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2…Matter and Electromagnetic Radiation: Particles and Waves
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 , 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’’ . 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
1 Foundations of Photochemistry
1.2.2 Wave–Matter Interactions
188.8.131.52 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.
184.108.40.206 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
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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
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
220.127.116.11 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 , with promising results being obtained in areas such as
wireless power transfer.
1.2.3 Wave–Wave Interactions
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 , 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.
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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 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
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
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 , 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.
18.104.22.168 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
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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. 22.214.171.124 and Ref. . |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.
126.96.36.199 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
188.8.131.52 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.
184.108.40.206 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:
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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.
220.127.116.11 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
London Routemaster bus
Fastest kicked football
Fast bowled cricket ball
a-particle from radium
H2 molecule at 200 °C
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
From Ref. 
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.
18.104.22.168 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.