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2…Matter and Electromagnetic Radiation: Particles and Waves

2…Matter and Electromagnetic Radiation: Particles and Waves

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1 Foundations of Photochemistry


1.2.1 Physics of Electromagnetic Waves

An electromagnetic wave is a periodic disturbance in the electric and magnetic

environment; it is a simultaneous oscillation of the electric and magnetic fields.

The electric and magnetic fields can be treated as vectors, whose direction of

oscillation are at right angles to one another and at right angles to the direction of

propagation of the wave (i.e. it is a transverse wave, Fig. 1.2). As the wave passes

a given point in space, a free moving charged particle will experience an oscillatory force and will itself oscillate with the same frequency as the wave. A similar

everyday example is the way that a cork floating on water bobs up and down as a

wave passes, and just as we can make a water wave by holding the cork and

making it oscillate up and down, an oscillating charged particle, such as an

electron, will also generate an electromagnetic wave.

Photochemistry deals with the interaction of electromagnetic waves of visible

and UV wavelength with the electrons in chemical structures. These interactions

are predominantly through the effect of the electric field on electric dipoles—

structures in which there is a separation of positive and negative charge, such as

atoms and molecules. These are termed electric dipole interactions, or, when they

result in a change of state, electric dipole transitions. Such transitions are the most

important processes involved in production of electronic excited-states. The

Fig. 1.2 The key properties of electromagnetic radiation


P. Douglas et al.

magnetic field of an electromagnetic wave will, however, also interact with

magnetic dipoles, leading to magnetic dipole transitions; it is this magnetic

interaction that gives spin spectroscopies such as Electron Spin Resonance (ESR)

and Nuclear Magnetic Resonance (NMR) spectroscopy. Magnetic dipole interactions may also be important in photochemistry, particularly in systems having

unpaired electrons. In addition, higher order, e.g. quadrupolar, interactions can be

important for some chemical species.

The key properties of electromagnetic waves are: velocity (V), wavelength (k),

frequency (m), amplitude, polarisation, intensity and coherence. These are illustrated in Fig. 1.2. The relationship between the first three is given by: V = km.

Polarisation can be either linear, or circular, and linear polarised light can be

represented as the sum of two equal amplitude, circularly polarised waves moving

clockwise and anticlockwise in phase. The intensity of the wave is proportional to

the square of the amplitude.

Many light sources, such as the Sun or typical domestic lighting, are polychromatic, i.e. many wavelengths are present. For detailed scientific studies and

many technological applications it is advantageous to use a monochromatic beam,

which has radiation of a single wavelength (and frequency). A typical example is

the red diode laser used as a bar code reader in a shop or as a laser pointer. In

practice, even laser sources are not completely monochromatic, but cover a very

small but finite range of wavelengths (the bandwidth). Lasers demonstrate another

important property of light, coherence. Standard illumination sources, such as

room lighting, involve an incoherent beam in which the waves are moving in

random phases with respect to one another. In a coherent light beam, such as that

generated by lasers, all waves are moving in phase with respect to each another

(Fig. 1.2). This has important optical implications since coherent light can be both

focused down to a very narrow beam so it is possible to obtain a very narrow spot

in which high light intensities are present [7], and also transmitted as a beam over

long distances with little divergence. The combination of laser light of appropriate

wavelength (typically in the near IR) and fibre optic cables has been one of the

main factors contributing to high speed, high density data transmission, such as in

international telecommunications and broad band internet. The development of

new laser sources, amplifiers and detectors is an important current area of interest

in applied photophysics (see Chap. 14).

It is, perhaps, convenient at this stage to distinguish between two related, but

distinct terms. Optics refers to ‘‘that branch of physical science concerned with

vision and certain phenomenon of electromagnetic radiation in the wavelength

range extending from the vacuum ultraviolet… to the far infrared’’ [8]. This is part

of the more general area of photonics, which involves both generating and utilising

photons of radiant energy. For more details see any standard textbook on the

subject [9].

1 Foundations of Photochemistry


1.2.2 Wave–Matter Interactions Refractive Index, Refraction and Dispersion

The velocity, V, of an electromagnetic wave in a vacuum is normally given the

symbol c (2.99792 9 108 m s-1). The thickness of a typical sheet of paper is

around 0.1 mm, and light takes about 3 9 10-13 s (300 fs) to pass from one side

to the other. According to the special theory of relativity, c is the maximum speed

at which energy can be propagated. In all other media the wave velocity is less

than this. The relationship between the two is the refractive index, RI (often given

the symbol n), of the medium, which is given by:

RI ẳ c=Vmediumị


where V(medium) is the wave velocity in the medium.

