultraviolet light. Sometimes electronic excitation can result in chemical changes, such as the fading of dyes, photosynthesis in plants, suntans, or even degradation of molecules. On other occasions, the electronically - excited state may undergo deactivation by a number of physical processes, either resulting in emission of light (luminescence) or conversion of the excess energy into heat, whereby the original ground state is reformed. 6 Electronically - excited states can also interact with ground - state molecules, resulting in energy - transfer or electron - transfer reactions provided certain criteria are met. There are three basic processes of light – matter interaction that can induce transfer of an electron between two quantized energy states: 1. A bsorption of light , a photon having energy equal to the energy difference between two electronic states can use its energy to move an electron from the lower energy level to the upper one, producing an electronically - excited state (Figure 1.2 ). The photon is completely destroyed in the process, its energy becoming part of the total energy of the absorbing species. 7 In order to understand how electrons of many - electron atoms arrange themselves into the available orbitals it is necessary to define a fourth quantum number: • The spin quantum number , m s , can have two possible values, +½ or − ½. These are interpreted as indicating the two opposite directions in which the electron can spin, ↑ and ↓ . The total spin, S, of a number of electrons can be determined simply as the sum of the spin quantum numbers of the electrons involved and a state can be specified by its spin multiplicity: A ground - state helium atom has two paired electrons in the 1s orbital (1s2). The electrons with paired spin occupy 10 the lowest of the quantized orbitals shown below (the Pauli exclusion principle prohibits any two electrons within a given quantized orbital from having the same spin quantum number): This species is referred to as a ground - state singlet and is designated by S0. Electronic excitation can promote one of the electrons in the 1s orbital to an orbital of higher energy so that there is one electron in the 1s orbital and one electron in a higher - energy orbital. Such excitation results in the formation of an excited - state helium atom. In the lowest excited - state helium atom there are two possible spin configurations: 11 ________________________________________________________________ MODELLING MOLECULES: ELECTRONIC STATES With regard to the different spin states in molecules, the following ideas are important: • An excited triplet state always has a lower energy than that of the corresponding excited singlet state. This is in line with Hund ’s rule: when two unpaired electrons occupy different orbitals, there is a minimum energy repulsion between the electrons when their spins are parallel. 12 DETERMINATION OF ABSORBED INTENSITY A photochemical reaction occurs by the absorption of photons of light by the molecules. Therefore, it is essential to determine the absorbed intensity of light for a study of the rate of reaction. An experimental arrangement for the purpose is illustrated in Fig.3. Light beam from a suitable source (tungsten filament or mercury vapour lamp) is rendered parallel by the lens . The beam then passes through a ‘filter’ or monochrometer which yields light of one wavelength only. The monochromatic light enters the reaction cell made of quartz. The part of light that is not absorbed strikes the detector . Thus the intensity of light is measured first with the empty cell and then the cell filled with the reaction sample. The first reading gives the incident intensity, I0, and the second gives the transmitted intensity, I. The difference, I0 – I = Ia, is the absorbed intensity. The detector generally used for the measurement of intensity of transmitted light is : (a) a thermopile (b) photoelectric cell (c) a chemical actinometer. Thermopile It is made of a series of thermocouples in which unlike metals such as bismuth and silver are joined together. One end of the couple is blackened with lamp black and the other end is left as such. When the radiation strikes the black end it absorbs energy and is heated up. The temperature difference between the two ends causes a current to flow in the circuit as indicated by the galvanometer. 