Radiation-electromagnetic

Electromagnetic Radiation and its Interaction with Atoms and Molecules 

In vacuum, the electric vector of a linearly polarized electromagnetic wave at any point in space is given by 

Radio waves Microwaves For IR R Voeu/n UV X-roys 1 -roys 

If the polarization directions of two lineariy polarized light waves, 1 and 2, with identical amplitudes , = , frequencies v, = vj, and directions of propagation x, are mutually orthogonal, and if the phases of the two waves are identical, B, = Bj = their superposition will produce a new linearly polarized wave 

The amplitude of the new wave is V2 times larger than that of either of the original waves, and its direction of polarization forms an angle of 4S° with the polarization directions of either of the two waves. If the phases of wave I and wave 2 differ by -ir/2, which according to Equation (1.2) is equivalent to a difference in optical path lengths of x = A/4, the superposition of the two waves results in a circularly polarized wave 

In changing from the classical to the quantum mechanical description of light, one of the principal results is that light is emitted or absorbed in discrete quanta known as photons, with an energy of 

The intensity of radiation is measured in erg s cm as the energy of radiation falling on unit area of the system in unit time this energy is related directly through Planck s constant to the number of quanta and their associated frequency. On the other hand, in the classical description of light as 

Scattering experiments can be performed by using very different kinds of radiation. The choice made by the experimentalist depends on a number of conditions which will be defined in the present chapter and in the next. 

An electromagnetic wave of wave vector 0 and of pulsation a is described, classically,1 by an electric field (r, t) and a magnetic field1 B (r, t) at position vector r and time t. The plane wave propagating in direction OZ of the reference 

the axes OX, O Y are called polarization axes. The wave polarization is determined by the complex numbers Ex, jT. If Ex (Ex is real, this polarization is linear. In the special case where Ex /Ey = + i, this polarization is circular. In general, it is elliptic. 

Each number Ex, Er is defined by two-real numbers. However, polarization is defined by only two observables  

To-day, lasers are the sources used to light-scattering experiments. The incident radiation is coherent and can be simply described with the help of plane waves (6.1.1). The measurable quantities associated with this type of radiation are  

When materials are exposed to electromagnetic radiation, it is sometimes important to be able to predict and alter their responses. This is possible when we are familiar with their optical properties and understand the mechanisms responsible for their optical behaviors. For example, in Section 21.14 on optical 

After studying this chapter, you should be able to do 

Compute the energy of a photon given its frequency and the value of Planck s constant. 

Briefly describe the electronic polarization that results from electromagnetic radi ation-atomi c interactions, and cite two consequences of electronic polarization. 

Briefly explain why metallic materials are opaque to visible light. 

Appendix A Elements of classical electrodynamics A.4 Electromagnetic radiation 

The propagation of electromagnetic fields in space and time is referred to as electromagnetic radiation. In vacuum, Maxwell s equations become 

Taking the curl of both sides of the third and fourth Maxwell equations and using the identity that relates the curl of the curl of a vector field to its divergence and its laplacian, Eq. (G.21), we find 

With these expressions for the fields, from the first and second Maxwell equations we deduce that 

Inside a material with dielectric constant e and magnetic permeability fx, in the absence of any free charges or currents. Maxwell s equations become 

Although it is more difficult to picture than water waves, light (electromagnetic radiation) also travels as waves. The various types of electromagnetic radiation (X rays, microwaves, and so on) differ in their wavelengths. 

Interestingly, scientists have recently shown that parrots have fluorescent feathers that are used to attract the opposite sex. Note in the accompanying photos that a bridgerigar parrot has certain feathers that produce fluorescence. Kathryn E. Arnold of the University of Glasgow in Scotland examined the skins of 700 Australian parrots from 

The back and front of a bridgerigar parrot. In the photo at the right, the same parrot is seen under ultraviolet light. 

Radiation provides an important means of energy transfer. For example, the energy from the sim reaches the earth mainly in the forms of visible and ultraviolet radiation. The glowing coals of a fireplace transmit heat energy by infrared radiation. In a microwave oven, the water molecules in food absorb microwave radiation, which increases their motions this energy is then transferred to other types of molecules by collisions, increasing the food s temperature. 

