Spectroscopy PDF

## Spectroscopy ### Spectrophotometer Light absorption can be used in analytical chemistry for the characterization and quantitative determination of substances. An instrument used to measure the absorbance by measuring the amount of light of a given wavelength that is transmitted through a sample...

## Spectroscopy ### Spectrophotometer Light absorption can be used in analytical chemistry for the characterization and quantitative determination of substances. An instrument used to measure the absorbance by measuring the amount of light of a given wavelength that is transmitted through a sample is termed a spectrophotometer. It measures the intensity of light passing through a sample solution in a cuvette and compares it to the intensity of the light before it passes through the sample. It is an instrument that combines the function of both spectrometer and photometer. It measures the absorbance that uses a monochromator to select the wavelength. A method to measure how much a chemical substance absorbs light by measuring light intensity as a beam of light passes through a sample solution using a spectrophotometer is called spectrophotometry. All spectrophotometers contain four components: - A source of light - An optical system or monochromator - A sample holder or cuvette - A light detector **Figure 3.3** A spectrophotometer. Light from a light source passes through a monochromator for wavelength selection. A sample is contained in a cuvette in a cuvette holder. Light passes through a cuvette and is detected by a detector. The detector measures the intensity of light after passing through the sample solution. This fraction of light collected by the detector is called the transmitted intensity (I). The initial intensity of light before passing through the sample solution is Io. The ratio between the two intensities I/Io is defined as transmittance. **Polychromatic** Electromagnetic radiation of more than one wavelength. **Monochromatic** Electromagnetic radiation of a single wavelength. ### Emission Spectroscopy The absorption of light promotes an atom or molecule from ground state to an excited energy state. An excited-state molecule can return to a lower energy state by means of either a nonradiative or a radiative transition. In the nonradiative transition, the energy is ultimately dissipated into heat. In the radiative transition, the energy is released in the form of light. Emission, the release of excitation energy in the form of light, following the absorption of light is also called photoluminescence. A graph of emission intensity versus wavelength is called an emission spectrum. Photoluminescence is divided into two categories: fluorescence and phosphorescence. Emission spectroscopy is a spectroscopic technique that examines the wavelengths of light emitted by atoms or molecules during their transition from an excited state to a lower energy state. **Fluorescence spectroscopy** is a type of emission spectroscopy. Fluorescence is a radiative process that occurs during the transition of electrons from a singlet excited energy state to a singlet ground state. Fluorophores, a component that causes a molecule to absorb the energy of a specific wavelength and then re-emit energy at a different but equally specific wavelength, play a central role in fluorescence spectroscopy. The amount and wavelength of the emitted energy depend on both the fluorophore and the chemical environment of the fluorophore. **Figure 3.4** Simplified energy diagram showing the absorption and emission of a photon by an atom or a molecule. From the work of Bohr on atomic spectra, it could be established that absorption or emission of radiation is possible because of the quantization of atomic and molecular energy levels. When a photon of energy hv strikes the atom or molecule, absorption may occur if the difference in energy, ∆E, between the ground state and the excited state is equal to the photon's energy. An atom or molecule in an excited state may emit a photon and return to the ground state. The photon's energy, hv, equals the difference in energy, ∆E, between the two states. ### Scattering Spectroscopy When light interacts with matter, the light may be absorbed or scattered or may not interact with the matter and pass straight through it. Scattering is a physical process that causes light to deviate from a straight trajectory. It is different from absorption: in the case of absorption, specific wavelengths disappear when light encounters the matter. But both processes cause a light beam to be attenuated when passing through the solution of matter and the transmitted light intensity decreases. Scattering spectroscopy measures certain physical properties by measuring the amount of light that a substance scatters at certain wavelengths. ### Principles of Absorption Spectroscopy When electromagnetic radiation passes through