15 The current is proportional to intensity of radiation. The thermopile is previously calibrated against a standard source of light. Photoelectric Cell A photoelectric cell (Fig. 30.5) can be conveniently used for measuring intensity of light. The light striking the active metal electrode (cesium, sodium or potassium) causes the emission of electrons. A current flows through the circuit which can be measured with an ammeter. The intensity of light is proportional to the current. Chemical Actinometer 16 A chemical actinometer uses a chemical reaction whose rate can be determined easily. One such simple device is Uranyl oxalate actinometer. It contains 0.05 M oxalic acid and 0.01 M uranyl sulphate in water. When it is exposed to radiation, oxalic acid is decomposed to CO2, CO and H2O. The concentration of oxalic acid that remains can be found by titration with standard KMnO4 solution. The used up concentration of oxalic acid is a measure of the intensity of radiation. LAWS OF PHOTOCHEMISTRY There are two basic laws governing photochemical reactions: Grothus–Draper Law When light falls on a cell containing a reaction mixture, some light is absorbed and the remaining light is transmitted. Obviously, it is the absorbed component of light that is capable of producing the reaction. The transmitted light is ineffective chemically. Early in the 19th century, Grothus and Draper studied a number of photochemical reactions and enunciated a generalization. This is known as Grothus-Draper law and may be stated as follows: It is only the absorbed light radiations that are effective in producing a chemical reaction. However, it does not mean that the absorption of radiation must necessarily be followed by a chemical reaction. When the conditions are not 17 Evidently, the primary reaction only obeys the law of photochemical equivalence strictly. The secondary reactions have no concern with the law. Quantum yield (or Quantum efficiency) It has been shown that not always a photochemical reaction obeys the Einstein law. The number of molecules reacted or decomposed is often found to be markedly different from the number of quanta or photons of radiation absorbed in a given time. The number of molecules reacted or formed per photon of light absorbed is termed Quantum yield. It is denoted by φ so that For a reaction that obeys strictly the Einstein law, one molecule decomposes per photon, the quantum yield φ = 1. When two or more molecules are decomposed per photon, φ > 1 and the reaction has a high quantum yield. If the number of molecules decomposed is less than one per photon, the reaction has a low quantum yield. CALCULATION OF QUANTUM YIELD By definition, the quantum yield, φ, of a photochemical reaction is expressed as: or Thus, we can calculate quantum yield from: (a) The amount of the reactant decomposed in a given time and 20 (b) The amount of radiation energy absorbed in the same time The radiation energy is absorbed by a chemical system as photons. Therefore, we should know the energy associated with a photon or a mole of photons. 21 SOLVED PROBLEM 2. When a substance 4 was exposed to light. 0.002 mole of it reacted in 20 minutes and 4 seconds. In the same time 4 absorbed 2.0 « 10° photons of light per second. Calculate the quantum yield of the reaction. (Avogadro number N= 6.02 « 1073) SOLUTION Number of molecules of A reacting = 0.002 x N=0.002 * 6.02 x 107 Number of photons absorbed per second = 2.0 « 106 Number of photons absorbed in 20 minutes and 4 seconds = 2.0 = 10° « 1204 No. of molecules reacted Quantum yield ® = No. of photons absorbed _ 0.002 « 6.02 x 107 ——_—___ = 5.00 = 107 2.0 « 10° x 1204 SOLVED PROBLEM 3. When irradiated with light of 5000 A wavelength, 1 x 10“ mole of a substance is decomposed. How many photons are absorbed during the reaction if its quantum efficiency is 10.00. (Avogadro number N= 6.02 = 10°3) SOLUTION Quantum efficiency of the reaction = 10.00 No. of moles decomposed =1x107+ No. of molecules decomposed =1 = 10 = 6.02 « 10 =6.02 x 10! we know that, _ No. of molecules decomposed $= No. of photons absorbed _ 6.02 x 10° "No. of photons absorbed 19 No. of photons absorbed = = = 6.02 x 1018 ho 22 It is noteworthy that A consumed in (2) is regenerated in (3). This reaction chain continues to form two molecules each time. Thus the number of AB molecules formed in the overall reaction per photon is very large. Or that the quantum yield is extremely high. ________________________________________________________________ Examples of high quantum yield The above reasons of high quantum yield are illustrated by citing examples as below: ( i ) Decomposition of Hl. The decomposition of hydrogen iodide is brought about by the absorption of light of less than 4000 Å. In the primary reaction, a molecule of hydrogen iodide absorbs a photon and dissociates to produce H and I. This is followed by secondary steps