Thus we visualize electromagnetic radiation ( light ) as a wave that carries energy through space. Sometimes, however, light doesn t behave as 

You will, of course, be familiar with the visible part of the electromagnetic spectrum. This radiation is, by definition, visible to the human eye. Other detection systems reveal types of radiation which are beyond the visible region of the spectrum, with these being classified as radiowaves, microwaves, infrared, ultraviolet. X-rays, and 

A significant discovery made about electromagnetic radiation was that the velocity of propagation in a vacuum was constant for all regions of 

If you can visualise one complete wave travelling a fixed distance each cycle you should be able to see that the velocity of this wave is the product of the wavelength X (the distance between adjacent peaks) and Xh. frequency v (the number of cycles per second). It follows that  

The presentation of spectral regions may be in terms of wavelength, either as metres or as submultiples of a metre. The following units are commonly used in spectroscopy  

Another unit which is commonly used in infrared spectroscopy is the wavenumber v, which is expressed in cm . This is the number of waves in a length of one centimetre and is given by the following relationship  

Example Problem Estimate the fraction of 1.0 MeV photons that will be transmitted through a lead absorber that is 5 cm thick (the thickness of lead bricks commonly used in radiation shields). 

Approximately 2% will be transmitted. Notice that the half-thickness for these photons in lead, xi/2 = In 2/ x is 0.87 cm. 

As the first step in our exploration of this revolution in science we will consider the properties of light, more properly called electromagnetic radiation. 

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The nature of waves. Many of the properties of ocean waves are the same as those of light waves. Note that the radiation with the shortest wavelength has the highest frequency. 

Waves are characterized by wavelength, frequency, and speed. As shown in Fig. 12.2, wavelength (symbolized by the Greek letter lambda. A) is the distance between two consecutive peaks or troughs in a wave. The frequency (symbolized by the Greek letter nu, v) is defined as the number of waves (cycles) per second that pass a given point in space. Since all types of electromagnetic 

Electromagnetic radiation has oscillating electric (f) and magnetic (W) fields in planes perpendicular to each other and to the direction of propagation. 

In this equation A is the wavelength in meters, i is the frequency in cycles per second, and c is the speed of light, a defined quantity with the exact value of 2.99792458 X 10 m/s. In the SI system, cycles is understood, and the unit cycles per second becomes 1/s, or s, which is called the hertz (abbreviated Hz). 

The properties of electromagnetic fields are described empirically by four coupled equations that were set forth by J.C. Maxwell in 1865 (Box 3.1). These very general equations apply to both static and oscillating fields, and they encapsulate the salient features of electromagnetic radiation. In words, they state that  

Both E and B are always perpendicular to the direction of propagation of the radiation (i.e., the waves are transverse). 

if we look in the direction of propagation, a rotation from the direction of E to the direction of B is clockwise. 

The constant e in Eqs. (B3.1.1) and (B3.1.4) is the dielectric constant of the medium, which is defined as the ratio of the energy density (energy per unit volume) associated with an electric field in a medium to that for the same field in a vacuum. As weTl discuss later in this chapter, the difference between the energy densities in a condensed medium and a vacuum reflects polarization of the medium by the field. 

In free space, or more generally, in a uniform, isotropic, nonconducting medium with no free charges, pq and J are zero and e is independent of position and orientation, and Eqs. (B3.1.1) and (B3.1.4) simplify to div/J = 0 and cm B = (elc)dEldt. E and B then can be eliminated from two of Maxwell s equations to give  

The quantum theory explains the unique behavior of charged particles that are as small and move as rapidly as electrons. Because of its close relationship to electromagnetic radiation, an appreciation of quantum theory requires an understanding of the following important points related to electromagnetic radiation  

So far as the classification of the type of spectroscopy performed is concerned, the characterisation of the dynamical motions of the nuclei and electrons within a molecule is more important than the region of the electromagnetic spectrum in which the corresponding transitions occur. However, before we come to this in more detail, a brief discussion of the nature of electromagnetic radiation is necessary. This is actually a huge subject which, if tackled properly, takes us deeply into the details of classical and semiclassical electromagnetism, and even further into quantum electrodynamics. The basic foundations of the subject are Maxwell s equations, which we describe in appendix 1.1. We will make use of the results of these equations in the next section, referring the reader to the appendix if more detail is required. 

