Electromagnetic radiation, commonly referred to as light, underpins all spectroscopic techniques, ranging from the highly energetic gamma rays, through x-rays, ultraviolet, visible, infrared, microwaves to the low-energy radio waves. The principles of wave- and particle-like behaviour determine the nature of the radiation and its interaction with matter, whether in the form of subatomic, atomic, molecular or macromolecular structures

Andrews, D.L.

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University of East Anglia digital repository

EFiElectromagnetic RadiationDavid L Andrews, University of East Anglia, Norwich, UK& 1999 Elsevier Ltd. All rights reserved.This article is reproduced from the previous edition, volume 1,pp 397–401, & 1999, Elsevier Ltd.SymbolsBgure 1 Oscillating elecmagnetic field vectorB0 magnetic field amplitudec speed of lightc0 speed of light in vacuoE photon energyE electric field vectorE0 electric field amplitudeh Planck constant_ Planck constant/2pk wave vectornk refractive index at wavelength lp photon momentumS spint timek wavelengthm frequencym wavenumberx circular frequencyElectromagnetic radiation is the technical term forlight; not just visible light, but any light, ranging righttric field E and magnetic field B associatethrough from radio frequencies to gamma rays. As thename suggests, light of all kinds is radiated throughconjoined electric and magnetic fields, as shown byMaxwell in the mid-nineteenth century. To fully appre-ciate the nature of electromagnetic radiation, however,we first have to consider both its wave-like and photonicaspects.Waves and PhotonsIn the case of monochromatic (single-frequency) radia-tion, light propagates as a wave with a well-definedrepeat or wavelength l (Figure 1). Travelling at thespeed of light, c, these waves oscillate at a characte-ristic frequency n given by c/l. The electric field, themagnetic field and the direction of propagation aremutually perpendicular, and for convenience may bechosen to define a set of Cartesian axes (x, y, z), respec-tively. With propagation in the z direction, the electricfield vector points in the x direction and oscillates in thexz plane:Eðz; tÞ ¼ E0 sinðkz otÞ ½1d with mononchromatic radiation.451452 Electromagnetic Radiationwhere E0 is the field amplitude and where also for con-ciseness we introduce k ¼ 2p=l and o ¼ ck ¼ 2pn. Themagnetic field vector accordingly points in the y directionand oscillates in the yz plane:Bðz; tÞ ¼ B0 sinðkz otÞ ½2with amplitude B0. Given that the electric and magneticfields oscillate in phase and in mutually perpendicularplanes, eqns [1] and [2] together satisfy Maxwell’sequations provided the amplitudes are related byE0 ¼ cB0. In fact most spectroscopy involves the inter-action of matter with the electric rather than the mag-netic field of the radiation, because of its strongercoupling – usually by a factor of a thousand or more –with atomic and molecular charge distributions.The speed of travel of an electromagnetic wave asdescribed above can be understood in terms of the motionof any part of the waveform, such as the crest. Theinterval Dt between the arrival of two successive crests atany given point is given by oDt ¼ 2p, while at any timetheir spatial separation Dz also satisfies kDz ¼ 2p. So thespeed of propagation Dz=Dt ¼ o=k ¼ c, which in vacuotakes the value c0 ¼ 2:9979  108 m s1.On the radiation travelling through any substance, theelectronic influence of the atoms or molecules traversedby the light reduces the propagation speed to a value lessthan c0; then one obtains c ¼ c0=nl where nl is therefractive index of the medium for wavelength l;accordingly, k ¼ 2pnl=l. The significance of the refrac-tive correction is greatest in the solid or liquid phase,especially at wavelengths close to an optical absorptionband of the medium.A fundamental paradox in the nature of electro-magnetic radiation, to some extent apparent even in theearliest scientific studies by Newton and others, is that itexhibits not just wave-like but also particle-like (cor-puscular) properties, and both prove to be of keyimportance in spectroscopy. In particular, it is onlythrough the association of discrete units of energy withelectromagnetic radiation of any given frequency that wecan properly understand atomic and molecular transi-tions and the appearance of spectra.In the modern quantum representation of lightdeveloped by Planck, Einstein, Dirac and others, we nowunderstand the twin wave and particle attributes througha description in terms of photons (a term in fact firstintroduced by the thermodynamicist Lewis). As such,electromagnetic radiation of a given frequency n is seento propagate as discrete units of energy E ¼ hn, where his the Planck constant.With the key concepts in place, we can now take alook at some of the more detailed aspects of electro-magnetic radiation in two stages F first by more fullyenumerating the properties of photons in general terms,and then by examining those more specific features thatrelate to particular wavelength or frequency regions ofthe electromagnetic spectrum.Photon PropertiesMassPhotons