A cycle is considered complete when a Hght wave starts at zero and then crosses the X-axis twice. The wave in Figure 1. Frequency is a measure of the number of cycles of a Hght wave per unit time. The arrow denotes the distance between adjacent crests, and is called the wavelength, X. Note also the definition of a cycle. Another property used to describe Hght is its wavenumber. A wavenumber measures the number of cycles in a light beam per unit length.
If we substitute Equation 1. These equations also show that these three quantities are related to each other. Throughout this book, we will usually refer to hght waves by their wavenumber. However, at times it will be more convenient to refer to a hght beam's frequency or wavelength. As mentioned above, hght can also be thought of as a particle. A particle of light is called a photon. A photon has no mass, but it does have energy. Note that high wavenumber light has more energy than low wavenumber light.
The Electromagnetic Spectrum There are types of hght in addition to the visible hght that we can detect with our naked eyes. All the different types of light are called the electromagnetic spectrum. Each different type of light can be characterized by a different frequency, wavelength, wavenumber, or energy.
A section of the electro- magnetic spectrum is illustrated in Figure 1. Note that in reading Figure 1. When performing a quantitative absorption experiment, the first thing to decide upon is what type of hght to use in the analysis.
Also illustrated is how wavelength, wavenumber, frequency, and energy change across the spectrum. The types of light listed in Figure 1. The lowest energy Ught seen in Figure 1. When this type of Ught is absorbed by a molecule, there is an increase in the rotational energy of the molecule.
This is why microwave spectroscopy is sometimes called rotational spectroscopy. This technique is typically limited to gases because gas phase molecules are free to rotate, whereas soHd and Hquid phase molecules are not.
Although microwave spectrometers exist, and have been used to perform quantitative analyses, their use is not widespread. However, far-infrared absorbances are low in energy, and are typically found in heavy molecules such as inorganic and organometallic substances. Most organic molecules do not absorb in the far infrared, limiting the types of molecules this wavenumber range can be used to analyze. Many of the molecules in the universe of which there are more than 10 million give usable mid-infrared spectra.
Mid- infrared absorbances are intense, and often times only a miUigram of material is needed to obtain a spectrum. Additionally, almost every type of material, including solids, liquids, gases, polymers, and semi-solids can have their mid-infrared spectra measured. A disadvantage of the strength of mid- infrared absorbances is that it is easy for a sample to absorb all the hght impinging on it at a given wavenumber, making it difficult to record a spectrum.
This problem with mid- infrared samples is called the thickness problem. However, mid-infrared Hght is commonly used for quantitative analysis. Throughout the rest of this book, the terms mid-infrared and infrared will be used interchangeably.
Like in the mid-infrared, molecules vibrate when they absorb near-infrared light, but with higher energy than in the mid-infrared. A disadvantage of near-infrared absorbances is that they are typically times weaker than mid-infrared absorbances.
This is bad if only a small amount of sample is available. However, near-infrared samples do not suffer from a thickness problem, so sample preparation can be faster and easier compared to mid-infrared spectroscopy. Because of this, and of the high performance of near-infrared spectrometers, there has been an explosion of quantitative applications of near-infrared spectroscopy in the last 30 years. The highest energy Hght we will consider in this book is the ultraviolet and visible UV-Vis.
Although UV-Vis absorbances can be intense, only molecules with certain types of chemical bonds absorb UV-Vis light, somewhat limiting the types of molecules that can be analyzed. Despite this limitation, UV-Vis light was historically the first type of light widely used in quantitative analysis, and is still widely used today.
Beer's Law The basis of most quantitative spectroscopic analyses is Beer's law. This law relates the amount of Hght absorbed by a sample, a spectroscopically observable property, to the concentration of absorbing species in the sample.
This relationship is what aHows absorbance measurements to be used to predict concentrations. To derive Beer's law, we assume the experi- mental setup shown in Figure 1.
We also assume that monochromatic Hght of wavelength A, impinges upon the sample perpendicular to one of its faces. Light intensity is defined as the number of photons of light hitting a unit area per unit time.
The thickness ox pathlength of the material is denoted by L. An infinitesimally thin slab of the absorbing material is denoted by dL. An infmite- simally thin slab of the material is denoted by dL. Ep is the energy of the photon. One way to think about how molecules absorb light is to consider the interaction as a colUsion between two particles.
Imagine photons of light and molecules as simple particles shaped like spheres. When two particles colHde be they molecules or billiard balls , several different types of colHsion can occur. The particles may undergo an elastic collision, which is illustrated in Figure 1. By definition, an elastic colHsion results in no net energy exchange between the molecules. After the colHsion, the photon still has energy hcW, and the methane molecule is still at rest.
