Basic science A knowledge of basic physics is essential to understanding how radiation originates and behaves. This chapter works through what an atom is; what keeps it stable vs. radioactive and unstable; and if it is unstable, how radioactivity is released. Atomic structure The Rutherford-Bohr model of an atom Electrons Electron shells The number of electron shells orbiting the nucleus is different depending upon the atom. A very simplistic model is that each shell has a letter symbol and a maximum number of electrons it can hold. The maximum number of electrons a shell can hold is 2n 2 n = shell number Shell number Letter symbol Maximum number of electrons 1 K 2 x 1 2 = 2 2 L 2 x 2 2 = 8 3 M 2 x 3 2 = 18 Types of Electrons Electrons are either bound or free. Atoms consist of: Nucleus: contains positive protons (p) and neutral (n) Electrons: circling the nucleus within energy "shells" Describing an Atom Atoms are displayed in the format shown where: A = mass number (p + n) Z = atomic number (protons) X = chemical symbol of the atom The and protons (collectively called nucleons) give the atom its mass. This isn't the actual mass but that relative to other atoms. 1 atomic mass unit (amu) = 1/12 the mass of a carbon-12 atom. The amu's of different components of atoms are shown in the table below. Relative mass Charge Neutron 1 0 n Proton 1 +1 p Symbol Bound Electrons: These are the electrons that are held in orbit around the nucleus in the electron shells by the attractive force of the positive nucleus. The binding energy is the positive energy required to overcome the pull of the nucleus and release the electron from the shell. This is of the same magnitude as the actual (negative) energy of the electron that is released if the electron is freed. Free Electrons: These are electrons that are not bound in an electron shell around a nucleus. They have a kinetic energy of: Kinetic energy = 1/2 mv2 Where: m = mass v = velocity The actual and binding energy of electrons is expressed in electron volts (ev) or kev (1keV = 1000 ev) Key points: 1 ev = 1.6022 x 1019 Joules Increased atomic number = Increase in binding energy of electrons (more protons and, therefore, more energy is needed to release the electrons of the greater positive pull. Increased distance from the nucleus of the electron = Decrease in binding energy (decrease in the positive pull of the protons) Electron 0 (1/2000) -1 e-
Nuclear Stability The nucleus is composed of protons and. The protons repel each other (electrostatic force) but the nucleus is kept held together by the strong nuclear force. Strong Nuclear Force (aka strong interaction): There is a strong force of attraction at distances between nucleons of <10-15m which changes to a repulsive force at <10-16m. The nucleons are kept apart at a distance of ~5 x 10-16m, the distance at which there is the greatest attraction. Electrostatic Force (aka coulomb force): This is the force of repulsion between protons. At a distance of 10-15 to 10-16 m the strong attractive interaction (strong nuclear force) is much greater than the repulsive electrostatic force and the nucleus is held together. Electromagnetic radiation Electromagnetic waves Electromagnetic (EM) radiation arises from oscillating electric and magnetic fields. It can be considered either as a stream of quanta (photons, particles) or waves. Concerning the wave aspect, they can be considered to be sinusoidally varying electric and magnetic field vectors pointing at right angles to one another and to the direction of the travel of the wave. Segrè Chart As the atomic number increases (i.e. the number of protons) more are required to prevent the electrostatic forces pushing the protons apart and to keep the nucleus stable. The Segrè chart shows the proportion of needed to keep the nucleus stable as the number of protons increases (the "line of stability"). If an atom has too many or too few and does not lie upon the "line of stability", it becomes unstable and s to a more stable form. This is the basis of radioactivity and is discussed later in the "Electromagnetic Radiation" chapter. An atom is composed of, protons and electrons Neutrons and protons form the nucleus and, collectively, are called nucleons A neutron has a mass of 1 and a charge of 0 A proton has a mass of 1 and a charge of +1 An electron has a mass of 0 and a charge of -1 The mass number (A) of an atom is the number protons and The atomic number (Z) is the number of protons Electrons are held in electron shells which each hold a maximum number of electrons (max