The refractive index is a measure of the degree of interaction between the wave

and the medium. If the electrons in the medium are easily perturbed by the wave,

i.e. if the medium has a high polarisability, the interaction is strong and the RI

high. This depends upon the wavelength, chemical structure, phase (i.e. whether

the material is solid, liquid or gas) and temperature.

When moving between two different transparent media the wavelength of the

wave is reduced in proportion to the velocity, but its frequency remains constant. If

the refractive index is wavelength dependent, a polychromatic wave is dispersed as

it travels through the medium. Dispersion causes a separation of wavelengths as

the radiation moves; thus a pulse of white light is broadened, and separated spatially in wavelength, as it travels through a dispersing medium.

If a wave is incident on an interface between media of varying refractive

indices, the direction of propagation is altered, and the wave is ‘bent’, or refracted,

by the interface. The angle between incident (h1) and refracted (h2) rays is given

by Snell’s law:

sinh1 =sinh2 ¼ V1 =V2 ¼ n1 =n2


where n1 and n2 are the refractive indices of the media at either side of the

interface, as illustrated in Fig. 1.3.

It is this behaviour that allows the focusing and movement of beams of light by

the curved surfaces of lenses. If one of the media is dispersive then the degree of

bending is wavelength dependent, and white light is dispersed into its various

colours by a prism. Transmission and Reflection

Light incident on an interface between media of different RI will be subject to

either transmission or reflection at the interface. If the interface is flat, such as a


P. Douglas et al.

Fig. 1.3 The refraction and/or reflection of light at an interface depend on the refractive indices

of the surrounding media. As the angle of incidence (h1) of the wave impinging on the surface

normal increases from 0° to larger angles, the refracted ray becomes dimmer (the degree of

refraction decreases) and the reflected ray becomes brighter (the degree of reflection increases).

For a flat, polished surface the angle of incidence equals the angle of reflection. When the angle

of incidence approaches the critical angle, hc, the refracted ray can no longer be observed. For

h1 [ hc, the light is said to be ‘totally internally reflected’

polished surface, the light is reflected at an angle equal to that of the incident

beam; the surface acts as a mirror, a speculum, and the phenomenon is termed

specular reflection. The fraction of reflected light increases with the difference in

RI between the media and also with the angle of incidence, such that for a very

shallow angle of incidence, almost any interface is a good mirror (see Fig. 1.3).

Anti-reflection coatings employ thin layers of media of intermediate RI for

enhanced transmission.

If the interface is totally irregular, such as a finely ground powder, the light is

reflected more diffusely as diffuse reflectance. Reflection spectroscopy, particularly diffuse reflectance, is a widely used technique for studying solids and surfaces. The reflected light is collected in an integrating sphere, or some similar

optical arrangement, and there is usually the facility to collect or reject the

specularly or diffusely reflected components. Diffuse reflectance spectroscopy is

discussed in more detail in Chap. 14.

As a coloured material is ground from bulk to a powder, the fraction of light

which is reflected from the surface increases and less light penetrates into the bulk

material where selective absorption causes colour. Thus the intensity of the colour

of a material decreases as it is ground; intensely blue copper sulfate crystals can be

ground to a white powder.

It is possible to create materials with either multi-layered structures, continuously varying mixes of materials, or nanostructures, such that RI varies continuously across an interfacial region rather than at a definite optical interface. These

materials, analogies of which are found in nature, offer enhanced optical properties

for a number of applications, such as reduced glare from liquid crystal display

(LCD) computer monitors and televisions and improved signal-to-noise ratio in


1 Foundations of Photochemistry

9 Total Internal Reflection and the Evanescent Wave

When light passes from a medium of high RI to one of low RI there is a critical

angle of incidence, hc, depending upon the RIs of the media, above which all light

is reflected back into the medium of high RI. Thus, as illustrated in Fig. 1.3, all

light incident at an angle greater than the critical angle is totally internally

reflected. This phenomenon is used in fibre optic cables in which light can be

transmitted along the cable without serious loss in intensity because it is trapped

within it by total internal reflection. It is also responsible for loss of emission

efficiency from flat surface displays and lamps. Total internal reflection is also

found, and used to advantage, in some natural structures. It is responsible, for

example, for the sparkle of cut diamonds or the mirror like appearance of the water

surface seen when you are swimming under water. Although light incident at

greater than the critical angle is totally internally reflected, the wave itself penetrates for some fraction of a wavelength into the outer medium; this is the evanescent wave. The evanescent wave can interact with any substance adsorbed to or

