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Radiation physics

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  • 1. Physics Applied to Radiology Chapter 5
  • 2. Electromagnetic Energy Spectrum
    • continuous range of energy
      • spectrum indicates that the distribution of energies exist in an uninterrupted band rather than at specified levels
    • released by accelerating charged particles
      • moves through space or matter as oscillating magnetic & electric fields
        • needs no carrier medium but can have one
        • can penetrate or interact with matter
  • 3. Electromagnetic Spectrum
    • transverse energy waves traveling as magnetic & electric fields  to each other
      • maxima and minima of wave occur simultaneously
      • unlike other waves, needs no carrier
  • 4. Electromagnetic Spectrum Chart light
  • 5. EMS Relationships
    • Which of the following has the highest energy?
      • Radio waves or visible light
      • frequency = 3.2x10 19 Hz or 4.9x10 14 Hz
      • wavelength = 8.5x10 -6 m or 4.2x10 -12 m
  • 6. EMS Relationships (cont.)
    • Which of the following has the longest wavelength?
      • microwave or ultraviolet waves
      • energy = 2.3x10 -5 eV or 57keV
      • frequency = 3.1x10 8 Hz or 8.9MHz
  • 7. EMS Relationships (cont.)
    • Which of the following has the lowest frequency?
      • Red light or yellow light
      • energy = 980 eV or 6.25x10 -2 keV
      • wavelength = 8325 mm or 4.78x10 -3 m
  • 8. General Characteristics of EMS
    • no mass or physical form
    • travel at speed of light ( c ) in a vacuum (or air)
      • c = 3 x 10 8 m/s
    • travel in a linear path (until interaction occurs)
    • dual nature: wave vs. particle
    • unaffected by
      • electric or magnetic fields
      • gravity
  • 9. Characteristics (cont.)
    • obeys the wave equation
      • c =   
    • obeys the inverse square law
      • I 1 d 1 2 = I 2 d 2 2
  • 10. EM Interactions with Matter
    • sections may overlap
    • general interactions with matter include
      • scatter (w or w/o partial absorption)
      • absorption (full attenuation)
  • 11. EM Interactions (cont.)
    •  probability if matter size  the wavelength
      • examples:
        • radiowaves vs. TV antena
        • microwaves vs. food
        • light vs. rods & cones in eye
        • x rays vs. atom
    • ionization occurs only EM energy > 33 to 35 eV
      • high ultraviolet, x-ray, gamma
  • 12. Dual Nature of EM Radiation
    • continuously changing force fields
      • energy travels as sine WAVE
      • macroscopic level
    • photon or quantum
      • small bundle of energy acting as a PARTICLE
      • microscopic level
  • 13. PARTICLE vs. WAVE (in general)
    • Wave
      • extended in space
      • always in motion
      • repeating
    • Particle (mass)
      • localized in space
      • moving or stationary
  • 14. Wave Characteristics
    • cycle:
      • one complete wave form or repetition
    crest trough
  • 15. Wave (cont.)
    • amplitude
      • max. displacement from equilibrium
    + - 0
  • 16. Wave (cont.)
    • wavelength 
      • distance traveled by wave
      •  = d/cycle
      • Unit meter
     m
  • 17. Wave (cont.)
    • frequency f or 
      • number of cycles per unit time
      • Unit hertz Hz #/t
      • Example below: 2 cycles/s = 2 Hz
    time = 1 s 1 2
  • 18. Wave (cont.)
    • For the wave depicted below, determine the frequency and wavelength.
      • t = 25 ms d = 58 nm cycles = 4.5
      • f = #/t = 4.5 cycles/25 ms = 4.5/25 x10 -3 = 180 Hz
      •  = d/cycle = 58 nm/ 4.5 cyc. = 58 x 10 -9 /4.5 = 1.3 x 10 -8 m
    time = 25 ms d = 58 nm
  • 19. Wave (cont.)
    • velocity v (general) c (EM radiation)
      • speed each cycle travels
      • Unit m/s
    • total distance wave moves in time period
    • v of EM radiation always = c
  • 20. Mathematical Relationships for EM Waves
    • wave equation
      • general: v =  f  or  v 
      • EM radiation: c =  f  or c    
        • constant velocity at c
          • v = c = 3x10 8 m/s
    •  of EM are inversely proportional
      •       f    or vice versa 
  • 21. Inversely Proportional
    • as one goes up other goes down
      • v =   f
      • same   
      • 100 = 1 100
      • 100 = 2 50
      • 100 = 4 25
      • 100 = 5 20
      • 100 = 10 10
  • 22. Example
    • An x-ray photon has a wavelength of 2.1nm. What is its frequency?
      • f    = 2.1x10 -9 m c = 3x10 8 m/s
      • c =   f
      • f  = c / 
      • = [3x10 8 m/s] / [2.1x10 -9 m]
      • = 1.428571428571 x 10 17 /s
      • = 1.4 x 10 17 Hz
  • 23. Example #2
    • A radio station broadcasts at 104.5 MHz. What Is the wavelength of the broadcast?
