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3…The Building Blocks of Photochemistry: The Proton, Neutron, Electron and Photon
P. Douglas et al.
Table 1.2 Fundamental properties of the four particles involved in photochemical
Electric charge (C)
Spin quantum number
1.672621777(74) 9 10-27
1.602176565(35) 9 10-19
1.674927351(74) 9 10-27
9.10938291(40) 9 10-31
-1.602176565(35) 9 10-19
The masses of the proton and neutron are similar but not identical. The mass of the
electron is much smaller, 1/1840, that of the proton. Although the photon has zero
rest mass, it is always moving at the speed of light and has relativistic mass.
220.127.116.11 Electric Charge
The electron and proton carry equal but opposite charge, while both the neutron
and photon have zero charge. Charged particles interact through the electrostatic,
or Coulombic force (after the French physicist Charles-Augustin de Coulomb, who
in 1785 first published the law that describes how charged bodies interact) .
The force between two bodies of charges q1 and q2 separated by a distance, r, in a
medium of relative permittivity (also called dielectric constant), e, is given by:
F ¼ ke q1 q2 er 2
where ke is the Coulomb constant. (ke is also written as 1/(4pe0) where the constant, e0, is the permittivity of free space.) The force depends on the product of the
two charges and is inversely proportional to the distance between them—the force
increases rapidly as the bodies approach one another. When the two charges are of
the same sign the force is positive, corresponding to repulsion; when different, it is
negative, corresponding to attraction.
The electrostatic energy of two charges at distance r, when the reference zero
energy is when they are at infinite separation, is given by:
E ẳ ke q1 q2 =er:
The energy of two opposite charges at any finite distance r is negative and
increases (becomes more positive) as they are pulled apart, until it is zero at
r = ?; the energy of two bodies with the same sign charges increases as they are
pushed together. The relative permittivity is an important property of the medium,
since it determines the strength of charge interactions. The forces and energy
between two charged bodies in hexane, a non-polar solvent, with e * 1.9, are
forty times stronger than those in water, a polar solvent, with e * 80. This difference is an important factor in influencing the chemistry in those media.
1 Foundations of Photochemistry
It is the electrostatic force of attraction between the negatively-charged electron
and positively-charged nucleus that leads to the formation of stable atoms and
We are so familiar with the idea that charge only occurs in units of the fundamental charge we do not usually speak of it as being quantised.
The spin of fundamental particles and the spin quantum number are not familiar
everyday concepts. Spin is a property of fundamental particles, and also groups of
fundamental particles, such as atomic nuclei. Spin has no true counterpart in the
macroscopic world. It was introduced as an additional property of electrons to
account for the fine detail in atomic emission spectra. This detail could be rationalised if it was assumed the electron had an intrinsic magnetic moment, as if it
behaved in some ways like a tiny bar magnet. The term spin was chosen for this
electron property by analogy with a spinning charged body, which will generate a
magnetic moment. But this cannot be taken literally; while the electron magnetic
moment is a measurable property, the electron does not behave as if it were a
spinning charged body, even though this might sometimes be a useful picture.
Although spin was originally introduced rather arbitrarily, Dirac showed that
electron spin arises naturally when quantum mechanics and relativity are combined.
The electron, neutron, proton and photon have intrinsic quantised, non-zero,
angular momentum, in the same way that they have intrinsic mass, and electrons
and protons have intrinsic quantised charge. The magnitude of this intrinsic spin
angular momentum is described by the spin quantum number, s, through the
Spin angular momentum ẳ ẵss ỵ 1ị1=2 :h=2p
where h is Planck’s constant. The value h/2p occurs so regularly in quantum
mechanics that it is given its own symbol, "
h, pronounced ‘‘h cross’’ or ‘‘h bar’’,
sometimes called the reduced Planck constant, and sometimes the angular
momentum unit (amu) (the units of h are the same as those of angular momentum).
Not only is the absolute spin angular momentum of a particle quantised in this
way, but also the direction in which the spin vector can point, i.e. the amount of
spin angular momentum along any specified axis. If we do keep the analogy of a
spinning body, a child’s spinning top for example; in our macroscopic world we
can make such a top spin at any speed and point it in any direction we desire with
respect to an axis, the vertical axis for example. In the quantum world the ‘fundamental particle top’ can only spin at one fixed speed and it is also only allowed
to point at certain angles to the vertical. For a spin particle, such as an electron
or proton, the spin angular momentum can be aligned with a reference direction in
only one of two specified ways, to give a spin angular momentum component of
P. Douglas et al.
either + or - "
h along the reference axis. These two arrangements are colloquially known as ‘‘spin up’’ and ‘‘spin down’’ (often represented by arrows
pointing up, :, or down, ;), and identified more formally by the quantum number,
ms, which for electrons can take values of + or -.
The interaction of the spin angular momentum of the electron with an external
magnetic field is the basis of ESR spectroscopy, while the interaction of the spin
of the proton with an external magnetic field gives proton NMR spectroscopy
(1H NMR) and Magnetic Resonance Imaging (MRI).
For the photon, the spin quantum number also generates two spin angular
momentum components, +1 and -1, corresponding to left- and right-handed circularly polarised light. (As will be discussed later the general number of orientations of spin angular momentum is given by 2S ? 1 and we might then expect
three possible spin angular momentum components for the photon, i.e. +1, 0, -1;
however relativistic quantum theory forbids the ms = 0 component for particles
travelling at the speed of light, leaving ms = ? 1 (left circularly polarised), and
-1(right circularly polarised).