Although it is simplest to describe and represent graphically the example of plane polarised radiation, it is also instructive to consider the more general case [2], For propagation of the radiation along the Y axis, the electric field E can be decomposed into components along the Z and X axes. The electric field vector in the X/ plane is then given by 

This dual nature of light appears puzzling to most students of this field, and cannot be resolved by any simple picture. From our point of view it is sufficient to consider that light is a stream of photons which travels in a straight line at constant velocity c (c = 3 X 108 ms-1). Each photon has an electric vector E and a magnetic vector H that allow interactions with electrons and nuclei through electric and magnetic forces. 

A beam of light is monochromatic if all photons have the same energy (the same frequency or wavelength in the wave picture). A beam of light is completely polarized if all the photons have parallel electric and magnetic vectors (E and H). 

Light is also characterized by its frequency, v, which is the number of wave cycles that pass a point in a second. The unit for frequency is seconds-1 (s-1), also called cycles per second or hertz (Hz). The product of the wavelength times the frequency equals the speed of light (c)  

The energy of one light photon (e) is equal to the frequency times Planck s constant or Planck s constant times the speed of light divided by the wavelength  

The quantities and symbols given here have been selected on the basis of recommendations by IUPAP [4], ISO [5.g], and IUPAC [19-21] as well as by taking into account the practice in the field of laser physics. 

Example radiant intensity 7e, SI unit W sr-1 luminous intensity 7V, SI unit cd photon intensity 7P, SI units s 1 sr 1 

The integrated intensity of an electronic transition is often expressed in terms of the oscillator strength or f value , which is dimensionless, or in terms of the Einstein transition probability Ay between the states involved, 

The optical rotation due to a solute in solution may be specified by a statement of the type 

The same information may be conveyed by quoting either the specific optical rotatory power a/yl, or the molar optical rotatory power a/cl, where y is the mass concentration, c is the amount (of substance) concentration, and l is the path length. Most tabulations give the specific optical rotatory power, denoted [a]2. The wavelength of light used X (frequently the sodium D line) and the Celsius temperature 0 are conventionally written as a subscript and superscript to the specific rotatory power [a]. For pure liquids and solids [a]2 is similarly defined as [a]J = a/pi, where p is the mass density. 

However, before we examine atomic structure, we must consider the revolution that took place in physics in the first 30 years of the twentieth century. During that time experiments were carried out, the results of which could not be explained by the theories of classical physics developed by Isaac Newton and many others who followed him. A radical new theory called quantum mechanics was developed to account for the behavior of light and atoms. This new physics provides many surprises for people who are used to the macroscopic world but it seems to account flawlessly (within the bounds of necessary approximations) for the behavior of matter. 

Classification of electromagnetic radiation. Spectrum adapted by permission from C. W. Keenan, D. C. Kleinfelter, and J. H. Wood, General College Chemistry, Sixth Edition, Harper Row Publishers, Inc., 1980. 

Length units used to report wavelength include  

Infrared (IR) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy (Chapter 14) both use a form of electromagnetic radiation as their energy source. To understand IR and NMR, therefore, you need to understand some of the properties of electromagnetic radiation— radiant energy having dual properties of both waves and particles. 

The particles of electromagnetic radiation are called photons, each having a discrete amount of energy called a quantum. Because electromagnetic radiation also has wave properties, it can be characterized by its wavelength and frequency. 

You come into contact with many different kinds of electromagnetic radiation in your daily life. For example, you use visible light to see the words on this page, you may cook with microwaves, and you should use sunscreen to protect your skin from the harmful effects of ultraviolet radiation. 

The speed of electromagnetic radiation (c) is directly proportional to its wavelength and frequency  

Materials Characterization Yang Leng 2008 John Wiley Sons (Asia) Pte Ltd 

the wavenumber is number of waves in a 1 cm-long wavetrain. It is convenient for us to remember that wavenumber is proportional to the frequency of the electromagnetic wave (v) with a constant factor that is the reciprocal of the speed of light (c). 