no. electrons per shell = 2n2 where n=shell number) Electrons have a binding energy that is the same as their actual negative energy binding energy = the positive energy required to release the electron from its shell = negative energy released by electron when it is freed The further away from the nucleus the electron is, the smaller its binding energy The larger the atom, the greater the binding energy Amplitude (A): corresponding to the peak field strength Wavelength (λ): distance between successive peaks. Units = m (metres) Frequency (f): the number of peaks passing a given point in one second, f = 1/T. Units = s-1 (per second) or Hz (hertz) Velocity (c): the distance travelled by a peak in one second. Quantum Aspects velocity = frequency x wavelength c = fλ When considering EM radiation as particles, the particles are small packets, or quanta, of energy called photons that travel in straight lines. The energy of the photon packets is measured in joules, but this is inconveniently small when describing EM radiation so the unit of electron-volt is used (1 ev = 1.6 x 10-19 J). Intensity The intensity (i.e. photon energy or field strength) is related to the characteristics of the wave by Planck's constant. E = hf Key: E = photon energy h = Planck's constant f = frequency
Rearranging the earlier equation of velocity = fλ and assuming that the velocity is fixed (1) gives you: f = 1 / λ i.e. the frequency is inversely proportional to the wavelength. Substituting this into the Planck's constant equation give you: E = h / λ i.e. the photon energy is inversely proportional to the wavelength. From these equations we now know that: As the frequency increases, so does the energy of the wave (directly proportional) As the wavelength increases, the energy of the wave decreases (inversely proportional) Definitions Putting the two equations together gives: Intensity 1 / d2 This relationship between the distance from the beam and the energy of the beam is the inverse square law as the intensity is inversely proportional to the distance from the beam squared. However, this law only strictly applies if: Beam coming from point source No scatter or absorption of the beam Radiation is both a wave and particles An electromagnetic wave is sinusoidal perpendicular to time and distance Frequency = 1 / period (units = s-1 or Hz) Velocity = f x λ Intensity proportional to frequency Intensity inversely proportional to wavelength Inverse square law states intensity is inversely proportional to the distance squared but only if: Beam comes from point source No scatter or absorption of the beam Radioactive The diagram represents a beam emanating from a point source (S). As the beam moves further from the source, it spreads (area B is larger than area A). Photon fluence = number of photons per unit area at a given time and given cross-section of beam (e.g. number of photons in square B) Energy fluence = total amount of energy of different photons at a given time at a given cross-section of the beam per unit area (total energy of photons in square B) Energy fluence rate = total energy per unit area passing through a cross section per unit time (watts/mm2) (e.g. total energy of photons in square B per second). Aka beam intensity. Inverse Square Law As the beam moves further from the source, the area of the beam increases. The area of the beam is the distance squared. A d2 Key: A = area d = distance This means the same number of photons are spread over a larger area and the strength of the beam decreases (the intensity is inversely proportional to the area). Intensity 1 / A Radioactive generally involves the emission of a charged particle or the capture of an electron by the nucleus to form stable nuclides. The amount of = the radioactivity = the number of nuclear transformations per second. Nomenclature Nuclide Radionuclide Metastable Isomer Isotone Isotope nuclear species with specific number of and protons that exists in a defined nuclear energy state (e.g. 99mTc is a different nuclide to 99Tc) radioactive nuclide a radionuclide that exists for a long time in a higher energy state before falling to ground state (e.g. 99mTc) long lived excited state of a nuclide e.g. 99mTc is an isomer of 99Tc nuclides with the same number of (isotone) but with a different number of protons nuclides with the same number of protons (isotope) but with a different number of N.B. the number of protons determines the element of an atom. You can change the number of (and, therefore, the mass number) and the atom will still be the same element.
