FRCR I – Basic Physics Nick Harding Clinical Scientist Radiotherapy Department Castle Hill Hospital Hull & East Yorkshire Hospitals NHS Trust email: nicholas.harding@hey.nhs.uk

FRCR LECTURES Lecture I – 10/09/2018: Lecture II – 17/09/2018: Structure of Matter: the Atom and the Nucleus Lecture II – 17/09/2018: Radioactivity Lecture III – 20/09/2018: Interactions of EM Radiation with Matter Lecture IV – 20/09/2018: Interactions of Electrons with Matter

BIBLIOGRAPHY Radiological Physics P. Dendy, B. Heaton – Physics for Radiologists Medical Imaging J. Bushberg et al – The Essential Physics of Medical Imaging S. Webb – The Physics of Medical Imaging P. Allisy-Roberts, J. Williams – Farr’s Physics for Medical Imaging Radiotherapy F Khan – The Physics of Radiation Physics

Atoms & Nuclei

WHAT IS AN ATOM? Definition: Άτομο {átomo} – something that cannot be divided any further The smallest division of an element in which the physical and chemical properties of the element are maintained

STRUCTURE OF THE ATOM - - - + - e- n0 Electron Neutron Proton p+ Densely packed nucleus -

SIZE OF THE ATOM Radius of an atom is: Radius of the nucleus is: Thus, size of atom is 104=10,000 times more than that of nucleus Football vs 2km

Protons + Neutrons + Electrons STRUCTURE OF THE ATOM Particle Charge Mass (kg) Mass (amu) Proton + 1.6726×10-27 kg 1.007276 Neutron Neutral 1.6749×10−27 kg 1.008665 Electron - 9.1094×10−31 kg 0.000549 Mass of atom Protons + Neutrons + Electrons The atom is electrically neutral Protons = Electrons 1amu = mass of 1/12th of C-12 =1.661x10-27 kg

NUCLEAR FORCES Two main forces in the nucleus: Coulombic (electrical) forces – between protons Repulsive Strong nuclear forces – between all nucleons Attractive Strong forces operate over short nuclear distances

Li 7 3 ATOMIC NOTATION Α = 7 Z = 3 Ν = 4 Z = 3 Mass Number Atomic Number Z = 3 Neutron Number Ν = 4 Atomic Number Z = 3

The Periodic Table Li 7 3

ELEMENTS Elements are groups of atoms with the same number of protons (Z) physical properties e.g. density, melting and boiling point, electrical conductivity chemical properties e.g. reactions with water, oxygen, acids There are more than 120 chemical ELEMENTS 92 naturally occurring

ELEMENTS

ISOTOPES IsotoPes are atoms of the same element but with different mass number (A) same atomic number (Z) i.e. same number of Protons different neutron number they have the same physical and chemical properties but different nuclear properties

ISOTOPES

ISOBARS / ISOTONES / ISOMERS Nuclides with the same mass number (A) are called ISOBARS eg. Mo-99 and Tc-99 Nuclides with the same number of Neutrons (A – Z) are called ISOTONES eg. I-131 (Z=53) and Xe-132(Z=54) A-Z = (131-53) = (132 – 54) = 78 Nuclides with the same atomic (Z) and mass numbers (A) but different nuclear Energy states are called ISOMERS eg. Tc-99 and Tc-99m

Electron Orbitals

BOHR’S ATOMIC MODEL The Bohr model (1913) Electrons orbit around the nucleus at fixed distances; Each electron in a shell which has a discrete energy state; Electron shells designated letters K,L,M… and quantum numbers 1,2,3… respectively. Max number of electrons in each shell is 2n2 where n is the quantum number so 2 x 12, 2 x 22= 8, 2 x 32 = 18 and so on; Outer shell is referred to as the valence shell; The Bohr model (1913)

ELECTRONIC STRUCTURE

ELECTRONIC STRUCTURE Hydrogen Z=1 ionisation excitation Each orbit is associated with a discrete energy state called binding energy (or orbital binding energy); It is the energy required to remove an electron completely from the atom The atom is then ionised; The “zero” energy is for a electron completely disassociated with the atom; The energy levels are negative because the bound electrons have to absorb energy to reach this state i.e. an electron in the L shell of H has to absorb 3.40 eV of energy to be ionised; ionisation excitation Hydrogen Z=1

ELECTRONIC STRUCTURE Hydrogen Z=1 K orbital has largest energy – it is closest to the positive nucleus; Binding energy increases with Z – more positive charge in the nucleus means that there is stronger attraction; NB the eV is a unit of energy – the energy acquired by an electron in a vacuum when in a voltage of 1V. 6.24 x 1018 = 1 Joule ionisation excitation Hydrogen Z=1

ELECTRONIC STRUCTURE

EXCITATION & IONISATION Excitation of the atom energy transferred to an orbiting electron electron “jumps” from lower to higher energy levels the atom is “excited” In the above diagram of hydrogen the energy required to excite an electron from the K shell to the M shell is: 13.6 eV – 1.51 eV = 12.09 eV

EXCITATION & IONISATION Ionisation of the atom energy transferred to an orbiting electron electron removed from the electric field of nucleus the atom is “ionised” As described above, the ionisation energy is the energy of the shell i.e. the ionisation energy of the K shell of hydrogen is 13.6 eV.