a material, a portion of the electromagnetic radiation may be absorbed. If that occurs, the remaining radiation, when it is passed through a prism, yields a spectrum with a gap in it, called an absorption spectrum. The absorption spectrum is characteristic of a particular element or compound, and does not change with varying concentration. At a given wavelength, the measured absorbance has been shown to be proportional to the molar concentration of the absorbing species and the thickness of the sample the light passes through. This is known as the Beer-Lambert law. ### Beer-Lambert Law When radiation falls on homogeneous medium, a portion of incident light is reflected, a portion is absorbed and the remainder is transmitted. The two laws governing the absorption of radiation are known as Lambert's law and Beer's law. **Lambert's Law** states that when monochromatic light passes through a transparent medium, the intensity of transmitted light decreases exponentially as the thickness of absorbing material increases. **Beer's Law** states that the intensity of transmitted monochromatic light decreases exponentially as the concentration of the absorbing substance increases. **Mathematical expression of Beer-Lambert law:** The relationship between concentration, length of the light path, and the light absorbed by a particular substance is expressed mathematically as shown below: **A = log** (Io/I) = **ε.c.l** Where: - **A** = Absorbance - **Io** = Intensity of incident light - **I** = Intensity of light transmitted through the sample - **ε** = Extinction coefficient or absorption coefficient for an absorbing compound - **C** = Concentration of absorbing material in the sample - **l** = Path length (cm) If the concentration is expressed in molarity, ε is termed as the molar absorption coefficient or molar extinction coefficient. Its unit is M-1 cm-1. If the concentration is expressed in g/liter, ε becomes the specific absorption coefficient. The absorbance is a dimensionless quantity. Theoretically, absorbance (A) can have any positive value; in practice, for UV and visible spectrometers, 'A' normally varies between zero and one. The ratio of the intensity of the transmitted light (I) to the intensity of the incident light (Io) is called transmittance (T). **T = I/Io** It measures the amount of light transmitted after passing through the medium. The smaller the transmittance, the greater the absorption of light. Transmittance is always a numerical value between zero (all light absorbed) and one (no light absorbed). It is common to convert transmittance into percent transmittance (%T). It is 100 × T. **%T = I/Io × 100% = T × 100%** Percent transmittance varies between 100% (all light transmitted) and 0% (no light transmitted). The transmittance and absorbance are inversely related. Moreover, the inverse relationship between transmittance and absorbance is not linear, it is logarithmic. **A = log10 (1/T) = -log10 T = -log10 (%T/100) = -log10%T + log10 100 = 2-log10%T** ### Molar Extinction Coefficients vs. Absorbances for 1% Solutions A molar extinction coefficient in the calculation gives an expression of concentration in terms of molarity: **A/Emolar × l = Molar concentration** However, many literatures do not provide molar extinction coefficients. Instead, they provide absorbance values for 1% (= 1g/100mL) solutions measured in a 1 cm cuvette. These values can be understood as percent solution extinction coefficients (Epercent). Consequently, when these values are applied as extinction coefficients in the general formula, the units for concentration, c, are percent solution (i.e. 1% = 1g/100mL = 10mg/mL). **A/Epercent × 1 = Percent concentration** If one wishes to represent concentration in terms of mg/ml, then an adjustment factor of 10 must be made when using these percent solution extinction coefficients (i.e. one must convert from 10 mg/ml units to 1 mg/ml concentration units). **A/Epercent × 10 = Concentration in mg/ml** The relationship between molar extinction coefficient (Emolar) and percent extinction coefficient (Epercent) is as follows: ** (Emolar) 10 = (Epercent) × (molecular weight of protein)** ### In Infrared Spectra - **Position of band depends on:** - Mass of atoms – Light atoms give high frequency. - Bond strength – Strong bonds give high frequency. - **Strength of band depends on:** - Change in dipole moment - A large change in dipole moment gives strong absorption. - **Width of band depends on:** - Hydrogen bonding - Strong H-bond gives wide peak. ### Nuclear Magnetic Resonance Nuclear magnetic resonance (NMR) is a spectroscopic technique that involves a change in nuclear spin energy in the presence of an external magnetic field. It is based on the magnetic properties of nuclei that result from a property called nuclear spin. NMR allows us to detect atomic nuclei and say what sort of environment they are in, within their molecule. For example, the hydrogen of the hydroxyl group in propanol is different from the hydrogens of its carbon skeleton. With the help of a proton NMR, one can easily distinguish between these two sorts of hydrogens. '¹H NMR' and 'proton NMR' are interchangeable terms. The hydrogen atom is denoted by H. Likewise, carbon NMR (¹³C NMR) can easily distinguish between the three different carbon atoms in propanol. **Figure 3. 