Nuclear stability the chapter on "Atomic structure" we covered nuclear stability and referred to the Segré chart. What the line of stability shows is that as the number of protons increases, the proportion of needed to keep the nucleus stable increases. When the nuclide doesn't lie on the line of stability it becomes unstable and radioactive. Decay model of Nuclides The model of nuclides above includes all nuclides; stable and radioactive. The area the nuclide lies in determines the type of radioactivity the nuclide goes through to become stable and is discussed later. Radioactive The of a nuclide is exponential i.e. it theoretically never reaches zero. The S.I. unit of radioactivity is the Becquerel (Bq): Types of radiation 1 Bq = 1 transformation per second When a nuclide undergoes radioactive it breaks down to fall into a lower energy state expending the excess energy as radiation. The radioactivity released can be: Alpha particles Beta particles Gamma particles (or photons) Others 1. Alpha particles Symbol: α Formed of 2 protons and 2 (i.e. a helium atom) Positively charged Relatively heavy Short range of travel 2. Beta particles Symbol: β Electrons emitted from radioactive nuclei Carry negative charge Split into β- (negatron) and an antimatter equivalent β+ (positron) Lighter and smaller than α 3. Gamma particles Symbol: γ Identical to x-rays except for the origin (x-rays originate from electron bombardment, gamma particles from radioactive atoms) Result of transition between nuclear energy levels Very high energy 4. Others X-rays Internal conversion: γ ray energy transferred to inner shell electron which is then emitted from the nucleus Auger electron: ejected from electron shells as a result of same radioactive processes that create electron shell vacancies. Competes with emission of x-rays. Neutrinos and anti-neutrinos: electrically neutral particles with very little mass emitted from atomic nuclei during β+ and β- respectively Spontaneous fission: very heavy nuclides are so unstable they split into two smaller nuclides emitting in the process Decay models There are several ways in which a nuclide can to its more stable form. These are: 1. Alpha 2. β- 3. β+ (aka positron emission) 4. Electron capture 5. Isomeric transition 6. Gamma 1. Alpha (α) This occurs in heavier nuclides with too many nucleons. The parent nuclide emits a helium atom (α particle). This type of occurs in the nuclides in the yellow section of the model graph in the nuclides that are very heavy. 2. Beta minus (β-) This occurs in nuclides in the green area of the model graph as they have too many. The neutral neutron s into a negative electron, a positive proton and an electron antineutrino (i.e. the charge on both sides of the equation remains the same)
3. Beta plus (β+) aka positron emission This occurs in the nuclides in the red area of the model graph as these have too few. The extra proton s into a neutron, a positron (β+ or e) and an electron neutrino (ve). This form of radioactivity with the production of a positron is important in PET imaging. 4. Electron capture This competes with β+ as it occurs in proton rich nuclei. If the energy difference between the parent and daughter nuclides is too low for positron emission an inner shell electron is captured by the nucleus converting a proton into a neutron (i.e. positive + negative = neutral) 5. Isomeric transition A radionuclide in a metastable excited state s to its ground state by isomeric transition and the number of protons and remain the same. The energy difference (energy released) is emitted as γ radiation. The Z and A remain unchanged. What is released and the method of depends on the characteristics of the radionuclide Type of Alpha Occurs in Produces Daughter nuclide Heavy nuclei b- Too many b+ Too few Too many protons Helium atom (2p and 2n) n p + e - + v - e Neutron becomes proton electron and p n + β + + v - e Proton becomes neutron and positron (b+) A minus 4 Z minus 2 e.g. Tc-99m Tc-99 + 140 kev γ rays 6. Gamma (γ) Released by hyperexcited nucleus to move to lower energy state after β or α. Points to help understanding 1. The charge on both sides of the equation must remain the same 2. Simplistically speaking, a neutron is made of a proton and an electron n = p +e n = +ve + -ve This means: A neutron will into a proton and an electron (b- ) A proton and an electron will join to form a neutron (electron capture) Electron capture Isomeric transition Too few but not enough energy for b+ Metastable excited nuclides p + e - n Electron captured and combines with proton to form γ radiation Z equal 3. Simplistically speaking (again) a proton is made of a neutron and a positron (b+) (b+ ) p = n + b+ +ve = n + +ve 4. The mass (A) remains the same except for alpha The number of protons in an atom determines its element Radionuclides transform to a more stable nuclide by releasing energy in the form of radiation Radioactivity is measured in Becquerels (Bq). 1 Bq = 1 transformation / second Radiation can be alpha, beta or gamma particles