Module 1

1. Module 1 Structure of the Atom

2. Fundamental Knowledge • Components • Energy levels, binding energy & electron transitions • Atomic electron(e-) structure & associated energy levels define chemical & radiation-associated properties • Properties of the nucleus determine its energy characteristics & changes w/in nucleus define its radioactive nature • Different transformation (“decay”) processes w/in nucleus determine type of radiation produced & nuclide classification

3. Composition • Electrons • - charge • Very little mass compared to nucleus • # of e- vs. # of protons • Nucleus • Made up of nucleons • Protons (+ charge) • Neutrons (no charge) • Held together with strong nuclear force

4. Timeline of the Atom From the Greek ‘a-tomos’: indivisible Democritus 460BC Dalton 1803 AD Thomson 1897 Rutherford 1912 Bohr 1913 Modern Quantum Cloud Model post 1930 Discovery of + Nucleus; Point-like; most of mass; e- orbiting Quantized e- orbital model Discovery of e- + substance w/ e- imbedded Mostly empty space w/ tiny massive nucleus w/ p+ & n; Cloudlike region of e- Solid

5. Rutherford’s gold foil experiment Thompson’s Model Expected Result: e- "It was as if you fired a 15” naval shell at a piece of tissue paper & the shell came right back & hit you" -Rutherford Uniform + charge Rutherford’s Model Actual Result:

6. If nucleons were 10 cm across, then quarks & electrons would be < 0.1 mm in size & the entire atom would be ~10 km across! Structure Electron <10-18 m Nucleus ~10-14 m Quark <10-19 m e- u u d d d u u d u Neutron & Proton ~10-15 m u d d e- Atom ~10-10 m

7. 4) Draw the parts of an atom. Hey! Mrs. Olsen, why did you mark me wrong on question #4? I drew it to actual size. You left it blank Caulfield.

8. What Are little (Nucleons) made of? Three quarks for Muster Mark!Sure he has not got much of a bark And sure any he has it's all beside the mark. —James Joyce, FinnegansWake 1H u p+ u d n0 u d d I’ve done it-I’ve found the most basic particle! • Up Quark Charge = + • Down Quark Charge = - • Quark Types • Up & Down • Strange & Charm • Truth(Top) & Beauty(Bottom) I’ve done it-I’ve found the most basic particle! I’ve done it-I’ve found the most basic particle!

9. Symbols • Atomic Number (Z) • # of protons in nucleus of atom • Unique for each element • Mass Number (A) • # of protons + neutrons in nucleus • Collectively known as nucleons • Elements designated by: () • Electrically neutral atoms have same # of protons & electrons

10. Special variations in nuclides • Isotopes • Same element • (Z unchanged) w/ different #’s of neutrons (A different) • Isotones • 2 different nuclides • (Z different) w/ same # of neutrons • Isobars • 2 different nuclides • (Z different) w/ same mass # (A) • Isomers • Same element • w/ different excited states of nucleus

11. Characteristics of constituents Mass stated in terms of atomic mass unit (amu) = mass of [Mass of 1 mol of 12C=12.0000 g; since it is a whole # carbon chosen as reference standard for relative weights (atomic weights)] has 6 protons & 6 neutrons, ∴protons & neutrons have mass ≈1 amu therefore

12. Bohr model of the atom Classical Physics Nobel Prize (1922) Niels Bohr (1885-1962) proposed that e- restricted to certain fixed orbits; e- can jump from one orbit to another by absorbing or emitting radiation e- in orbit around atomic nucleus should continuously emit radiation, thus spiral into + charged nucleus in short time →Atoms shouldn’t exist!

13. Bohr Model Assumptions • e- travels around nucleus → circular orbit • e- energy α distance from nucleus • Lowest energy = ground state • Higher energy states = excited state • Limited # of specific allowed energy levels • Amount of energy emitted or absorbed • = difference in energy levels of orbits • Energy absorbed by e- jumping from lower to higher energy orbit • Energy emitted by e- falling from higher to lower energy orbit proportional to

14. Electron Orbitals/shells n=7 n=6 e- shells designated (from inner shell outwards): → K, L, M, N …. n=5 n=4 n=3 n=2 n=1 • Shells assigned quantum numbers (n): • →n=1 (K shell), n=2 (L shell), 3, 4, … • →max # of e- s / shell is 2n2 • e.g., • K shell can have 2(1)2 = 2 e- • M shell can have 2(2)2 = 8 e- + Energy emitted by atom K L M N O P Energy absorbed by atom

15. Chemical Properties • Outer shell e- determine chemical properties of element • e- in outer shells available to form bonds called valence e- • Atoms trade electrons to form bonds • e.g. Salt, sodium chloride (NaCl) • Na has 1 valence e-, so it gives it to Cl • Clbecomes - charged • Na becomes + charged, thus forming an ionic bond.