are elementary particles with zero rest mass –necessarily so, since, from special relativity theory, noparticle with a finite mass can move at the speed of light.VelocityThe speed of light is normally quoted as speed in vacuo,c0, with refractive corrections applied as appropriate; thefree propagation of any photon also has a well-defineddirection, usually denoted by the unit vector kˆ.EnergyPhoton energy is linked to optical frequency n throughthe relation E ¼ hn (where h ¼ 6:6261 1034 J s). Eachphoton essentially conveys an energy E from one piece ofmatter to another, for example from a television screen toa human retina.FrequencyThe optical frequency n expresses the number of wavecycles per unit time. Also commonly used in quantummechanics is the circular frequency o ¼ 2pn (radiansper unit time), in terms of which the photon energy isE ¼ _o where _ ¼ h=2p. The lower the optical fre-quency, the more photons we have for a given amount ofenergy; and the larger the number of photons, the moretheir behaviour approaches that of a classical wave (this isone instance of the ‘large numbers’ hypothesis of quan-tum mechanics). It is for this reason that electromagneticradiation becomes increasingly wave-like at low fre-quencies, and why we tend to think of radiofrequency andmicrowave radiation primarily in terms of waves ratherthan particles.WavelengthThe wavelength l of the electric and magnetic waves isgiven by l ¼ c=n. In spectroscopy, common reference ismade to its inverse, the wave number n¼ 1/l, usuallyexpressed in cm1.MomentumEach photon carries a linear momentum p, a vectorquantity of magnitude h=l ¼ _ k pointing in the directionof propagation. It is then convenient to define a wavevector or propagation vector k ¼ kkˆ such that p ¼ _ k. Sincethe photon momentum is proportional to frequency,Electromagnetic Radiation 453photons of high frequency have high momenta and soexhibit the most particle-like behaviour. X-rays andgamma rays, for example, have many clearly ballisticproperties not evident in electromagnetic radiation oflower frequencies.Electromagnetic FieldsThe electric and magnetic fields, E and B, respectively,associated with a photon are vector quantities orientedsuch that the unit vectors (Eˆ, Bˆ, kˆ) form a right-handedorthogonal set.PolarizationFor plane-polarized (also called linearly polarized)photons, the plane within which the electric field vectoroscillates can sit at any angle to a reference plane con-taining the wave vector, as shown in Figures 2a and 2b.Other polarization states are also possible: in theright- and left-handed circular polarizations depictedin Figures 2c and 2d, the electric field vector sweepsFigure 2 Polarization states: (a) and (b) plane; (c) and (d)circular.out a helix about the direction of propagation. Ellipticalpolarization states are of an intermediate nature, betweenlinear and circular. Together, the wave vector andpolarization of a photon determine its mode.SpinMany of the key properties of photons as elementaryparticles relate to the fact that they have an intrinsic spinS¼ 1, and so are classified as bosons (particles with integerspin as opposed to half-integer spin particles of mattersuch as electrons). As such, photons collectively display abehaviour properly described by a Bose–Einstein dis-tribution. At simplest, this means that it is possible fortheir oscillating electromagnetic fields to keep in step asthey propagate. Through this, coherent beams of highlymonochromatic and unidirectional light can be pro-duced; this is of course the basis for laser action.Angular momentumThe intrinsic spin of each photon is associated with anangular momentum, a feature that plays an importantrole in the selection rules for many spectroscopic pro-cesses. Circularly polarized photons have the specialproperty of quantum angular momentum: the two cir-cular polarization states, left- and right-handed, respec-tively carry þ1 or 1 unit of angular momentum, _.Regions of the SpectrumWe can now delineate the properties of the variousspectral regions shown in Figure 3. Looking across theelectromagnetic spectrum, it is immediately apparentthat there is enormous difference in scale between theextremes of wavelength (or frequency), and it is notsurprising to find that they encompass an enormous rangeof characteristics.Gamma-RaysThis is a region of highly penetrating radiation with thehighest optical frequencies (exceeding 3 1019 Hz), andan upper bound of 10 pm on the wavelength. Spectro-scopy in this region primarily relates to nuclear decayprocess, as in the Mo¨ssbauer effect.X-raysThis region encompasses both ‘hard’ X-rays (wavelengthsdown to 10 pm) and less penetrating ‘soft’ X-rays(wavelengths up to 10 nm) with optical frequencieslying between 3 1019 and 3 1016 Hz. With thecapacity to produce ionization by electron detachment,photon energies in this region are often reported inelectronvolts (eV), and run from around 105 eV down toFigure 3 The electromagnetic spectrum.Table 1 The visible spectrumColour Wavelengths (nm)Red 780–620Orange 620–595Yellow 595–575Green 575–495Blue 495–455Violet 455–380454 Electromagnetic