as shown below : In the overall reaction, two molecules of hydrogen iodide are decomposed for one photon (hv) of light absorbed. Thus the quantum yield is 2. ( ii ) Hydrogen-Chlorine reaction. This is a well-known example of a photochemical chain reaction. A mixture of hydrogen and chlorine is exposed to light of wavelength less than 4000 Å. The hydrogen and chlorine react rapidly to form hydrogen chloride. In the primary step, a molecule of chlorine absorbs a photon and dissociates into two Cl atoms. This is followed by the secondary reactions stated below: 25 The Cl atom used in step (2) is regenerated in step (3). Thus, the steps (2) and (3) constitute a self-propagating chain reaction. This produces two molecules of HCl in each cycle. Thus, one photon of light absorbed in step (1) forms a large number of HCl molecules by repetition of the reaction sequence (2) and (3). The chain reaction terminates when the Cl atoms recombine at the walls of the vessel where they lose their excess energy. The number of HCl molecules formed for a photon of light is very high. The quantum yield of the reaction varies from 104 to 106. ________________________________________________________________ Causes of low quantum yield The main reasons of low quantum yield are: (a) Deactivation of reacting molecules. The excited molecules in the primary process may be deactivated before they get opportunity to react. This is caused by collisions with some inert molecules or by fluorescence. (b) Occurrence of reverse of primary reaction. Here the primary reaction generally yields a polymer. The product then undergoes a thermal reaction giving back the reactant molecules. The reverse thermal reaction proceeds till the equilibrium state is reached. 26 (c) Recombination of dissociated fragments. In a primary process the reactant molecules may dissociate to give smaller fragments. These fragments can recombine to give back the reactant. (AB) + hv ⎯⎯→ A + B A + B ⎯⎯→ (AB) Thus, the secondary reactions involving the fragments to form the product will not occur. This will greatly lower the yield. The yield of particular photochemical reaction may be lower than expected for more than one reason cited above. Examples of low quantum yield The examples listed below will illustrate the above causes of low quantum yield: (i) Dimerization of Anthracene. When anthracene, C14H10, dissolved in benzene is exposed to ultraviolet light, it is converted to dianthracene, C28H20. 2C14H10 + hv ⎯⎯→ C28H20 Obviously, the quantum yield should be 2 but it is actually found to be 0.5. The low quantum yield is explained as the reaction is accompanied by fluorescence which deactivates the excited anthracene molecules. Furthermore, the above reaction is reversible. The transformation of the product back to the reactant occurs till a state of equilibrium is reached. This further lowers the quantum yield. (ii) Combination of H2 and Br2. When a mixture of hydrogen and bromine is exposed to light, hydrogen bromide is formed. The reaction occurs by the following possible steps. 27 Certain molecules (or atoms) when exposed to light radiation of short wavelength (high frequency), emit light of longer wavelength. The process is called fluorescence and the substance that exhibits fluorescence is called fluorescent substance. Fluorescence stops as soon as the incident radiation is cut off. Examples. (a) a solution of quinine sulphate on exposure to visible light, exhibits blue fluorescence. (b) a solution of chlorophyll in ether shows blood red fluorescence. Fluorescent minerals, shown under ultraviolet light. 30 Tonic water is clear under normal light, but vividly fluorescent under ultraviolet light, due to the presence of the quinine used as a flavoring. Explanation. When a molecule absorbs high energy radiation, it is excited to higher energy states. Then it emits excess energy through several transitions to the ground state. Thus the excited molecule emits light of longer frequency. The color of fluorescence depends on the wavelength of light emitted. ________________________________________________________________ Phosphorescence When a substance absorbs radiation of high frequency and emits light even after the incident radiation is cut off, the process is called phosphorescence. The substance which shows phosphorescence is called phosphorescent substance. Phosphorescence is mainly caused by ultraviolet and visible light. It is generally shown by solids. Examples. (a) Sulphates of calcium, barium and strontium exhibit phosphorescence.