The only thing that has changed is the direction of travel of the photon, and to a lesser extent, the position of the methane molecule. Elastic colHsions between photons and molecules result in a phenomenon called Rayleigh scattering, in which the direction but not the energy of the photon is changed. The intensity of Rayleigh scattering is proportional to the fourth power of the wavenumber of the photon, W, involved in the scattering.
Molecules in the upper atmosphere preferentially scatter blue light, which is why the sky is blue. In this type of collision, energy is exchanged between the particles, and they leave the colHsion with different energies than before the colHsion. This is illustrated in Figure 1. The photon's energy after the colHsion is Ei i for inelastic.
The concentric circles in Figure 1. Also, note that the direction of the photon has changed after the colHsion. Inelastic collisions between molecules and photons give rise to a phenomenon called Raman scattering. Thus, after the colHsion the inelastically scattered photon carries chemical information.
When the intensity and the wavenumber of these photons are analyzed and plotted, one obtains a Raman spectrum. Raman spectra are similar to infrared spectra in that they measure the vibrational energy levels of a molecule. Raman spectra can be used to quantitate chemical species, but is beyond the scope of this book.
A third thing that can occur when a photon encounters a molecule is a totally inelastic collision. After the collision the photon has disappeared; all its energy has been absorbed by the molecule leaving it excited. This phenomenon is known as absorbance. The wavenumber of the light absorbed and the intensity with which it is absorbed depends upon the molecule involved in the collision.
Thus, chemical information can be derived from a plot of absorbance intensity versus wavenumber, called an absorbance spectrum. Such a spectrum is seen in Figure 1.
A totally inelastic colUsion between a photon and a molecule results in the disappearance of the photon, and the transfer of all the photon's energy into the molecule.
The total amount of light absorbed by a sample is simply equal to the total number of photons that undergo totally inelastic colHsions with molecules. The decrease in the number of photons leaving the sample will give rise to an absorbance feature in the spectrum of the sample.
Now, photons may also be scattered by macroscopic-size particles such as dust grains, leading to a decrease in photons exiting the sample as well. Experimentally, this will look hke absorbance but it is not. Thus, we are tacitly assuming that our sample has no other species present other than molecules that will interact with the light beam.
In Figure 1. The more photons and molecules there are in dL, the more coUisions will occur. The number of molecules in dL is simply determined by the analyte concentration, c. The number of photons present is given by the intensity of Hght in dL, which is simply L Additionally, the thicker the slab dL, the more photons will be absorbed because there are more molecules encountered.
Equation 1. Remember that molecules and photons can undergo several different types of collisions. Only some percentage of these colhsions will be totally inelastic. It is the number of totally inelastic collisions that determines the amount of hght absorbed. To calculate the number of these colhsions, we must multiply the right-hand side of Equation 1.
This number is called the absorptivity, and is denoted with the Greek letter epsilon, s. The absorptivity can also be thought of as a probabihty, it is the probabihty that a photon-molecule collision wiU be totally inelastic. The absorptivity depends upon the identity of the molecule absorbing the hght, and the wavelength of hght being absorbed. By inserting the absorptivity into Equation 1. We can then remove the proportionahty sign from Equation 1.
We can combine terms and rewrite Equation 1. The right-hand integration limits are for the entire thickness of the sample, L. Note that s and c have both been brought outside the integration sign. This means that we are assuming that the concentration and the absorptivity are not a function of pathlength.
In essence, we are assuming that the concentration and absorptivity are the same everywhere in the sample, i. However, it is traditional to express Beer's law using base 10 logarithms rather than natural logarithms.
We divide the right-hand side of Equation 1. What this equation tells us is that the amount of light absorbed by a sample depends on the concentration of the analyte, the thickness of the sample, and the sample's absorptivity.
Also, note that the relationships in Beer's law are Hnear. For example, doubling the pathlength or concentration of a sample doubles its absorbance.
Many spectrometers are capable of measuring spectra with the F-axis in absorbance units. An example of a spectrum plotted in absorbance units is seen in Figure 1.
Because the relationship between absorbance and concentration is Hnear, the peak height or area of an analyte's absorbance band will vary hnearly with concentration.
Transmittance measures the fraction of light transmitted by the sample. Percent transmission measures the percentage of light transmitted by a sample. Note that the peaks point down. Rearranging Equation 1. Most spectroscopic software packages allow you to switch between the two units, and Equation 1. If we substitute Beer's law Eq. It is absolutely necessary that you use spectra plotted in absorbance units for quantitative analysis because of the linear relationship between absorbance and concentration.
Some further discussion of the absorptivity is in order. The absorptivity is the proportionality constant between concentration and absorbance.