12** ¹H NMR distinguishes the colored hydrogens and ¹³C NMR distinguishes the boxed carbons. NMR spectroscopy is used to detect nuclei, but only those nuclei that have a magnetic property as a result of nuclear spin. Spin comes in multiples of 1/2 and can be + or -. Not all atomic nuclei have nuclear spin. The rules for determining the net spin of a nucleus are as follows; - If the number of neutrons and the number of protons are both even, then individual spins are paired and the overall spin becomes zero (i.e. nuclei have no spin). - If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin (i.e. 1, 2, 3). - If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin (i.e. 1/2, 3/2, 5/2). **Table 3.2** Number of protons, number of neutrons and nuclear spin quantum number of some elements | Number of protons | Number of neutrons | Spin quantum number (I) | Element | |---|---|---|---| | Even | Even | 0 | ¹²C, ¹⁶O | | Odd | Odd | Integer (1,2,...) | ¹⁴N | | Even | Odd | Half-integer (1/2, 3/2,...) | ¹³C | | Odd | Even | Half-integer (1/2, 3/2,...) | ¹⁹F, ¹⁵N | For each nucleus with spin, the number of allowed spin states - it may adopt - is determined by its nuclear spin quantum number (I). A nucleus of spin quantum number I has 2I + 1 allowed spin states. For example, ¹H has the nuclear spin quantum number I = 1/2 and has two allowed spin states [2(1/2) + 1 = 2] for its nucleus, -1/2 and +1/2. For the chlorine nucleus, I = 3/2 and there are four allowed spin states [2(3/2) + 1 = 4] for its nucleus, -3/2, -1/2, +1/2 and +3/2. **Table 3.3** Spin quantum numbers and number of spin states of some common element | Element | ¹H | ¹H | ¹²C | ¹³C | ¹⁴N | ¹⁶O | ¹⁷O | ¹⁹F | |---|---|---|---|---|---|---|---| | Spin quantum number | 1/2 | 1/2 | 0 | 1/2 | 1 | 0 | 5/2 | 1/2 | | Number of spin states | 2 | 2 | 0 | 2 | 3 | 0 | 6 | 2 | The hydrogen nucleus ¹H has a nuclear spin that can assume either of two spin states, -1/2 and +1/2. The ¹²C nucleus has no spin whereas ¹³C nucleus has spin that can assume either of two spin states, -1/2 and +1/2. ### Physical Basis of NMR NMR spectroscopy is based on the magnetic properties of nuclei that result from a property called nuclear spin. All nucleus with spin act like a tiny magnet. We can compare the behaviour of a nucleus acting like a tiny magnet with magnetic compass placed in an external magnetic field. Imagine for a moment that we were able to 'switch off' the Earth's magnetic field. Compass needle (made of a magnetic material) will point randomly in any direction. However, as soon as we switched on the Earth's magnetic field back, the needle would point North-their lowest energy state. If we wanted needle to point South, we would have to apply force (energy). But after removal of external force, the needle would return to its lowest energy state, pointing North. How hard it is to turn the compass needle depends on how strong the magnetic field is and also on how well the needle is magnetized. If the needle is not magnetized at all, it is free to rotate. Nevertheless, there is an important difference between a compass needle and the atomic nucleus acting like a tiny magnet. A real compass needle can rotate through 360° and have a virtually infinite number of different energy levels, all higher in energy than the lowest energy state (pointing North). When atomic nuclei acting like tiny magnets are placed in an external magnetic field, they have different energy levels. Fortunately, the number of energy levels an atomic nucleus can adopt is very less. For example, a ¹H or ¹³C nucleus in a magnetic field can have two energy levels. Let's take an example of the hydrogen nuclei in a chemical sample. In the discussion, the word 'proton' is used for '¹H nuclei'. In the absence of an external magnetic field, the nuclear magnetic poles are oriented randomly. When an external magnetic field is applied to ¹H nuclei, they can either align themselves parallel to the field, which would be the lowest energy state, or they can align themselves antiparallel to the field, which is higher in energy. The magnetic poles of nuclei with a spin of +1½ are oriented parallel to the applied field, and those nuclei with a spin of -1/2 are oriented antiparallel to the applied field. **Figure 3.13** In the absence of an external magnetic field, the nuclear magnetic poles are oriented randomly (with arrows indicating their magnetic, north-south, polarity). In an external magnetic field