18.104.22.168 Fermions and Bosons
Particles with half-integral spin interact with one another differently to those with
integral spin, most notably in the way they fill available energy levels. Particles
with half-integral spin are called fermions because their distribution among energy
levels follows Fermi-Dirac statistics in which at most only two particles can
occupy any given energy level. Particles with integral spin are called bosons
because their distribution among energy levels is governed by Bose–Einstein
statistics, where any number of particles can occupy the same energy level. It is
the half-integral spin of electrons, their fermionic nature, as much as anything,
which, through its influence on atomic structure, defines the nature of bulk matter.
22.214.171.124 Movement and Energy of an Electron in an Electric Field:
the Electron Volt
When an electron is placed in an external electric field an electric force will act on
it, the electron will accelerate, and its kinetic energy will change. The energy
gained by an electron when it moves through a potential difference of 1 Volt
makes a useful unit of energy: the electron volt, eV. 1 eV = 1.60219 9 10-19 J
(the energy of a photon of 1240 nm wavelength is 1 eV; a photon of 620 nm is
2 eV and one of 413 nm is 3 eV). The relationship between electron volts and
some other commonly used energy units, along with some comparative energy
outputs, are given in Table 1.3.
1 Foundations of Photochemistry
Table 1.3 The relationship between common energy units and some comparative energies
1 eV =
1 cal =
1.986 9 10-19 J
96.486 kJ mol-1
23.060 kcal mol-1
1 J s-1
Sun’s radiation for 1 year
Tsar Bomba hydrogen bomb
Largest man made nuclear explosion
Largest planned man made conventional
explosion (4.8 kton ammonium nitrate fuel oil)
Combustion of 3 L diesel
Kinetic energy of Formula One racing car
Burning 2 sugar cubes (* 6 g)
Muzzle energy of 0.44 pistol
Lifting 1 kg 1 metre
Human heart beat
Tapping a keyboard key
Kinetic energy of a housefly
1 grain of sand falling 1 cm
Photon of visible light
An electron moved through 1 V
Spin flipping an electron
BBC radio 4 longwave ‘photon’
1.4 The Structure of the Atom
1.4.1 The Atomic Nucleus: Protons, Neutrons, Nuclear Spin
The nuclei of the atoms of the chemical elements are composed of neutrons and
protons. Every nucleus of any given element has the same number of protons and
this number, the atomic number, usually given the symbol Z, is different from that
of any other element. In the ‘natural’ elements, Z ranges from hydrogen with one
proton to uranium with 92. ‘Artificial’ elements with up to 116 protons have, so
far, been prepared in nuclear reactors, although the distinction between natural and
artificial elements is, of course, arbitrary. In addition to protons, the nuclei of all
elements other than hydrogen (1H) contain neutrons.
For electrical neutrality, the atom must have the same number of electrons as
protons. However, the number of neutrons in an atom of an element can vary, and
variation in the number of neutrons gives rise to isotopes. The number of neutrons
is the neutron number, usually given the symbol N. The sum of the neutrons and
protons is the atomic mass number, symbol A. The atomic nucleus is very small,
with a diameter of ca. 10-15 m, and the protons and neutrons are held together in
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this very small volume by the strong nuclear force. This is a very strong, but short
range (ca. fm range), attractive force between proton–proton, proton–neutron, and
neutron–neutron, which is independent of electric charge. As the atomic number
increases, charge repulsion between protons increases also, and the number of
neutrons required for a stable nucleus, in which the strong force between all
particles is greater than the electrostatic repulsion between protons, increases.
Thus, the neutron to proton ratio for the elements increases rapidly with Z. But this
nucleus stabilisation by neutrons is limited in effect, and above an atomic number
of 83 (Bi) all nuclides are unstable to radioactive decay (209Bi, Z = 83, is the
heaviest stable nucleus).
The way the spins of the protons and neutrons in the nucleus combine can lead to
nuclei with spin quantum numbers (I), varying from 0 to 6, and isotopes of the same
element can have, and usually do have, different spin quantum numbers. Isotopic
nuclear spin is important in NMR. For example, 12C has I = 0 and 13C has I = ,
so that NMR spectroscopy is not possible with 12C nuclei but is possible with 13C.
Fortunately for chemists the natural carbon isotopes include *1 % 13C, and 13C
NMR is a very important tool in chemical structure elucidation . Nuclear spin
can also have subtle effects in other spectroscopies , and nuclear mass is
important in molecular vibrational and rotational spectroscopies.
There is an electrostatic force of attraction between electrons and the nucleus
and for atoms with more than one electron, there is also electrostatic repulsion
between electrons. Since the electron mass is much smaller than that of the
nucleus, the centre of mass of an electron-nucleus system lies much more closely
to the nucleus than the electron. The force of attraction between a nucleus and
electron acts on both bodies equally, and since F = ma, the electron is accelerated
much more by this attraction than the nucleus. This gives us a simple atomic
model: a very small, yet relatively massive, slow moving positively-charged
nucleus around which there are relatively light, rapidly moving, negativelycharged electrons, all held together by electrostatic forces. These electrostatic
forces, nucleus–electron and electron–electron, control the momentum, and also,
through the de Broglie relationship, the wavelength of an electron as it moves
around the nucleus. So between them, the nature of the electrostatic force and the
mass of the electron determine the shapes of the stable electron waves in atoms.
1.4.2 Electron Waves in Atoms: Atomic Orbitals
126.96.36.199 Electron Waves
The physical boundaries of a musical instrument, the length of a string or column
of air, or the area of a drum, restrict the possible shapes and frequencies, and hence
energies, of the sound waves the instrument can produce. In a similar way the
‘boundaries’ of a molecule created by the electrostatic forces between electrons