pressed close to the interface, and this forms the basis of evanescent wave, or

Attenuated Total Reflection (ATR), spectroscopy. Here, the spectroscopic monitoring beam is contained within an optical fibre, or transparent crystal and the

material to be studied is adsorbed or pressed against the fibre or crystal; the

technique is now very widely used, particularly in infrared spectroscopy. Another

important application for a variety of devices is evanescent wave coupling, where

evanescent waves can be transmitted from one medium to another if appropriate

conditions are met. Evanescent wave coupling is a hot topic of research in the field

of nanophotonics [8], with promising results being obtained in areas such as

wireless power transfer.

1.2.3 Wave–Wave Interactions Interference

When two or more waves overlap the amplitudes at any position are the sum of the

amplitudes of the individual waves. Constructive interference occurs when the

waves reinforce each other, destructive interference when they cancel each other

out (Fig. 1.4). The effect resulted in one of the most important experiments in

optics carried out by Thomas Young at the beginning of the nineteenth Century,

where he passed sunlight through two slits in an opaque material, and observed

distinct fringes due to interference. This experiment established the wave nature of

light. A modification was subsequently used by Michelson and Morley in a classic

experiment [10], which showed that light did not need any medium for transmission. This experiment failed to achieve the original objective of these

researchers, but instead laid part of the basis from which the special theory of

relativity was developed.


P. Douglas et al.

Fig. 1.4 Constructive and destructive interference of two identical waves. In constructive

interference, the two waves reinforce each other to produce a wave with twice the amplitude.

However, in destructive interference, the two waves are 180° out of phase, and the amplitudes

exactly cancel out Diffraction

Diffraction occurs when light waves pass through small openings, around obstacles, or are incident upon a sharp edge. When light passes through a small aperture

an interference pattern is observed, rather than a spot of light and a sharp shadow.

The light wave spreads in various directions beyond the aperture and into regions

where shadows would be expected if the wave travelled in straight lines. Even

though matter seems to be involved in these examples, diffraction is actually a

wave–wave interaction with interference between waves made apparent by the

blocking of some light paths by opaque objects.

Diffraction is crucially important in optics, since light cannot be focused to a

smaller size than the diffraction limit, first defined by the German physicist Ernst

Abbe as:

d ẳ k=2nsinhị


where d is the diffraction limit (i.e. the finest spatial resolution that can be

resolved), and k is the wavelength of a light beam, travelling through a medium of

refractive index, n, and converging to a spot with angle h. The denominator (nsinh)

is called the numerical aperture (NA) and can reach *1.4 with modern optics,

such that the diffraction limit is roughly given by k/2. Thus, the diffraction limit is

in the order of 200–400 nm for wavelengths in the visible spectral region

(400–800 nm).

This limits the spatial resolution of optical devices and the size of patterning

produced by techniques such as photolithography. A pair of objects separated by a

distance smaller than the diffraction limit cannot be resolved into two separate

images. The resolution of an ordinary optical microscope is improved by

increasing the RI of the medium between the lens and object (i.e. using an oil

objective lens) and/or using short wavelengths of light.

There are also now a number of techniques in optical microscopy, which do

manage, with certain systems, to overcome the diffraction limit [11], such as

1 Foundations of Photochemistry


Scanning Near-field Optical Microscopy (SNOM) and Stimulated Depletion

Emission Microscopy (STED) and these are discussed more fully in Chap. 14. Standing Waves: Localised Waves and Energy Levels

If a wave is constrained within a fixed volume of space, only certain waveforms,

known as standing waves, are stable; for all but these certain wavelengths,

interference of the wave within the volume prevents formation of a stable wave.

This phenomenon is most obvious in stringed musical instruments where the

length of the string determines which vibrations are allowed.

The boundary condition for a light wave trapped between two mirrors (similarly,

a wave on a string), at a separation, L, is that at the surface of the mirrors (the fixed

ends of the string) the wave displacement is zero (i.e. there is no movement of the

string). These positions of zero displacement are termed nodes. Under these conditions, the only wavelengths that are stable over time are given by:

k ẳ 2L=n


m ẳ nc=2L


or, in terms of frequency:

where n is an integer (not to be confused with the use of n for refractive index). All

other wavelengths are destroyed by interference. Thus, constraining a wave in

space by introducing boundary conditions naturally generates a system of fixed

wavelengths, frequencies and energies; the properties of the waves are not continuously variable but are quantised as a consequence of the boundary conditions

and we call n a quantum number. The value of n is not continuous but limited to

discrete values. For a light wave between two mirrors, or a wave on a string, n can

be any positive integer, but for some other types of waves and boundary conditions

the quantum number can be half integral, positive or negative, zero, and in some

cases, the quantum number itself is restricted to only certain integral or half

integral values, or zero. When first encountered, quantum numbers can seem to be

mysterious things, but they arise naturally from waves constrained in space. Also,

since the value of the quantum number(s) fixes all the properties of the given wave,

the quantum number itself can be used as a label to describe the wave, or any

property of the wave such as energy, succinctly.