or applied magnetic field, the spin state +1/2 is aligned parallel to the field, while the spin state -1/2 is aligned antiparallel to the applied field. More nuclei are oriented along with the applied field because this arrangement is lower in energy. In the absence of an external magnetic field, the two spin states have the same energy. But when an external magnetic field is applied, the two spin states have different energies: the +1½ spin state has lower energy than the -1/2 spin state. The energy difference between two spin states is a function of the strength of the applied magnetic field. The stronger the applied magnetic field, the higher the energy difference between the possible spin states. However, the energy difference between the two nuclear spin states is very small-so small that a very, very strong magnetic field is required to see any difference at all. **Figure 3.14** Effect of increasing magnetic field at a ¹H nucleus on the energy difference between its +1/2 and -1/2 spin states. The two spin states have identical energies when the external magnetic field is absent. The difference in energy between the two spin states depends on how strong the applied external magnetic field is, and also on the properties of the nucleus itself. The energy difference between the two spin states grows with increasing field. The stronger the magnetic field, the higher the energy difference between the two states. Thus, for a nucleus in an external magnetic field, the difference in energy between two spin states in an applied magnetic field depends on: - How strong the magnetic field is, and - The magnetic properties of the nucleus itself. The energy difference between the two spin states is given by the fundamental equation of NMR: **∆E = hγHB/2π** Where: - h is Planck's constant, - B, is the magnitude of the magnetic field at the H¹ nucleus (proton), in gauss; and - γH is a fundamental constant of the proton, called the gyromagnetic ratio. The value of this constant is 26,753 radians gauss-1 s-1. This equation shows that when the external magnetic field is zero, there is no energy difference between the spin states and as the magnetic field is increased, the energy difference between the two spin states increases. When the ¹H nuclei in a chemical sample are subjected in a magnetic field; each ¹H nucleus is in one of two spin states that differ in energy by an amount ∆E, and; a small excess of ¹H nuclei have spin +1/2. Even at a very strong magnetic field, the difference in the populations of the two spin energy states is very small. If the sample is now subjected to electromagnetic radiation with energy exactly equal to ∆E, this energy is absorbed by some of the ¹H nuclei in the +1/2 spin state. The absorbed energy causes these protons to 'flip' their spins and assume a more energetic state with a spin 1/2. Since the energy difference between the two states even in a very very strong external magnetic field is so small, the amount of energy needed to flip the nuclei can be provided by electromagnetic radiation of radio wave frequency. Radio waves flip the nucleus from the lower energy state to the higher state. This absorption phenomenon, called nuclear magnetic resonance, can be detected in a type of absorption spectrometer called an NMR spectrometer. ### Circular Dichroism Light is a transverse electromagnetic wave. The electric and magnetic fields in an electromagnetic wave oscillate along directions perpendicular to the propagation direction of the wave. Light can be unpolarized or polarized depending on how the electric field is oriented. In un-polarized light, the electric field vector oscillates in more than one plane; all perpendicular to the direction of propagation. If the electric field vector oscillates in single plane perpendicular to the direction of propagation, it is called linearly or plane polarized light. The orientation of a linearly polarized light is defined by the direction of the electric field vector. Linear polarization is obtained by passing unpolarized light through a polarizer that absorbs all electric field vectors not lying along a particular plane. If the electric field vector rotates around the propagation axis maintaining a constant magnitude, it is called circularly polarized light. Circularly polarized light is the antithesis of linearly polarized light. In linear polarized light, the direction of the vector stays constant and the magnitude oscillates whereas in circularly polarized light, the magnitude stays constant while the direction oscillates. Circularly polarized light is obtained by superimposing two plane polarized light of same wavelengths and amplitudes but having a phase difference of 90°. A phase difference of 90° means that when one wave is at its peak, then the other one is just crossing the zero line. **Figure 3.18** Linearly polarized light results when the direction of