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3…The Building Blocks of Photochemistry: The Proton, Neutron, Electron and Photon

3…The Building Blocks of Photochemistry: The Proton, Neutron, Electron and Photon

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P. Douglas et al.



Table 1.2 Fundamental properties of the four particles involved in photochemical

transformations

Mass (kg)

Electric charge (C)

Spin quantum number



Proton



Neutron



Electron



Photon



1.672621777(74) 9 10-27

1.602176565(35) 9 10-19

‘



1.674927351(74) 9 10-27

0

‘



9.10938291(40) 9 10-31

-1.602176565(35) 9 10-19

‘



0

0

1



1.3.1.1 Mass

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.



1.3.1.2 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) [13].

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

ð1:9Þ

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:



1:10ị



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



17



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

molecules.

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.



1.3.1.3 Spin

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

following equation:

Spin angular momentum ẳ ẵss ỵ 1ị1=2 :h=2p



1:11ị



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



18



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).



1.3.1.4 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.



1.3.1.5 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



19



Table 1.3 The relationship between common energy units and some comparative energies

Relationships between

Comparative energies/J

energy units

1 eV =

=

=

1 cal =

=

1W =



1.986 9 10-19 J

96.486 kJ mol-1

8065.5 cm-1

4.184 J

23.060 kcal mol-1

1 J s-1



Big Bang

1068

Sun’s radiation for 1 year

1034

Volcanic eruption

1019

Tsar Bomba hydrogen bomb

1017

Largest man made nuclear explosion

Largest planned man made conventional

1013

explosion (4.8 kton ammonium nitrate fuel oil)

Lightning flash

1010

Combustion of 3 L diesel

108

Kinetic energy of Formula One racing car

106

Burning 2 sugar cubes (* 6 g)

105

Muzzle energy of 0.44 pistol

103

Lifting 1 kg 1 metre

10

Human heart beat

1

Tapping a keyboard key

10-2

Kinetic energy of a housefly

10-5

1 grain of sand falling 1 cm

10-9

Photon of visible light

10-18–10-19

An electron moved through 1 V

10-19

Molecular vibration

10-20

Spin flipping an electron

10-24

BBC radio 4 longwave ‘photon’

10-28



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



20



P. Douglas et al.



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 [14]. Nuclear spin

can also have subtle effects in other spectroscopies [15], 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

1.4.2.1 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



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