16. Periodic Table of the Elements Noble Gases Alkali Metals Halogens Elements: Are laid out in order of increasing _________. In same ________behave chemically similar to one another. In same ________ have the same # of e- shells. atomic # 1 2 column 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 row 2.8.1 2.8.2 2.8.3 2.8.4 2.8.5 2.8.6 2.8.7 2.8.8

17. Electron Cloud More modern view of electron orbitals, taking into account quantum mechanics

18. Radiation from Electron Transitions Characteristic X-rays Auger Electrons

19. Electron Transitions Emitted radiation resulting from transition from higher → lower energy orbitals can be in form of visible, UV & x-ray photons Emitted photon Absorbed photon Excitation & De-excitation

20. Electron Binding Energy Eb: Energy required to completely remove orbital e- from atom (ionize) • Note dependence on distance from nucleus & atomic #, Z Valence e- Valence e- Zero Zero L Series L Series Energy (eV) → Energy (eV) → K Series K Series Hydrogen Z=1 Tungsten Z=74

21. Electron Volts • Energy given to e- by accelerating through 1 Volt of potential difference, = 1.6x10-19 Joule Voltage = 1 Volt -

22. Characteristic X-rays • If energy emitted > 100 eV, characteristic x-ray results • Energy characteristic to each atom • Named according to shell where vacancy occurred • If vacancy filled w/ e- in adjacent shell, subscript is alpha(α) • Nonadjacent shell, subscript beta (β) M L K Characteristic x-ray • Example of Lα characteristic x-ray • Ex-ray=Eb (vacant shell) – Eb (transition shell)

23. Characteristic X-ray

24. Auger Electrons • Competing process of de-excitation • Energy transfer directly to orbital e- • Ejected w/ kinetic energy = difference b/t transition energy & binding energy of ejected e-

25. Model of Hydrogen Atom

26. Fluorescent Yield • Probability that e- transition results in characteristic x-rays • Auger emission predominates: • Low Z elements • e- transitions in outer shell of heavy elements

27. Radiation from Nuclear Processes Gamma Rays Internal Conversion Electrons Mass Defect Nuclear Fission & FUSION

28. Fundamentally speaking… • Physicists developed a theory called ‘The Standard Model’ that explains what the world is & what holds it together • Simple, comprehensive theory that explains all the 100’s of particles & complex interactions w/ only: • 6 Leptons & 6 Anti-Leptons • 6 Quarks & 6 Anti-Quarks • Force Carriers • All known matter particles are composites of quarks & leptons, & they interact by exchanging force carrier particles

29. 4 Fundamental forces & their carriers Electromagnetic Leptons Strong Electric Charge Gluons (8) Photon Tau Neutrino Tau -1 0 Muon Neutrino Muon -1 0 Quarks Atoms Light Chemistry Electronics Electron Neutrino Electron -1 0 Fundamental Forces Mesons Baryons Nuclei Fundamental Particles Quarks Gravitational Weak Electric Charge Graviton? Bosons (W,Z) Top Bottom Strange Charm Neutron decay Beta radioactivity Down Up Solar system Galaxies Black holes Neutrino interactions Burning of the sun

30. Antimatter • For each particle of matter →corresponding anti-particle • Anti-particle has = mass • Anti-particle has = but opp. charge • Opp. spin in case of neutral particle • Particle & anti-particle meet →annihilate & release energy • Most of universe is made of matter (rather than antimatter) • Anti-particle denoted by bar • Proton, p • Anti-proton,

31. Gravitational Force • Weak • Very long Range • Always attractive • Acts between any 2 pieces of matter in the universe

32. Electromagnetic Force • Governs behavior of electrical charges & bar magnets • Weaker than Strong Force • Long Range • Attractive or Repulsive • Acts only between pieces of matter carrying electrical charge

33. Weak nuclear Force • Very weak • Very short range • Responsible for radioactive decay of subatomic particles • e.g. beta decay • Initiates hydrogen fusion in stars

34. Strong Nuclear Force • Very strong • Attractive • Very short range • ~10-13 cm • Responsible for holding nuclei of atoms together