The waves, and relative energies for n = 1, 2, 3, 4 are shown in Fig. 1.5. Note

than in addition to the nodes at the ends of the wave, the wave shapes themselves

can generate nodes at various points on the wave; in this case the number of these

internal nodes is given by n-1. The actual wave shape (vibration of a string) is not

limited to only one of these fundamental mode vibrations, and it may be much

more complex; but all vibrations, however complex, can be represented by the

addition or subtraction, that is, a superposition or linear combination, of different

fundamental modes. By the reverse process, any complex waveform can be


P. Douglas et al.

Fig. 1.5 The first four stable waveforms for a trapped light wave. As n increases, the number of

places where the wave exhibits zero displacement (nodes) also increases. W(x) is the

wavefunction—see Sect. and Ref. [6]. |W(x)|2 describes the probability of finding the

particle (i.e. the light wave, or photon) in space. When n is small, the particle has a higher

probability of being at the centre, than it does of being near the edges, but as n gets large, the

particle has an approximately equal probability of being anywhere between x = 0 and x = L. For

particle waves, such as electron waves, the trapped wave in one dimension (1D) is often referred

to as a particle in a 1D box, or particle on a string

resolved into a summation of fundamental modes. This process, known as Fourier

Transformation (FT), is widely used in the analysis of complex waves, and forms

the basis of Fourier Transform spectroscopy. Wave Pulses

While an infinitely long sine wave (Fig. 1.2) is the common representation of an

electromagnetic wave, it is possible to generate pulses of electromagnetic radiation

that last for no more than a few tens of femtoseconds (fs) and which are therefore only

a few hundred microns (lm) in length. This has important implications in photonics.

1.2.4 Physics of Particles Mass, Acceleration, Velocity, Momentum, Angular Momentum,

Kinetic and Potential Energy

Mass is a familiar concept. The behaviour of objects with mass under the influence of

forces and when in collision is the subject of Newton’s laws of motion. If an

otherwise free object of mass, m, is acted upon by a constant force, F, then that object

undergoes a constant acceleration, a, in the direction of the force, where F = ma. If

1 Foundations of Photochemistry


the force is removed, the object does not stop but continues moving with constant

velocity, V. Force and velocity are vector quantities; they have direction as well as

magnitude. An important property of a moving mass is linear momentum, p, where

p = mV. The kinetic energy, KE, of a moving body is given by ‘mV2.

Rotating objects also have angular momentum. Consider an object of mass, m,

revolving in a circle of radius r. The rotation can be described by an angular

velocity, x, in units of radians s-1 (2p radians = 360°, so the time taken for one

complete revolution is x/2p). The object has a linear velocity, V, at a tangent to the

circumference of the circle, (to see this, imagine the direction the object would fly

off if the force of attraction to the centre was suddenly removed) and has angular

momentum, L, given by, L = r 9 mV. The length of the arc moved by the object

in 1 s is V, and since the circumference of a circle is 2pr then the change in angle

per second, i.e. the angular velocity, x, is given by V/r radians s-1. Thus the

angular momentum expressed in terms of angular velocity, is:

L ¼ xmr 2


where the angular momentum vector L is normal to the plane of the circle. Since

the object can revolve clockwise or counter clockwise, L can point up or down.

A body spinning on its axis also has angular momentum, and thus a spinning

body which is also revolving about a point has two types of angular momentum:

the angular momentum due to its spinning, and the angular momentum due to its

rotation about a point. These momenta can combine to reinforce each other, i.e.

both vectors can point up or down, or they can oppose one another with one

pointing up and one pointing down. The angular momenta of electrons in atoms

and molecules, and restrictions on how these can combine, and can change upon

absorption of light, is very important in photochemistry. Universal Conservation Laws

Angular momentum, linear momentum and energy are all subject to universal

conservation laws such that in any interaction the total angular momentum, total

linear momentum, and total energy, before and after the event, remain unchanged.