the electric field vector is restricted to a plane perpendicular to the direction of propagation while its magnitude oscillates. In circularly polarized light, the magnitude of the oscillation is constant and the direction oscillates. A circularly plane polarized light may be right or left-handed circularly polarized depending on the rotation direction. For left circularly polarized light with propagation towards the observer, the electric field vector rotates counter-clockwise. For right circularly polarized light, the electric field vector rotates clockwise. The superposition of left and right circularly polarized light beams of equal amplitudes can result in linearly polarized light. Thus, linear polarized light can be viewed as a superposition of opposite circular polarized light of equal amplitude and phase. **Figure 3.19** Schematic representation of right circularly polarized and left circularly polarized light. In both cases, the length of the vector remains constant. In linearly polarized light, the electric vector stays in the same plane but its length changes. **Optical rotatory dispersion (ORD) and circular dichroism (CD)** are two phenomena that result when chiral molecules (molecules that have no plane and center of symmetry) interact with polarized light. Most of biological molecules are chiral molecules and thus they are optically active. An optically active compound shows a phenomenon called optical rotation. It means that the plane of polarization of a linearly polarized light rotates as it passes through an optically active medium. The technique of ORD measures the ability of optically active compounds to rotate plane polarized light as a function of the wavelength (i.e. wavelength dependence of optical rotation). **Chiral molecules** Most of chiral molecules contain one or more chiral center(s). Any tetrahedral carbon atom that has four different substituents is a chiral center. A molecule is not chiral (even if it has chiral centers) if it has a plane or center of symmetry. To be a chiral molecule there should be no plane and center of symmetry. **Figure 3.20** When plane-polarized light is passed through a solution containing an optically active compound, there is net rotation of the plane polarized light. The plane-polarized light is rotated either clockwise (dextrorotatory) or counterclockwise (levorotatory) by an angle. **Circular Dichroism** is an absorption spectroscopy. Dichroism is a word derived from Greek which means two-colors, because the sample under analysis has one color if illuminated with the right polarized light and a different color if illuminated with the left one. The color, in fact, depends on light absorption. Circular dichroism is observed when optically active matter absorbs left and right circularly polarized light slightly different. In fact, circular dichroism is the absorption difference between left and right circularly polarized light at a given wavelength. Absorption is quantitated by the molar extinction coefficient (ε). Optically active samples have distinct molar extinction coefficients for left ( εL ) and right ( εR ) circularly polarized light. The difference in absorbance of left and right circularly polarized light is a measure of circular dichroism. Thus, **CD = AL - AR = ∆A** From **Beer-Lambert law** the difference in the absorbance of left and right circularly polarized light (i.e. ∆A) can be given by, **∆A = (εL - εR ).c./** **∆A = ∆ε.ε./** where, c is the molar concentration and l is the path length (cm) where, ∆ε is the molar circular dichroism. The differential absorption of the left and right circularly polarized light means that the amplitudes of the right and left circularly polarized components of the transmitted beam will differ. The superposition of the two components is no longer a linearly polarized wave but it rotates along an ellipsoid path. Such a light wave is called an elliptically polarized light. How elliptical the plane-polarized wave becomes after traversing the medium is determined by the difference between the absorptions of the two circularly polarized components. In the most extreme case, the material almost completely extincts one left or right component and then the transmitted wave almost becomes a perfect circularly polarized light because the other circular component disappears. The ellipticity is proportional to the difference in the absorbance of the two components, A₁ - AR. Thus, the CD is equivalent to ellipticity. The relationship between CD and ellipticity (θ) is given by: **θ = 2.303 (AL-AR) / 180 / 4π = 33 (AL-AR) = 33 ∆A degree** **Units of CD data** CD data are presented in terms of either ellipticity [θ] or differential absorbance (∆A). The data are normalized by scaling to molar concentrations of either the whole molecule or the repeating unit of a polymer. For far-UV CD of proteins, the repeating unit is the peptide