The wavenumber represents radiation energy, as does wavelength. As we know, electromagnetic waves can be considered as photons. The photon energy is related to the photon frequency 

The conversion constant (he) is about 2.0 x 10-23 Jems. For a wavenumber of 1000cm, the corresponding energy should be only about 2.0 x 10-20 J or 0.12 eV. Note that this is much smaller than the photon energy of X-rays, which is in the order of 10,000 eV. As shown 

The figure below represents part of a wave. The entire wave can be thought of as extending infinitely in both directions. One important characteristic of a wave is its wavelength (A), which is the distance between two consecutive peaks (or troughs) in the wave. 

On the figure above, draw a line connecting two points whose separation is equal to the wavelength of the wave. If there is more than one way to do this, draw a second line. 

Suppose that the wave depicted above were traveling to the right at a speed of 35 cm/sec, and that A = 2.5 cm. 

The frequency (/) of a wave is defined as the number of wavelengths per second which travel past a given point. 

Indicate whether the following statement is true or false, and explain your reasoning  

In the last 200 years, vast amounts of data have been accumulated to support atomic theory. When atoms were originally suggested by the early Greeks, no physical evidence existed to support their ideas. Early chemists did a variety of experiments, which culminated in Dalton s model of the atom. Because of the limitations of Dalton s model, modifications were proposed first by Thomson and then by Rutherford, which eventually led to our modern concept of the nuclear atom. These early models of the atom work reasonably well—in fact, we continue to use them to visualize a variety of chemical concepts. There remain questions that these models cannot answer, including an explanation of how atomic structure relates to the periodic table. In this chapter, we will present our modern model of the atom we will see how it varies from and improves upon the earlier atomic models. 

Surfers judge the wavelength, frequency, and speed of waves to get the best ride. 

The wavelength of this wave is shown by A. It can be measured from peak to peak or trough to trough. 

Birds in the parrot family have an unusual way to attract their mates— their feathers glow in the dark This phenomenon is called fluorescence. It results from the absorption of ultraviolet (UV) light, which is then reemitted at longer wavelengths that both birds and people can see. In everyday life this happens in a fluorescent bulb or in the many glow-in-the-dark products such as light sticks. 

Kathleen Arnold from the University of Glasgow, Scotland, discovered that the feathers of parrots that fluoresced were only those used in display or those shown off during courtship. She decided to experiment using budgerigars, with their natural colors. The researchers offered birds a choice of two companion birds, which were smeared with petroleum jelly. One of the potential compan- 

A seagull floating on the ocean moves up and down as waves pass. 

The diffraction of white light hy the closely spaced grooves of a compact disk spreads the Ight into its component colors. Diffraction is dne to the constroctive and destroctive interference of l ht waves. 

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wavelength and frequency are inversely proportional to each other for the same wave speed, shorter wavelengths correspond to higher frequencies. 

The electromagnetic radiation most obvious to us is visible light. It has wavelengths ranging from about 4.0 X 10 m (violet) to about 7.5 X 10 m (red). Expressed in frequencies, this range is about 7.5 X 10 Hz (violet) to about 4.0 X 10 Hz (red). 

0 Two waves that are traveling at the same speed. The upper wave has long wavelength and low frequency the lower wave has shorter wavelength and higher frequency. 

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Intermediate Organic Chemistry, Third Edition. Ann M. Fabirkiewicz and John C. Stowell. 2016 John Wiley Sons, Inc. Published 2016 by John Wiley Sons, Inc. 

Equation 10.1. Energy is related to frequency and wavelength by Plank s constant, h, as in Equation 10.2. These relationships are sumaiized in Table 10.1. 

The absorption of particular wavelengths (or frequencies) contributes specific energy to the molecule and the resulting changes can be cbaracter-ized and used to identify functionality in the molecule. Correlation charts that list this information are included within each section of this chapter. 

A FIGURE 8-1 The simplest wave motion— traveling wave in a rope 

As a result of the up-and-down hand motion (top to bottom), waves pass along the long rope from left to right. This one-dimensional moving wave is called a traveling wave. The wavelength of the wave, A— the distance between two successive crests—is identified. 

The aspect of quantum mechanics emphasized in this chapter is how electrons are described through features known as quantum numbers and electron orbitals. The model of atomic structure developed here will explain many of the topics discussed in the next several chapters periodic trends in the physical and chemical properties of the elements, chemical bonding, and intermolecular forces. 

The SI unit for frequency, s , is the hertz (Hz), and the basic SI wavelength unit is the meter (m). Because many types of electromagnetic radiation have very short wavelengths, however, smaller units, including those listed below, are also used. The angstrom, named for the Swedish physicist Anders Angstrom (1814 1874), is not an SI unit. 

