Table 1.1). The atomic nucleus therefore occupies a minute fraction (10−10 %) of the atomic volume, yet contains more than 99.9% of the atom’s mass. Electrons and protons each carry the same magnitude of electric charge (1.602 × 10−19 Coulombs), but of opposite sign. The difference in the observed interactions of electrons and protons is therefore mostly due to their different masses: Electrons are relatively light, so scatter easily in a material while protons are less easily scattered.
Table 1.1Properties of subatomic particles of interest to radiotherapy
Table 1.1 lists properties of subatomic particles of relevance to radiotherapy. Strictly, only the electron, positron and neutrinos (ν and ) are fundamental particles, while protons, neutrons and pions are composed of quarks. Atoms are composed of just electrons, protons and neutrons. The positron is the anti-particle of the electron (having the same mass but opposite charge) and is emitted during beta decay (β+) and in interactions of high energy photons with matter (see pair-production, Chapter 2). The annihilation of a positron with an electron provides the mechanism for positron emission tomography (PET). Neutrinos are uncharged particles of very small mass emitted during beta decay, sharing the energy released from the decay with the emitted beta particle (β+ or β−). Negative pions (π−), one of the triplet of pions (π0, π+, π−) are found in cosmic rays and are thought to be carriers of the strong force between nucleons. Despite their short life time (2.6 × 10−8 s), beams of these particles generated in physics laboratories have been used for radiotherapy treatment, due to their favourable energy-deposition characteristics. This is discussed briefly in Chapter 2.
When referring to subatomic particles, it is common practice to interchange mass and energy through Einstein’s famous expression:
1.1
Where c is the speed of light, 2.998 × 108 ms−1. Taking the electron as an example, the energy, E, associated with a mass, m of 9.109 × 10−31 kg is 8.187 × 10−14 Joules (J). It is more convenient to represent this very small magnitude of energy in units of the electron-volt (eV), where:
1.2
The electron mass’s energy-equivalence of 8.187 × 10−14 J therefore equals 511 000 eV or 0.511 MeV, as shown in Table 1.1. Mass, m, in equation 1.1 is strictly relativistic mass, which increases as a particle’s speed approaches the speed of light according to Einstein’s theory of special relativity. The notation, m0, generally refers to the concept of constant mass that we are more familiar with, corresponding to that of a particle at rest (rest mass) and the quantity m0c2 is then the corresponding energy associated with the particle (rest energy). The terms rest-energy and rest-mass are commonly interchangeable and both quoted in terms of energy.
The conversion of mass to energy and vice versa is demonstrated in pair-production and annihilation (Chapter 2), where the energy of an incident, mass-less photon is converted into the mass and kinetic energy of an electron and positron pair. The positron eventually annihilates with an electron (its anti-particle), releasing the combined rest mass of both particles, and any remaining kinetic energy, in the form of photons.
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) are fundamental particles, while protons, neutrons and pions are composed of quarks. Atoms are composed of just electrons, protons and neutrons. The positron is the anti-particle of the electron (having the same mass but opposite charge) and is emitted during beta decay (β+) and in interactions of high energy photons with matter (see pair-production, 
1.1
1.2