This inequaUty shows that the absorptivity of water depends on the wavenumber, and illustrates that the absorptivity for any molecule varies with the wavenumber.
For a given molecule and wavenumber of light, the absorptivity is a fundamental physical constant of the pure molecule. The absorptivity can be thought of as an "inherent absorbance. A quick look at Beer's law Eq.
These units may be hard to understand, but further analysis shows that these units make sense. Recall that the absorptivity represents the probability of a photon- molecule collision being totally inelastic. Do the units of the absorptivity express themselves as a probabihty? Physicists often express probabilities in units of area, and call the quantity a cross section. Imagine throwing a baseball at the broad side of a barn. The probabihty of your hitting the barn increases the larger its area, and decreases the smaller its area.
It all depends upon the size of the target. Additionally, your probabihty of hitting the barn is higher the closer you are to it, and lower the farther you are from it.
In this case, the absolute area of the barn does not change, but the apparent area, how big the barn appears to you, changes with your distance from it. This apparent area is called the apparent cross section of the barn. Simply stated, the apparent cross section measures how large the barn appears to be from where you are standing. The same concept can be applied to photon-molecule colHsions. From the point of view of a photon, the molecule appears "large," and the interaction between the two has a large apparent cross section.
This is measured experimentally as a large absorptivity. Molecules that absorb light weakly have a low probabiHty of undergoing totally inelastic coUisions with photons. From the point of view of the photon, the molecule appears "small," and the interaction is characterized by a small cross section.
This is measured experimentally as a small absorptivity. Are the units of the absorptivity consistent with this idea of apparent cross section? Since probability can be expressed in area as well, what the absorptivity measures is the apparent section of a mole of analyte molecules with respect to totally inelastic photon collisions.
Consequently, this quantity is called the molar absorptivity. The units of the absorptivity do make sense when thought of as a probability. Variables Affecting the Absorbance and Absorptivity For a calibration to be legitimately appHed to standard and unknown samples alike, the absorbance reading for a given concentration of the analyte must be reproducible. To achieve this, an understanding of the variables other than concentration that affect the measured absorbance is essential.
The purpose of this section is to discuss the important variables that must be controlled when performing quantitative spectroscopic analyses. This will involve discussing the physical processes behind the absorbance of Hght by molecules. Though this discussion is mathematical by its very nature, the amount of complex math has been minimized.
For the mathematical underpinnings of the concepts presented here, consult Appendix 1 at the back of this chapter, or any of the undergraduate texts on physical chemistry or quantum mechanics cited in the bibliography.
Therefore, energy is quantized. A quantum of energy is extremely small, and the fact that energy comes in discrete but small packets is not important for the consideration of the physics of the macroscopic world. However, in the microscopic world of atoms and molecules energy quantization has a huge impact upon how matter and energy interact.
The field of physics that deals with the behavior of atoms, molecules, nuclei, and quanta of energy is called quantum mechanics. Quantum mechanics has Uttle to tell us about physical systems that are unbound, i. Imagine an electron moving through a vacuum or a baseball being thrown by a pitcher as examples of unbound systems.
However, any time microscopic particles are bound, such as the electrons and protons in a molecule, their energy levels become quantized. This means that the particles in the system cannot have just any energy, but that only certain specific energies are allowed. The rotational, vibrational, and electronic energies of molecules are quantized. The reason that molecules have discrete spectral bands and absorb light at discrete energies is that their energy levels are quantized. There are a number of things that determine the quantized energy levels of a molecule, including its mass, type of atoms present, the strength of the chemical bonds, and the arrangement of the atoms in space.
Two hypothetical quantized energy levels for a molecule are shown in Figure 1. When a molecule absorbs a photon of Ught, it is said to make a spectroscopic transition from the lower to the upper energy level, as indicated by the arrow in Figure 1. For a photon to be absorbed and give rise to the transition seen in Figure 1.
Figure 1. A photon can only be absorbed if its energy happens to match a AE in a molecule. If the energy of a photon does not match any of the AEs in a molecule, it will pass through unabsorbed. Thus, Equation 1. It tells us that absorbance can take place, but says nothing about the probability of absorbance taking place. For the transition seen in Figure 1. As a result, no light would be absorbed.
More specifically, it is the difference between the number of molecules in the upper and lower energy levels that determines the number of photons that can be absorbed. The fewer the molecules with energy Eu the fewer are available to absorb light of energy AE and make the transition to Ey.
The Boltzmann distribution assumes that energy levels are populated due to random thermal processes collisions. Solving Equation 1. By substituting Equation 1. Thus, changes in the temperature can affect the measured absorbance even at constant pathlength and concentration.