bond. The mean residue weight (MRW) for the peptide bond is calculated from MRW=M/(N-1), where M is the molecular mass of the polypeptide chain (in Da), and N is the number of amino acid residues in the chain; the number of peptide bonds is N-1. The **mean residue ellipticity (MRE)** at wavelength λ is given by, **[θ]MRE = MRW × θλ / 10 × l × c** Where, θλ = observed ellipticity (in degrees), l = path length (in cm) and c = concentration (in g/ml) If we know the molar concentration (c) of a solute, the molar ellipticity at wavelength λ is given by, **[θ]molar = 100 × θλ / cxl** The units of mean residue ellipticity and molar ellipticity are degrees cm² decimol-1. ### Applications of Circular Dichroism Circular dichroism is an excellent method for the study of the conformations adopted by proteins and nucleic acids in solution. Although not able to provide the detailed residue-specific information as obtained from NMR and X-ray crystallography, analysis by CD has a number of advantages. CD analysis can be made on molecules of any size and also, even in very small concentrations. It allows to study dynamic systems and kinetics. It provides one of the best methods for monitoring any structural alterations that might result from changes in environmental conditions, such as pH, temperature, and ionic strength. However, it only provides qualitative analysis of data. It does not provide atomic-level structural analysis. Also, the observed spectrum is not enough for claiming one and only possible structure. CD has a wide range of potential applications in the study of structure and function of biomolecules such as proteins and nucleic acids. Following are some important applications. 1. Determination of protein's secondary and tertiary structure. 2. Comparison of the secondary and tertiary structure of wild-type and mutant proteins. 3. Nucleic acid structure and changes upon protein binding or melting. 4. Determination of conformational changes due to protein-protein interactions, protein-DNA interactions and protein-ligand interactions. ### Analysis of Protein’s Structural and Conformational Changes Circular dichroism relies on the differential absorption of left and right circularly polarized light by chromophores. Depending on the wave-length of the light used for the generation of circularly polarized light, there are **far-UV CD (190-250 nm), near-UV CD (250-320 nm) and visible CD.** Proteins possess a number of chromophores which can give rise to CD signals. In proteins, the chromophores of interest include the peptide bond, aromatic amino acid side chains and disulphide bonds. The peptide bonds have an absorption range of 240 nm to 190 nm. This region is called the 'far-UV' region. The aromatic side chains of tyrosine, tryptophan and phenylalanine absorb light in the 260 nm to 320 nm region. This region is the 'near-UV' region. The three residues, phenylalanine, tyrosine and tryptophan, exhibit fine structure peaks between 255-270 nm, 275-285 nm, and 290-305 nm, respectively. The disulphide bonds absorb light near 260 nm and are generally quite weak. In addition, various non-protein cofactors can also absorb light over a wide spectral range, such as pyridoxal phosphate around 330 nm, flavins in the range 300 nm to 500 nm (depending on oxidation state), heme groups strongly around 410 nm with other bands in the range from 350 nm to 650 nm (depending on spin state and coordination of the central Fe ion) and chlorophyll moieties in the visible and near IR regions. The CD spectrum in the far-UV region (240 nm-190 nm) gives quantitative information about the overall secondary structure of the protein. CD spectra can be readily used to estimate the fraction of a molecule that is in the a-helix, the ẞ-sheet, or random coil conformation. **Figure 3.21** Circular dichroism spectra in far-UV region and protein secondary structure. The absorption spectrum of synthetic polypeptide, poly-L-glutamate, in the far UV region (between 180 nm and 250 nm). The a-helix, β-sheet and random coil structures give rise to a characteristic shape and magnitude in the CD spectrum. ### Theory of X-Ray Diffraction A molecular structure resolved at atomic level means that the positions of each atom can be distinguished from those of all other atoms in three-dimensional space. The closest distance between two atoms in space is the length of a covalent bond, and a typical length of a covalent bond is approximately 0.12 nm. If we require to resolve the atoms of a macromolecule, the wavelength of light required for our atomic microscope would necessarily be <0.24 nm. This falls into the X-ray range of the electromagnetic spectrum. However, X-rays cannot be focused and thus cannot form an image of an object in the same manner as a light microscope. We rely on the constructive and destructive interference caused by scattering radiation from the regular and