EXCITATION & IONISATION

ELECTRON CASCADE Electron removed from its shell (i.e. ionisation) by an X-Ray photon a γ-Ray photon a charged particle (e.g. electron, proton) Vacancy created in shell usually filled by an electron from outer shell Secondary vacancy in outer shell filled by an electron transition from a more outer shell The phenomenon is called Electron Cascade

CHARACTERISTIC X-RAYS Electrons moving between shells have to lose their energy – they do this by emitting a photon i.e. light in the visible, UV or X-ray part of the spectrum; Electron transitions ----> emission of radiation These are so called Characteristic X-rays; Characteristic of the atom itself due to the different energy levels in different atoms; Naming convention comes from the orbital in which the vacancy occurred i.e. a vacancy in the K-shell is a K-characteristic X-ray. If a vacancy is filled by an adjacent shell is given a subscript α (alpha) i.e. a vacancy in the K-shell being filled by an electron from the L-shell is Kα; If a vacancy is filled by a non-adjacent shell it is given subscript beta i.e. a vacancy in the K-shell being filed by an electron from the M-shell is Kβ. The energy of the characteristic X-ray is the difference in the binding energies so for Tungsten below: Energy of Kα (L-shell to K-shell) = 69.5 keV – 11 keV = 58.5 keV

CHARACTERISTIC X-RAYS De-excitation of a tungsten atom

X-RAY TUBE

PRODUCTION OF X-RAYS

X-RAY SPECTRUM

AUGER ELECTRONS Energy not always released as a photon; Predominant in low-Z elements is Auger electron emission; Energy released  an orbital electron Ejected Auger electron has a kinetic energy equal to: the difference between the transition energy and the binding energy of the ejected electron (69.5 – 2.5) – 2.5 = 64.5 keV

AUGER ELECTRONS

FLUORESCENT YIELD Fluorescent yield (ω) is the probability characteristic X-Rays emitted Auger emission predominates in low-Z elements in electron transitions of the outer shells K-shell fluorescent yield is essentially <1% for elements with Z<10 (i.e. majority of soft tissue) 15% for Calcium (Z=20) 65% for Iodine (Z=53) ~ 80% for elements with Z>60

The Nucleus

NUCLEAR ENERGY LEVELS The nucleus has energy levels analogous to orbital electron shells often much higher in energy The lowest energy state is called the ground state Nuclei with excess energy are in an excited state Excited states (100s years>t>10-12 sec) referred to as metastable or isomeric states (e.g. 99Tcm)

NUCLEAR STABILITY Nuclear line of stability For Z up to 10 ~N=Z is a plot of N against Z For Z up to 10 ~N=Z For Z>10 more neutrons than protons (increases to ~1.5N per Z) Unstable nuclei above the curve -> Neutron-rich Unstable nuclei below the curve -> Neutron-poor Z=83 (Bismuth) is last element with stable isotopes 1

UNSTABLE NUCLEI Combinations of unstable nuclei DO exist over time  decay to stable nuclei Two kinds of instability neutron excess neutron deficiency (proton excess) Such nuclei have excess internal energy Stability achieved through conversion of a neutron to a proton a proton to a neutron Emission of energy

RADIOACTIVITY Nuclides (isotopes) decaying to more stable nuclei are Radioactive The process is called Radioactive Decay or Radioactivity A nucleus undergoes a series of radioactive decays until it reaches a stable configuration

GAMMA RAYS Analogous to the emission of characteristic X-Rays but generally much more energetic; Nucleus in excited state (often from nuclear decay); Nucleus decays to a lower (more stable) energy state Electromagnetic radiation emitted This electromagnetic radiation is called a γ-ray Gamma rays stem from the nucleus;

Internal Conversion Analogous to Auger electron process; Nucleus in excited state; Alternative mechanism of decay to gamma rays; All de-excitation energy transferred to orbital electron; Electron energy = excitation energy - binding energy; Hole left be electron filled by electron cascade.

Atomic and Nuclear Binding Energy Nuclear binding energy is energy required to completely separate nucleus into constituent parts; Nuclear binding energy >>> electron binding energy; Atomic binding energy is the sum of the two i.e. energy required to completely separate an atom into constituent parts; Bringing two subatomic particles together their total energy decreases due to strong nuclear force; ∴ bound sub-atomic particles have less energy than free particles

Mass Defect E=mc2 where c is speed of light = 3.00x108 m/s; (1amu = 931.5 MeV) As above, energy of bound particles is less than free particles -> mass of bound particles less than sum of mass of free particles; E.g. N-14 atom mass is 14.00307 amu; Mass of 7 p + 7 n + 7e is 14.11534 amu; Mass defect = 14.11534 – 14.00307 = 0.11227amu = 104.5MeV = atomic binding energy

Average Binding Energy Can take the above calc further and figure out the average binding energy per nucleon for all elements.

Nuclear Fission Splitting of a large nucleus into two smaller parts; Separate parts have a higher average binding energy; Overall total nuclear binding energy increases; This energy released as radiation and kinetic energy of the fragments; Typically also releases energetic neutrons -> more fission; Eg. U-235 + n -> U-236 -> Sn-131 + Mo-102 + 3n + energy Process used in nuclear power plants and atom bombs;

Nuclear Fusion Joining of two small nucleus atoms; Eg. H-3 + H-2 -> He-4 + n Overall nuclear binding energy (greatly) increases; Needs a large amount of (heat/kinetic) energy to initiate fusion – to overcome Coulomb forces; Eg. The sun, H-bomb (triggered by an atom bomb);

Any questions ? With thanks to Manos Papadopoulos for the original slides (2015).