(b) Fluorescein in boric acid shows phosphorescence in the blue region at 5700 Å wavelength. Explanation. As in fluorescence, a molecule absorbs light radiation and gets excited. While returning to the ground state, it emits light energy of longer wavelength. In doing so the excited molecule passes from one series of electronic states to another and gets trapped. This shows the emission of light which persists even after the removal of light source. Thus, phosphorescence could be designated as delayed fluorescence. A + hv ⎯⎯→ A* ⎯slow⎯→ hv′ 31 Phosphorescent powder under visible light, ultraviolet light, and total darkness Chemiluminescence Some chemical reactions are accompanied by the emission of visible light at ordinary temperature. The emission of light as a result of chemical action is called chemiluminescence. The reaction is referred to as a chemiluminescent reaction. Such a reaction is the reverse of a photochemical reaction which proceeds by absorption of light. The light emitted in a chemiluminescent reaction is also called ‘cold light’ because it is produced at ordinary temperature. Examples. (a) The glow of fireflies due to the aerial oxidation of luciferin (a protein) in the presence of enzyme luciferase. (b) The oxidation of 5-aminophthalic cyclic hydrazide (luminol) by hydrogen peroxide in alkaline solution, producing bright green light. Explanation. In a chemiluminescent reaction, the energy released in the reaction makes the product molecule electronically excited. The excited molecule then gives up its excess energy as visible light while reverting to ground state. 32 Franck–Condon Principle Absorption, or emission, in polyatomic molecules is governed by the Franck– Condon principle, enunciated by James Franck and Edward Condon in 1926. In its simplest form, the Franck–Condon principle may be formulated as follows: Changes in electronic distribution occur very fast in comparison with changes in bond angles and bond distances. Therefore, the nuclear configuration of a molecule, that is, the set of bond distances and bond angles, cannot change appreciably during the process of absorption or emission of light by the molecule. In the simplest case of a diatomic molecule, the Franck– Condon principle means that an electronic transition may be represented by a vertical line starting from ro and ending in an excited state with this very same r value, as depicted in Figure 2.3. Since r0> r0*, it follows that an excited vibrational level is virtually always reached in absorption. Evidently, as depicted in Figure 2.3, many upper vibrational levels can be reached provided that the field contains the necessary energy. Some molecules in the ground state have values of r much larger or much smaller than r0, since there is a distribution of r values in the molecules in the zero level of the ground state. Hence, there may exist absorption bands with long-wave tails rather than abrupt cutoff terminations. The absorption at the long-wave tails of bands is often found to be thermally sensitive. In the case of broad absorption bands, lowering of the temperature results almost invariably in a displacement of the band edge to shorter wavelengths, owing to the reduction of the thermally excited population. 35 In molecules in the gas phase, there are well-defined quantized rotational levels, which fill the gaps between the vibrational levels. Rotational structure has been observed and analyzed for molecules as large as phenol, indole, and anthracene. In solution, the rotational structure is completely obliterated since free rotation with quantized energy is no longer possible. The vibrational structure may still be recognized within an absorption band by the presence of peaks separated in energy by about 3 kcal. The last absorption band of aromatic hydrocarbons in nonpolar solvents often exhibits this clear vibrational structure. A further influence, of particular interest to the chemist or biologist, arises because of possible molecular interactions between the solvent and chromophore molecules. Electronic transitions with the greatest probability of absorption from S0 (v = 0): (a) where both electronic states have similar geometries, shown by the minima of the curves being coincident ; (b) where the excited state has a larger internuclear distance than the ground state 36 Absorption spectrum of a solution of anthracene in benzene, and the vibronic transitions responsible for the vibrational fine structure Energy - level diagram showing how the electronic and vibrational energy levels in the ground - state (S0 ) and first excited - state (S1 ) anthracene molecule are related to the absorption and fluorescence emission spectra. 