repeating lattice of a single crystal to determine the structure of macromolecules. A good way to understand X-ray diffraction is to draw an analogy with visible light. Light has certain properties that is best described by considering wave nature. Whenever wave phenomena occur in nature, interaction between waves can occur. If waves from two sources are in same phase with one another, their total amplitude is additive (constructive interference); and if they are out of phase, their amplitude is reduced (destructive interference). This effect can be seen in figure 8.1 when light passes through two pinholes in a piece of opaque material and then falls onto a white surface. Interference patterns result, with dark regions where light waves are out of phase and bright regions where they are in phase. If the wavelength of the light (λ) is known, one can measure the angle α between the original beam and the first diffraction peak and then calculate the distance d between the two holes with the formula **d = λ / sin α** The same approach can be used to calculate the distance between atoms in crystals. Instead of visible light, which has longer wavelength to interact with atoms, we can use a beam of X-rays. X-rays, like light, are a form of electromagnetic radiation, but they have a much smaller wavelength. The wavelengths of X-rays (typically around 0.1 nm) are of the same order of magnitude as the distances between atoms or ions in a molecule or crystal. If a narrow beam of X-rays is directed at a crystalline solid, most of the X-rays will pass straight through it. A small fraction, however, scatters by the atoms in the crystal. The electrons of an atom are primarily responsible for the scattering of X-rays. The number of electrons in a given volume of space (the electron density) determines how strongly an atom scatters X-rays. The interference of the scattered X-rays leads to the general phenomenon of diffraction. **Figure 8.1** Diffraction patterns. Any energy in the form of waves will produce interference patterns if the waves from two or more sources are superimposed in space. One of the simplest patterns can be seen when monochromatic light passes through two neighbouring pinholes and is allowed to fall on a screen. When the light passes through the two pinholes, the holes act as light sources, with waves radiating from each and falling on a white surface. When the waves are in the same phase, a bright fringe appears (constructive interference), but when the waves are out-of-phase they cancel each other out, producing dark fringe (destructive interference). **Figure 8.2** Interference occurs among the waves scattered by the atoms when crystalline solids are exposed to X-rays. There are two types of interferences depending on how the waves overlap one another. Constructive interference occurs when the waves are moving in phase with each other; and destructive interference occurs when the waves are out-of-phase. X-rays are electromagnetic radiation of wavelengths 0.1-100 Å. X-rays can be produced by bombarding a metal target (most commonly copper, molybdenum or chromium) with electrons produced by a heated filament and accelerated by an electric field. A high-energy electron collides with and displaces an electron from a lower orbital in a target metal atom. Then an electron from a higher orbital drops into the resulting vacancy, emitting its excess energy as an X-ray photon. A crystal is placed in an X-ray beam between the X-ray source and a detector, and a regular array of spots called reflections is generated. The spots are created by the diffracted X-ray beam; and each atom in a molecule makes a contribution to each spot. The electrons that surround the atoms are the entities which physically interact with the incoming X-ray to diffract them, not the atomic nuclei. The diffraction pattern is recorded on a photographic plate and then analyzed to reveal the nature of that lattice. The position and intensity of each spot in the X-ray diffraction pattern contain information about the positions of the atoms in the crystal that gave rise to it. An optical scanner precisely measures the position and the intensity of each reflection and transmits this information in digital form to a computer for analysis. The position of a reflection can be used to obtain the direction in which that particular beam was diffracted by the crystal. The intensity of a reflection is obtained by measuring the optical absorbance of the spot on the film, giving a measure of the strength of the diffracted beam that produced the spot. **Figure 8.3** In diffraction experiments, a narrow beam of X-ray is taken out from the X-ray source and directed onto the crystal to produce diffracted patterns. When the primary beam hits the crystal, most of it passes straight through, but some is diffracted by the crystal. These diffracted beams are recorded on a detector.