This means that at a fundamental physical level, absorbance does depend upon the temperature, and that a caHbration obtained with samples at one temperature will not necessarily give accurate results for samples at a different temperature. Temperature is one of the most important variables to control when performing quantitative spectroscopic analysis.
The practical impact of Equation 1. So, although temperature is an important parameter to control in spectroscopic quantitative analysis, the types of caHbrations most sensitive to this effect will be those involving spectroscopic transitions that are low in energy.
However, there are other ways in which changes in the temperature can affect caUbrations, as will be discussed below. This phenomenon can be seen in the spectrum of polystyrene in Figure 1. More generally, why do some molecules absorb hght more strongly than others? Recall from above the discussion of quantum mechanics. One of the postulates of quantum mechanics is that there exists for energy levels in a molecule a wavefunction that contains all the information about that energy level.
For the spectroscopic transition shown in Figure 1. If we could a priori know all the wave- functions of a molecule, we would know everything there is to know about the molecule. In the real world, this is not usually the case.
An important use of spectroscopy is to measure molecular energy levels, and use these to help formulate reaUstic wavefunctions for molecules. One of the important properties of wavefunctions is that their square gives a probability. For example, the probability of finding an electron at a specific place in a hydrogen atom is equal to the square of the electron's wavefunction at that point in space. Note that the transition probability depends upon the product of the wavefunctions of the two energy levels involved in a spectroscopic transition.
A dipole is simply two charges separated by a distance, and a dipole moment is a measure of charge asymmetry. The arrow represents the magnitude and direction of the dipole moment for the bond. The dipole moment is a vector quantity, having both a magnitude and a direction. Vector quantities can be represented by arrows, where the length of the arrow is proportional to the magnitude, and the arrow point gives the direction. The dipole moment vector for the H-Cl molecule is seen in Figure 1.
Each bond in a molecule will typically have a dipole moment called the bond dipole. The overall, or net dipole for a molecule, is the vector sum of the bond dipoles. This is expressed in Equation 1. For hydrogen chloride, since there is only one bond, the bond dipole and net dipole are the same. For a spectroscopic transition like the one shown in Figure 1. Thus, a molecule's electronic structure, the distribution of electrons and nuclei in space, determines the molecule's net dipole moment, and ultimately impacts the spectroscopic transition probability.
Recall from the derivation of Beer's Law that the absorptivity is simply a measure of the probability that a molecule will undergo a totally inelastic collision with a photon. The transition probability measures the probability with which a specific spectroscopic transition will be excited by absorption of a photon.
These two quantities are measuring the same thing, the probability of photon absorption. By making use of Equations 1.
The integrated intensity, or peak area, of a spectroscopic transition is called the dipole strength of the transition. Thus, we now have a picture of how molecules and light interact to give rise to absorption spectra. A more thorough quantum mechanical treatment of the absorption of light by molecules is given in the appendix to this chapter. There it is shown that treating a simple model of chemical bonds naturally gives rise to the quantized energy levels and selection rules that are such a large part of the absorption spectroscopy.
The appendix is recommended reading for anyone who truly wants to understand what gives rise to absorbance spectra. Given the impact of electronic structure on the absorptivity, what factors influence the electronic structure of a molecule?
Neighboring molecules, particularly in the solid and liquid phases, weakly interact with each other, which can alter the electronic structure of an analyte molecule. A good example of a molecular interaction is the hydrogen bonding that takes place in liquid water, as illustrated in Figure 1. The partial negative charge of one oxygen molecule interacts with the partial positive charge on the hydrogen of a second molecule, forming a hydrogen bond.
This type of intermolecular interaction affects the electronic structure of the molecules involved. This type of interaction is called hydrogen bonding, as indicated by the dotted Hnes. These water molecules are said to Hve in different chemical environments.
The strength and number of interactions between neighboring molecules partly determines a molecule's chemical environ- ment. Molecules in different chemical environments will have different electronic structures. We showed above that the absorptivity of a molecule depends upon the electronic structure, so the absorptivity depends upon the chemical environment. The water molecules in different chemical environ- ments in Figure 1. The absorptivity that is measured for a sample is averaged over all the chemical environments of the molecules in the Ught beam.
We call the overall chemical environment of a sample its matrix. Nanwell Contact Us Help Free delivery worldwide. This question contains spoilers… view spoiler [i want a pdf copy of this bookfrom where i can download it?
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It remains an elementary and non-mathematical introduction to molecular spectroscopy that emphasizes the overall unity of the subject jolecular offers a pictorial perception rather than a mathematical description of the principles of spectroscopy. This revision retains the features which have made it so popular with students and lecturers over the years.
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