37 at lower levels of vibrations followed by a continuum. This is called predissociation. H2 and Cl2 Reaction The quantum yield of H2-Cl2 combination is exceptionally high; it varies with the experimental conditions but is found to be between 104 and 106 in absence of O2 with light of wavelength 4800 A. The process occurs in the range 5460 to 4800 A with an apparently lower efficiency because only a small proportion of light absorbed is capable of dissociating Cl2 molecule. The mechanism can be proposed as Reaction (ii) between chlorine atom and hydrogen molecule is very rapid, since it is an exothermic process and has low energy of activation whereas corresponding reaction with bromine atom is very slow at ordinary temperature. Applying the steady state treatment with respect to chlorine atom, we can get 40 The rate law () is in agreement with experimental results. At high chlorine pressure, the termination step (iv) may be replaced by following equilibria This will lead to a different kinetic law. In presence of O2, the following chain termination processes take place: HO2 subsequently reacting to give products which do not propagate chains. The Photolysis of HI The kinetics of two photochemical reactions will be compared with the kinetics of the thermal reactions. In the absence of light, hydrogen iodide decomposes by the elementary reaction: 41 or possibly In the initial stages the reverse reaction can be ignored. In either case the rate of reaction can be written In the photochemical reaction, at wavelengths below about 327 nm, the mechanism is Other possible elementary reactions either have much higher activation energies or require three-body collisions. The rate of disappearance of HI is The steady-state requirement is Combining these two equations, we obtain By definition the quantum yield is,  = rate/ Ia 42 • Energy transfer, where the electronically – excited state of one molecule (the donor) is deactivated to a lower electronic state by transferring energy to another molecule (the acceptor), which is itself promoted to a higher electronic state. The acceptor is known as a quencher and the donor is known as a sensitizer. • Electron transfer: considered as a photophysical process, involves a photoexcited donor molecule interacting with a ground - state acceptor molecule. An ion pair is formed, which may undergo back electron transfer, resulting in quenching of the excited donor. 45 Jablonski Diagram The properties of excited states and their relaxation processes are conveniently represented by a Jablonski diagram , shown in Figure 3.2 and summarized in Table 3.1 . Most molecules possess an even number of electrons and all the electrons are paired in ground state. The spin multiplicity of a state is given by 2S + 1, where S is the total electronic spin. i) When the spins are paired (↑↓), the clockwise orientation of one electron is cancelled by the anticlockwise orientation of other electron. Thus, S = S1 + S2 = (1/2) – (1/2) = 0, S=0, 2S + 1 = 1,ie, spin multiplicity is 1. The molecule is said to be in the singlet ground state S. ii) On absorption of a suitable energy, one of the paired electrons goes to a higher energy level. The spin orientation of the two electrons may be either a) parallel (↑↑), then S = S1 + S2 = (1/2) + (1/2) = 1, so, 2S + 1 = 3, ie., spin multiplicity is 3. The molecule is in the triplet (T) excited state. b) or anti-parallel (↑↓), then S = S1 + S2 = (1/2) – (1/2) = 0, 2S + 1 = 1, ie., spin multiplicity is 1. The molecule is in the singlet (S) excited state. Since the electron can jump from the ground state to any of the higher electronic states depending upon the energy of the photon absorbed we get a series of a) singlet excited states ie., S1, S2, S3, etc., (first singlet excited state, second singlet excited state, third singlet excited state, etc.) and b) triplet excited states ie., T1, T2, T3, etc., (first triplet excited state, second triplet excited state, third triplet excited state, etc.). 46 Generally singlet excited state has higher energy than the corresponding triplet excited state. Thus, the energy sequence is as follows: ES1> ET1 , ES2> ET2, ES3> ET3 and so on. When a molecule absorbs light radiation, the electron may jump from S0 to S1, S2 (or) S3 singlet excited state depending upon the energy of the light radiation as shown in Jablonski diagram. For each singlet excited state there is a corresponding triplet excited state, ie. S1 → T1; S2 → T2; S3 → T3, etc. The molecule, whether it is in singlet or triplet excited state, is said to be activated. Thus, where A0 – ground state molecule and A* - excited state molecule. 