A distinctive feature of electromagnetic radiation is its constant speed of 2.99792458 X 10 m s in a vacuum, often referred to as the speed of light. The speed of light is represented by the symbol c, and the relationship between this speed and the frequency and wavelength of electromagnetic radiation is 

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X-ray Electromagnetic radiation of wave length c. 1 k. X-rays are generated in various ways, including the bombarding of solids with electrons, when they are emitted as a result of electron transitions in the inner orbits of the atoms bombarded. Each element has a characteristic X-ray spectrum. 

The sample should be liquid or in solution. It is pumped and nebulized in an argon atmosphere, then sent through a plasma torch that is, in an environment where the material is strongly ionized resulting from the electromagnetic radiation produced by an induction coil. Refer to the schematic diagram in Figure 2.8. 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

Figure Bl.2.1. Schematic representation of the dependence of the dipole moment on the vibrational coordinate for a heteronuclear diatomic molecule. It can couple with electromagnetic radiation of the same frequency as the vibration, but at other frequencies the interaction will average to zero.

As discussed in more detail elsewhere in this encyclopaedia, many optical spectroscopic methods have been developed over the last century for the characterization of bulk materials. In general, optical spectroscopies make use of the interaction of electromagnetic radiation with matter to extract molecular parameters from the substances being studied. The methods employed usually rely on the examination of the radiation absorbed. 

A number of surface-sensitive spectroscopies rely only in part on photons. On the one hand, there are teclmiques where the sample is excited by electromagnetic radiation but where other particles ejected from the sample are used for the characterization of the surface (photons in electrons, ions or neutral atoms or moieties out). These include photoelectron spectroscopies (both x-ray- and UV-based) [89, 9Q and 91], photon stimulated desorption [92], and others. At the other end, a number of methods are based on a particles-in/photons-out set-up. These include inverse photoemission and ion- and electron-stimulated fluorescence [93, M]- All tirese teclmiques are discussed elsewhere in tliis encyclopaedia. 

Non-polarized electromagnetic radiation, of course, comprises two perpendicular polarizations, which can change both in amplipide and in phase with respect to each other. If the two polarizations are in phase with each other, the resultant is just another linearly polarized beam, with the resultant polarization direction given by a simple vector addition of the... 

The impulse can be due to sudden collision with particles or to exposure to electromagnetic radiation. The physical significance of tire fonn factoi n r transitions in atomic hydrogen,... 

Poul Jorgensen [13] has been involved in developing such so-called response theories for perturbations that may be time dependent (e.g. as in the interaction of light s electromagnetic radiation). 

Analysis of the electromagnetic radiation spectrum emanating from the star Sirius shows that = 260 nm. Estimate the surface temperature of Sirius. 

To get the frequency v in centimeters-, the nonstandard notation favored by spectioscopists, one divides the frequency in hertz by the speed of light in a vacuum, c = 2.998 x lO " cm s-, to obtain a reciprocal wavelength, in this case, 4120 cm-. This relationship arises because the speed of any running wave is its frequency times its wavelength, c = vX in the case of electromagnetic radiation. The Raman spectral line for the fundamental vibration of H2 is 4162 cm-. .., not a bad comparison for a simple model. 

Gaseous H CI has a strong absorption band centered at about X = 3.40 X 10 m in the infrared portion of the electromagnetic radiation spec-tmm. On the assumption that D bonds to Cl with the same str ength that H does, predict the frequency of vibration in Hz and rad of D CI. 

The electric field of electromagnetic radiation completes 4.00 x lO - " complete cycles in 1.00 s. What are the period and frequency of the oscillation, and what is its wavelength What is the frequency in units of cm ... 

The hydrogen atom attached to an alkane molecule vibrates along the bond axis at a frequency of about 3000 cm. What wavelength of electromagnetic radiation is resonant with this vibration What is the frequency in hertz What is the force constant of the C II bond if the alkane is taken to be a stationary mass because of its size and the H atom is assumed to execute simple harmonic motion ... 

To see how this result is used, consider the integral that arises in formulating the interaction of electromagnetic radiation with a molecule within the electric-dipole approximation ... 

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