      •  = ?? 104.5 x 10 6 /s =  [c = 3 x 10 8 m/s]
      • c =  f 
      •    = c / f  = [3 x 10 8 m/s] / [104.5 x 10 6 /s]
      • = 0.028708134 x 10 2 m
      • = 2.871 m
  • 24. Example #3
    • What it the frequency of microwave radiation that has a wavelength of 10 -4 m?
      • f  = ?? 1 x 10 -4 m =   [c = 3 x 10 8 m/s]
      • c =  
      • f  = c / 
      • = [3 x 10 8 m/s] / [1 x 10 -4 m ]
      • = 3 x 10 12 Hz
  • 25. Particle Nature (Quantum Physics)
    • Photon (quantum)
      • view as if a single unit of EM radiation
      • indivisible
    • Views EM radiation as a particle
      • "bundle of energy"
      • acts like a particle (but is not particle)
    • relates E to  (direct relationship)
      • "count" # of photons per unit time
      •   f =  E
  • 26. Mathematics
    • E  f
    • E = h f  
        • h = Planck’s constant
        • = 4.15 x 10 -15 eVs
    • units
      • usual energy units = J
      • EM energy units = variation of J
        • [eVs][/s] = eV
        • x rays & gamma rays usually in keV or MeV
  • 27. Example
    • What is the energy (keV) of an x-ray photon with a frequency of 1.6 x 10 19 Hz?
      • E = ?? 1.6x10 19 Hz = f [h = 4.15 x 10 -15 eVs]
      • E = h f
      • = [ 4.15 x 10 -15 eVs] [ 1.6 x 10 19 Hz]
      • = 6.64 x 10 4 eV
      • = [6.64 x 10 4 eV] / [10 3 ev / keV ]
      • = 6.64 x10 1 keV = 66 keV
  • 28. Example #2
    • What is the energy in MeV of an x-ray photon with a frequency of 2.85 x 10 21 Hz?
      • E = ?? 2.85x10 21 Hz = f [h = 4.15 x 10 -15 eVs]
      • E = h f
      • = [4.15 x 10 -15 eVs] [2.85 x 10 21 Hz]
      • = 11.8275 x 10 6 eV
      • = [11.8275 x 10 6 eV] / [10 6 ev / MeV ]
      • = 11.8 MeV
  • 29. Wave & Particle Theories Combined
    •    = inverse relationship   =  
    • E &  = direct relationship   =  E
    • E &  should have ??? .
    • inverse relationship   =  E
  • 30. Combination of Wave & Practical Theories
    • combine formulas: c =    E = h  
      • solve wave wave equation for frequency:  = c / 
      •  insert solution in quantum formula:
    [4.15 x 10 -15 eVs] [3 x 10 8 m/s]  m [12.4 x 10 -7 eVm]  m hc  m E eV =
  • 31. Shortcut Formulae
      • E eV = hc/  = [12.4x10 -7 eVm] /  m
      • by incorporating changes in prefixes you can arrive at the following shortcut formulae:
    nm = 10 -9 m  [12.4 keV A]  A  E keV = A = 10 -10 m  [1.24 keVnm]  nm E keV =
  • 32. Example
    • What is the  of an 85 keV x-ray photon?
      •  ?? 85 keV = energy need h & c
      • E eV = hc
      •  m
      •  m = [4.15 x 10 -15 eVs] [3 x 10 8 m/s]
      • E eV
      • = [12.4x10 -7 eVm]
      • 85 x 10 3 eV
      • = 0.1458823529412 x 10 -10 m
      • = .15 x 10 -10 m or .15A
  • 33. Shortcut method
      •  ?? 85 keV = energy
      • shortcut h & c
      • E keV = 12.4 /  A
      •  A = 12.4 / E keV
      • = 12.4 / 85
      • = 0.1458823529412
      • = .15 A
      
      • E keV = 1.24 /  nm
      •  nm = 1.24 / E keV
      • =1.24/ 85 = 0.01458823529412
      • = .015 nm
  • 34. Example #2
    • What is the energy of a .062nm x-ray photon?
      • keV = ?? .062 nm =  nm shortcut h & c for nm
      • E keV = 1.24 /  nm
      • = 1.24 / .062 nm
      • = 20 keV
  • 35. Matter and Energy
    • Relativity Formula
    • Enables calculation of matter equivalence for any photon
      • Must convert E in keV to E in J
      • 1 J = 6.24x10 18 eV
  • 36. Relativity problem example:
    • What is the matter equivalence of a 86keV x-ray photon?
      • ? = mass E = 86keV [c = 3x10 8 m/s]
  • 37. Relativity problem example:
    • How many electron-volts are contained in .25kg of matter?
      • ? = E m = .25 kg [c = 3x10 8 m/s]