35. Forces acting in nucleus Coulomb repulsion force (long range) Typical nuclear separation Force B/T Nucleons (N) Attractive Repulsive Nuclear separation (x10-15 m) 1 2 3 4 Strong nuclear force (short range) • Neutrons supply cohesive force that holds nucleus together • Strong force must overcome Coulombic repulsive forces b/t protons • Strong force extremely short range • Neutrons can only interact w/ immediately adjacent nucleons • Since Coulombic forces act over much longer range, protons can interact w/ each other throughout nucleus • # of neutrons must more rapidly than # of protons -104

36. Nuclear energy levels • Nucleus has energy levels similar to e- orbital shells • Lowest energy level: ground state • Higher energy states: excited state • Denoted by asterisk (*) • Lifetime of excited state usually very short • If excited state lasts > 10-12 sec → metastable • Denoted by m, as in Tc-99m

37. Nuclear stability • Only certain combos of nucleons (Z+N) stable • Low Z nuclides • ratio ~ 1 • High Z nuclides • ratio ~ 1.5 • Higher ratio req’d to offset Coulomb repulsion b/t protons • Plot Z vs. N shows a “Line of Stability”

38. Nuclear Line of Stability

39. Stability “Quirks” • Odd-Even Rule • Nucleons have something called quantum spin • If 2 similar particles spins pair: • Combined energy < individual particles • →More stable • If odd # of protons or neutrons • Unpaired spin • →Less stable • ‘Magic’ Numbers • Isotopes w/ specific #’s of protons & neutrons even more stable • p and/or n = 2, 8, 20, 28, 50, 82, 126 • 208 has 82 protons & 126 neutrons • If Z = N = Magic #  esp. stable • 416, 40

40. Nuclear Instability/radioactivity • Over time atoms w/ unstable ratio transform to stable nuclei • Radioactive Decay • Emit both particulate & EM radiation • Parent decays to Daughter nuclei • May be stable or radioactive • Frequently daughter in excited state • 2 kinds of instability: • Neutron excess • Neutron converted into proton: β- decay • Neutron deficiency (proton rich) • Proton converted into neutron: β+ decay • Or competing process of orbital electron capture • For heavier elements (Z>82): αdecay possible • Electrostatic repulsive forces ↑ more than nuclear force

41. De-excitation of nucleus • Nucleus transitions b/t excited & lower energy state w/ emission of energy • 2 competing processes: • Gamma Ray (γ) emission • Similar to characteristic x-ray emission • By def.γ originates in nucleus • Internal conversion electron • De-excitation energy transfers directly to orbital electron • Conversion e- ejected from atom • Energy = Eγ – E electron binding energy

42. Nuclear De-excitation Conversion Electron X-ray (Kα) Gamma Ray (Isomeric Transition) Internal Conversion

43. Nuclear binding energy • Energy req’d to separate nucleus into constituent parts • Atomic BE = Nuclear BE + Electron BE • Electron BE << Nuclear BE • Total energy of bound particles < separated free particles • Nuclear BE = Mass of Constituent particles (Z+N+e-) – Mass of atom • Mass difference = “Mass Defect” • Average BE/nucleon =

44. Mass Defect Example • 149Xe atomic mass = 139.92164 u • Constituent Particles mass = 141.16774 u • 54 protons • 54.392904 u • 86 neutrons • 86.74519 u • 54 electrons • 0.029646 u • Mass Defect = 1.2461 u

45. Mass-energy equivalence • Einstein’s famous equation • E=mc2 • c = 3 x 108 m/s (186,000 mph) • i.e. multiply mass of matter by square of speed of light in vacuum to get potential energy in nucleus • 1 amu = 931.494 MeV • In previous example: • mass defect = 1.2461u = 1160 MeV • Binding energy per nucleon: • Divide by 140 nucleons = 8.3 MeV/nucleon

46. Binding Energy/nucleon Note curve reaches max near middle & ↓ @ either end Fission Avg Binding Energy per Nucleon (MeV) Fusion Nucleon Binding Energy # of Nucleons in Nucleus, A

47. Fission Vs. fusion

48. Energy Yield FUSION fast particles FISSION U-235 slow neutron tritium deuterium n n n n + m = 1 + m = 3 m = 2 Cs-143 n + n n + One of many possible divisions n n n Rb-90 Conversion to energy per kg fuel mafter= 235.8 mafter= 4.98 1 unit = energy use of 1 US citizen in 1 year 676 units 176 units

49. End module 1

50. References • Bushberg et al. The Essential Physics of Medical Imaging 3rd Edition. Philadelphia: Lippincott Williams & Wilkins, 2012. • http://hyperphysics.phy-astr.gsu.edu/hbase/bohrcn.html#c1 • http://www.webelements.com/