FRCR I – Basic Physics

1. 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

2. FRCR LECTURES • Lecture I – 10/09/2018: • 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

3. 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

4. Atoms & Nuclei

5. 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

6. STRUCTURE OF THE ATOM Electron e- Neutron n0 - - - Protonp+ + Densely packed nucleus -

7. SIZE OF THE ATOM • Radius of an atom is: • 10-10 m • Radius of the nucleus is: • 10-14 m • Thus, size of atom is 104=10,000 times more than that of nucleus • Football vs 2km

8. STRUCTURE OF THE ATOM 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

9. 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

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

11. 7 3 Li The Periodic Table

12. 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

13. ELEMENTS

14. 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

15. ISOTOPES

16. 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

17. Electron Orbitals

18. BOHR’S ATOMIC MODEL • 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 2n2where 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)

19. ELECTRONIC STRUCTURE

20. ELECTRONIC STRUCTURE • 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

21. ELECTRONIC STRUCTURE • 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

22. ELECTRONIC STRUCTURE

23. 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

24. 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.

25. EXCITATION & IONISATION

26. 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

27. 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

28. CHARACTERISTIC X-RAYS De-excitation of a tungsten atom

29. X-RAY TUBE

30. PRODUCTION OF X-RAYS

31. X-RAY SPECTRUM

32. 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

33. AUGER ELECTRONS

34. 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

35. The Nucleus

36. 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)

37. NUCLEAR STABILITY • Nuclear line of stability • 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

38. 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

39. 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

40. 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;

41. 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.

42. 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

43. 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

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

45. 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;

47. 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);

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