1.2.5 The Link Between Waves and Particles

The link between the classical wave property of wavelength, k, and the classical

particle property of momentum, p, is given by the de Broglie equation:

k ¼ h=p:



P. Douglas et al.

In describing the behaviour of waves and particles, any wave must also be

viewed as being made up of particles each with momentum h/k, and any moving

particle must also be viewed as a wave of wavelength h/p. Particle Waves

The size of Planck’s constant, h, determines the broad boundary of mass at which

either the wave or particle properties of an object dominate in our experience of it.

The wavelengths of some everyday objects, moving atoms and fundamental particles are shown in Table 1.1. The wavelength of a heavy particle moving at

moderate speed is very short, while that for a particle of very small mass is

relatively long. If the wavelength of an object is very small, then wave behaviour

is not observable and our experience of that object is as a particle. If the wavelength is significant, then wave properties are apparent and our experience of that

object is predominantly as a wave. In our everyday world macroscopic particles do

not exhibit measurable wave properties. In the atomic and molecular world,

neutrons, protons, nuclei, and, most importantly for photochemistry, electrons do.

The wave property of electrons is shown directly in electron diffraction, and the

electron microscope. As described earlier the resolution of a microscope is

determined by the wavelength of the analysing wave. In an electron microscope

the resolution is controlled by the acceleration given to the electrons, since, from

the de Broglie relationship, high velocity electrons have shorter wavelengths than

low velocity electrons. The wave properties of neutrons are apparent in neutron

Table 1.1 The wavelengths of some everyday objects, moving atoms and fundamental particles




Velocity/m s-1

London Routemaster bus

Fastest kicked football

Fast bowled cricket ball


22-rifle bullet



a-particle from radium

100-volt a-particle

100-volt proton

10,000-volt electron


H2 molecule at 200 °C

100-volt electron

1-volt electron

7.4 9 106




12 9 10-3

6.6 9 10-24

6.6 9 10-24

1.67 9 10-24

9.1 9 10-28

3.3 9 10-24

9.1 9 10-28

9.1 9 10-28






1.51 9 107

6.9 9 104

1.38 9 105

5.9 9 107

2.4 9 103

5.9 9 106

5.9 9 105

6.9 9 10-27

2.5 9 10-23

1.66 9 10-22

1.1 9 10-21

2.8 9 10-17

6.6 9 10-3







Notes The wavelength of green light is about 500,000 pm; a 1 V electron has the same energy as

a 1240 nm photon; an atom is typically a few hundred pm in diameter; the potential energy of an

outer electron in an atom is a few eV and the wavelength of such an electron is comparable to an

atomic diameter


From Ref. [12]

1 Foundations of Photochemistry


diffraction and scattering experiments, while wave properties of atoms are seen in

atomic beam experiments.

Although directly observable quantum mechanical effects, such as interference

and diffraction, cannot be measured for everyday macroscopic objects, these

objects are made up of the nuclei and electrons of atoms, and since quantum

mechanical properties control the interactions between these small units, they also

control the bulk properties of matter. The structures of bulk matter itself, and all

interactions between matter and radiation, arise from the quantum mechanical

behaviour of the smaller units from which it is composed. Photons and Photon Energy

A photon is a discrete packet (or quantum) of electromagnetic radiation. Photons

are always in motion, and each individual photon carries momentum and, since it

is travelling at the speed of light, relativistic energy. For EMR in a vacuum,

c = km. Replacing k by cm in the de Broglie relationship gives:

c=m ẳ h=cm


mc2 ẳ hm


where mc2 is the relativistic energy. Thus, the energy of a photon is hm, the

relativistic mass is hm/c2, and the linear momentum is h/k.

For long wavelength, low momentum radiation, e.g. radio waves, it is the wave

properties which dominate in our experience (although this is due in part also to

the fact that radio waves are most often of interest because of their interaction with

electrons in bulk metals and gases, where quantisation is not such an obvious

property). For short wavelength, high energy, high momentum waves, e.g. c-rays,

particle properties are more apparent—we speak of c-rays and X-rays ‘knocking

out’ electrons from atoms.

The particle property of EMR waves is shown directly in the photoelectric

effect, and the scattering of c-rays by electrons, known as Compton scattering.

1.3 The Building Blocks of Photochemistry: The Proton,

Neutron, Electron and Photon

1.3.1 Fundamental Properties

The fundamental properties of the four particles involved in photochemical

transformations, the proton, neutron and electron which make up the atom, and the

photon, are given in Table 1.2.

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