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Resident Physics Lecture Christensen, Chapter 1 Radiation George David Associate Professor Department of Radiology Medical College of Georgia Physics Can Be Fun Whoops, I think I just lost an electron Atom #1 Are you sure? Atom #2 Yeah, I’m positive groan Atom #1 Atom #2 George David Associate Professor Department of Radiology Medical College of Georgia Memorize this. That’s an order! 109 106 103 10-1 10-2 10-3 10-6 10-9 10-12 Abbreviations giga mega kilo deci centi milli micro nano pico G (billion) M (million) K (thousand) d (tenth) c (hundredth) m (thousandth) m (millionth) n (billionth) p (millionth millionth) Angstrom = A = 10-10 m Energy Aside Kinetic Energy Energy of an object by virtue of its speed K.E. = (1/2) X mv2 m mass v velocity Potential Energy Energy of an object by virtue of its position What’s the Smallest Thing that is Sugar? Divide, divide, divide The smallest entity that is still sugar is the sugar molecule What’s in that Sugar Molecule? Different color balls? No! Atoms Interesting Fact You Already Knew There are only 92 naturally occurring types of atoms HOWEVER There are zillions of different types of molecules That’s way cool. Ever Seen This? Composition of the Atom Protons + Neutrons Electrons - Protons Positive charge Live in nucleus + Neutrons No charge (free?) Live in nucleus Ever-so-slightly more mass than proton Better than oldtrons? Electrons Negative charge Found outside - nucleus Exist only in designated shell locations Weighs 1/1836th as much as proton + Atomic Number # protons Defines element & its properties Color State Helium is helium because it has 2 protons # neutrons does not affect chemistry - + + - + + - Atomic Weight # protons + # neutrons # nucleons Specific elements often found with multiple atomic weights (isotopes) Always the same # protons Different # neutrons For a particular element, some isotopes may be stable, others unstable (radioactive) Helium Atomic Weight=4 - Helium Atomic Weight=3 + + - + + - Atomic Mass Unit (amu) Nominally 1 amu = the weight of a proton or neutron Officially 1 amu = 1/12 the weight of a carbon-12 atom Atomic # = 6 Particle Proton Neutron Electron Amu 1.00728 1.00867 .000549 Atomic Symbol Atomic Weight (# protons + # neutrons) Atomic # (# protons) 4 He 2 - + + - How Many Electrons? In a neutral atom (not negative or positive) # electrons = # protons - + + - Charge Theory Unlike charges attract - + Like charges repel + + Coulomb Forces • Equation + k q1 q2 F = -----------r2 F = Coulomb force q’s = charges of the two objects k = constant r = distance between objects Coulomb Equation Story k q1 q2 F = -----------r2 Force proportional to the magnitude of the charges - + + - + + + + + Coulomb Equation Story Force falls off with the square of distance k q1 q2 Twice as far: one quarter the force F = -----------r2 Three times as far: one ninth the force - + + + + + + + + - + + + - + + + + Orbital Electrons Electrons “-” charge very small mass compared to protons / neutrons Electrons reside only at certain energy levels or Shells Designations start at K shell K shell closest to nucleus L shell next closest Shells proceed up from K, L, M, N, etc. Except for K shell, all shells contain sub-shells L K - + + X- + - + Electrons & Shells Atom mostly empty space If atom were a baseball stadium, nucleus would be size of baseball Nucleus contains almost all of atom’s mass Electron shells determine element’s chemical properties Shell Capacities Shell Electron Capacity (2x2) 1 (k) 2 2 (l) 8 3 (m) 18 4 (n) 32 5 (o) 50 6 (p) 72 7 (q) 98 Binding Energy Definition Energy required to remove orbital electron from atom Ionization Negative electrons attracted to positive nucleus more binding energy for shells closer to nucleus - L K - + + + + K shell has highest binding force higher atomic # materials (higher Z) result in more binding energy more positive charge in nucleus - Electron Shells electrons attempt to reside in lowest available energy shell L K + + - + + - - Electron Shells electrons attempt to reside in lowest available energy shell L K - + + + + - - The Shell Game * Electrons can move from shell to shell to move to higher energy shell requires energy input equal to difference between the binding energy of the two shells Excitation Deposit energy here L Requires energy input! K - + + - + + The Shell Game Electron in higher shell & gap in lower shell = Potential Energy L K - + An atom with a gap in a lower shell is unhappy (unstable) + - Electrons will attempt to drop to lower shells to fill the gap + + The Shell Game For atom to move to lower energy L - shell, atom must release energy K Equal to difference between binding energy of shells Form of energy release - + + + - characteristic x-rays Energy released + Electromagnetic Radiation Transport of energy through space Properties of EM are combination of electric fields magnetic fields X-rays are one form of electromagnetic radiation No transport medium required Electromagnetic Radiation Examples x-rays radio waves microwaves visible light radiant heat Electromagnetic Radiation •EM sometimes act like particles, sometimes like waves •Particle concept explains •radiation interactions with matter •Wave concept explains •refraction •diffraction •polarization Particle concept (cont) •X-rays are discrete bundles of energy •quantum or photon •Photon Energy proportional to frequency •higher frequency => higher energy •energy measured in electron volts (eV) •energy gained by electron accelerated by 1 volt potential Energy = Planck’s Constant X Frequency E = hn Wave Properties of EM •Wavelength • distance between successive waves •Frequency • number of waves passing a particular point per unit time •Velocity (“c”) of light / x-rays • 186,000 miles/second OR • 3 X 108 meters/second •Wavelength & frequency • inversely proportional Velocity = Wavelength X Frequency c=l X n Wavelengths and EM Highest wavelength = lowest frequency Radio Infrared Visible light Ultraviolet Soft x-rays Diagnostic x-rays Therapeutic x-rays & gammas Lowest wavelength = highest frequency Velocity = Wavelength X Frequency c=l X n Energy vs. Wavelength as Equations Energy = Planck’s Constant X Frequency E = hn but Frequency = Speed of Light / Wavelength n=c/l so E = hc / l Energy (keV) = 12.4 / Wavelength (in Angstroms) E = 12.4 / l