Radiation100 eV (1 eV ¼ 1:602  1019 J). X-ray absorption andfluorescence spectra as such mostly relate to atomic coreelectronic transitions.UltravioletWith UV wavelengths running from 10 nm up to theviolet end of the visible range at around 380 nm, thisregion is commonly divided at a wavelength of 200 nminto the ‘far-UV’ region (wavelengths below 200 nm,often referred to as ‘vacuum UV’ because oxygen absorbshere) and the near-UV (200–380 nm). With photonenergies from 100 eV down to less than 10 eV – the latterbeing typical of the lowest atomic or molecular ioniza-tion energy – photoionization processes are associatedwith many of the techniques of ultraviolet spectroscopy.At the lower end of this region, photon energies arecomparable with valence bond energies. As such they arecommonly scaled by Avogadro’s number and reported inunits of kJ mol1; for example, the wavelength of 240 nmcorresponds to 500 kJmol1, a typical bond energy. Oneother form of division often applied to the near-UVregion relates to its photobiological effects and appliesprincipally to solar radiation; UV-A (320–380 nm) is therelatively safe region closest to the visible range; UV-B(280–320 nm) signifies radiation that can produceextensive tissue damage; UV-C radiation with wave-lengths below 280 nm is potentially more damaging but ismostly filtered out by atmospheric gases that absorb here,the most important being ozone.VisibleThe visible range extends from approximately 380 nm(violet) to 780 nm (red) (Table 1). The precise divisionsare a little arbitrary and depend on individual percep-tions, but the wavelengths given in Table 1 are areasonable guide. Note that the link with perceivedcolour is not 1:1 – for example, light containing an equalmixture of red and green wavelengths appears yellow,although no yellow wavelengths are present. The visiblerange spans near enough an octave of frequencies and is aregion in which photon energies are comparable with thebond energies of some of the weaker chemical bonds,running up from around 150 kJmol1 at the red end toover 300 kJmol1 at the other. Most of the spectroscopyin this range of wavelengths relates to electronic transi-tions unaccompanied by chemical change, and of courseall absorption or fluorescence processes responsible forcolour.InfraredThis is another region commonly subdivided, in this caseinto the near IR (wavelengths running from the red endof the visible spectrum at 780 nm out to 2.5 mm), the mid-IR (from 2.5 to 50 mm) and the far IR (50 mm to 1mm).The absorption of near-IR radiation is commonly asso-ciated with the excitation of low-lying electronic excitedstates and overtones or combinations of molecularvibrations. In spectroscopic connections, the unqualifiedterm ‘infrared’ generally refers to the mid-range, wherespectral positions are usually cited by reference to wave-numbers n¼ 1/l. In the mid-IR range between 200 andElectromagnetic Radiation 4554000 cm1, it is principally vibrational transitions thataccompany the absorption of radiation, with the corre-sponding nuclear motions less localized at the lower-wave number end of the scale. The far-IR region beyondrelates mostly to low-frequency molecular vibrations andinversions, or rotations in small molecules.MicrowaveWith wavelengths in the 1–100mm range and frequencieson the GHz (109Hz) scale, spectroscopy in the microwaveregion relates primarily to transitions involving molecularrotation, or others involving states of different electronspin orientation (electron spin resonance).RadioWith radiation of wavelengths exceeding 100mm wefinally run into the radio wave region, where frequenciesare commonly reported in MHz (106Hz). Photon ener-gies here are too small to lead to transitions associatedwith electronic or nuclear movement, but they can pro-duce transitions between spin states (nuclear magneticresonance).As a caveat by way of conclusion, it should be pointedout that the nature of transitions studied by a particularspectroscopic technique is not always so obviously linkedwith a particular optical frequency or wavelength regionif the elementary interaction involved in the spectro-scopy entails more than one photon. For example, Ramanspectroscopy allows molecular vibrational transitions tobe studied with visible or ultraviolet light, while multi-photon absorption of IR radiation can lead to electronicexcitations.See also: Light Sources and Optics.Further ReadingDitchburn RW (1976) Light, pp. 631--640. London: Academic Press.Fishbane PM, Gasiorowicz S, and Thornton ST (1993) Physics forScientists and Engineers, extended version, pp. 1009–1047. NewJersey: Prentice-Hall.Goldin E (1982) Waves and Photons, pp. 117--134. New York:Wiley.Hakfoort C (1988) Newton’s optics: The changing spectrum of science.In: Fauvel P, Flood R, Shortland M, and Wilson R (eds.) Let NewtonBe!, pp. 81--99. Oxford: Oxford University Press.Sheppard N (1990) Chemical applications of molecular spectroscopy –a developing perspective. In: Andrews DL (ed.) Perspectives inModern Chemical Spectroscopy, pp. 1--41. Berlin: Springer-Verlag.

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