47 The k's are the rate constants for the various processes ; the A10 and ATS are the Einstein coefficients for spontaneous emission. In this mechanism, M is intended to represent any atom or molecule that may be present. Then [M], the concentration of M, is proportional to the total concentration of all the species in solution ; in the gas phase, [M] is proportional to the total pressure. The emitted intensity of fluorescence, IemF, is given by If the system is under steady illumination, the [S1] and [T1] do not vary with time; the steady-state conditions are 50 Using this value of [S l] in the expression in Eq. (), we obtain for the fluorescence intensity, If we invert Eq. () and use the value in Eq. () for 'F ' we find that A plot of l/Iem versus [M], called a Stern-Volmer plot, should yield a straight line. From the measured value of Ia and a value of A10 we can obtain the quenching constant kq. The constant A10 can be calculated from the measurement of the molar absorption coefficient of the absorption band. 51 Lasers Laser is an acronym for “light amplification by stimulated emission of radiation.” It is a special type of emission involving either atoms or molecules (or their ions). Laser emission occurs when a species in an excited state is 52 Laser light has the highest intensity of any light on Earth. As an example, consider a Q-switched Nd:YAG laser that produces 7.0 × 1015 photons at 1064.1 nm during a pulse lasting 150 ps (1 ps = 10−12 s). Because E = hν = hc/λ, the total energy output per pulse is given by Now 1.3 millijoule may not seem like much, but it is generated in an extremely short period of time. We can calculate the peak power associated with such a laser beam as follows: The unit of power is the watt, denoted by W, where 1 W = 1 J s−1. Thus, 8.7 megawatts is the power output during the pulse of laser action. When such a laser beam is focused on a small target of, say, area 0.01 cm2, the power flux density is given by 55 This is nearly a gigawatt per square centimeter of instantaneous power flux density, which is sufficient to drill a hole in almost anything. Shorter pulses and smaller areas provide even higher power flux densities. Intense laser beams have been used to cut and weld metals and even to produce nuclear fusion. Medically, lasers are used in surgery. For example, a pulsed argon ion laser is employed to “spot-weld” a detached retina back onto its support (the choroid). This procedure has some advantages over the traditional treatment in that it is noninvasive and does not require the administration of anesthetics. A pulsed ultraviolet argon–fluoride excimer (excited dimer) laser is used to cut the cornea of a human eye in the LASIK "laser-assisted in situ keratomileusis" procedure for correcting vision Coherence. By coherent we mean that the photons in a laser are emitted in phase with one another and are moving in exactly the same direction. The high degree of coherence arises from the fact that the stimulated emission synchronizes the radiation of the individual molecules, so that the photon emitted from one molecule stimulates another molecule to emit a photon of the same wavelength that is exactly in phase with the first photon and so on. Monochromaticity. Laser light is highly monochromatic (having the same wavelength) because all the photons are emitted as a result of a transition between the same two atomic or molecular energy levels. Therefore, they possess the same frequency and wavelength. In the Nd:YAG laser, for example, the emitted light is centered at 1064 nm with a width less than 0.5 nm. Although narrow linewidths can be obtained also with ordinary light (from, say, an incandescent light bulb) and a monochromator (a prism or diffraction grating which separates light of 56 different wavelengths), the intensity of a laser beam at a particular wavelength can be six orders of magnitude or greater than that from a conventional source Spatial collimation. A property of many lasers is that they have very low spatial divergence; that is, they are highly spatially collimated. Unlike an incandescent light bulb, where the intensity decreases with distance, laser light tends to remain in a small tight waisted beam. Taking advantage of this collimation, a pulsed laser can be aimed at the moon, where a retroflector placed by astronauts reflects the laser back to Earth. Timing of the round-trip time for the laser pulse is used to measure the distance between Earth and its moon to a precision of about 1 cm. The size of the laser spot on the moon is only a few km in diameter, which is a divergence of less than 5 × 10−4 degrees. 57