Physics Applied to Radiology RADI R250 Fall 2003

1
Physics Applied to RadiologyRADI R250 -- Fall
2003

• Chapter 5

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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

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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

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Electromagnetic Spectrum Chart
light
5
EMS Relationships

• Which of the following has the highest energy?
• Radio waves or visible light
• frequency 3.2x1019Hz or 4.9x1014Hz
• wavelength 8.5x10-6m or 4.2x10-12m

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EMS Relationships (cont.)

• Which of the following has the longest
  wavelength?
• microwave or ultraviolet waves
• energy 2.3x10-5eV or 57keV
• frequency 3.1x108Hz or 8.9MHz

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EMS Relationships (cont.)

• Which of the following has the lowest frequency?
• Red light or yellow light
• energy 980 eV or 6.25x10-2keV
• wavelength 8325 mm or 4.78x10-3m

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General Characteristics of EMS

• no mass or physical form
• travel at speed of light (c) in a vacuum (or air)
• c 3 x 108 m/s
• travel in a linear path (until interaction
  occurs)
• dual nature wave vs. particle
• unaffected by
• electric or magnetic fields
• gravity

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Characteristics (cont.)

• obeys the wave equation
• c l n
• obeys the inverse square law
• I1d12 I2d22

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EM Interactions with Matter

• sections may overlap
• general interactions with matter include
• scatter (w or w/o partial absorption)
• absorption (full attenuation)

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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 gt 33 to 35 eV
• high ultraviolet, x-ray, gamma

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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

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PARTICLE vs. WAVE (in general)

• Wave
• extended in space
• always in motion
• repeating
• Particle (mass)
• localized in space
• moving or stationary

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Wave Characteristics

• cycle
• one complete wave form or repetition

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Wave (cont.)

• amplitude
• max. displacement from equilibrium

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Wave (cont.)

• wavelength l
• distance traveled by wave
• l d/cycle
• Unit meter

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Wave (cont.)

• frequency f or n
• number of cycles per unit time
• Unit hertz Hz /t
• Example below 2 cycles/s 2 Hz

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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
• l d/cycle 58 nm/ 4.5 cyc. 58 x 10-9/4.5
  1.3 x 10-8 m

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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

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Mathematical Relationships for EM Waves

• wave equation
• general v lf or v l n
• EM radiation c lf or c l n
• constant velocity at c
• v c 3x108m/s
• l n of EM are inversely proportional
• l f (or vice versa)

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Inversely Proportional

• as one goes up other goes down
• v l f
• same
• 100 1 100
• 100 2 50
• 100 4 25
• 100 5 20
• 100 10 10

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Example

• An x-ray photon has a wavelength of 2.1nm. What
  is its frequency?
• f ?? l 2.1x10-9m c 3x108m/s
• c l f
• f c / l
• 3x108m/s / 2.1x10-9m
• 1.428571428571 x 1017 /s
• 1.4 x 1017 Hz

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Example 2

• A radio station broadcasts at 104.5 MHz. What Is
  the wavelength of the broadcast?
• l ?? 104.5 x 106 /s n c 3 x 108 m/s
• c l f
• l c / f 3 x 108 m/s / 104.5 x 106 /s
• 0.028708134 x 102 m
• 2.871 m

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Example 3

• What it the frequency of microwave radiation that
  has a wavelength of 10-4 m?
• f ?? 1 x 10-4m l c 3 x 108 m/s
• c l n
• f c / l
• 3 x 108 m/s / 1 x 10-4m
• 3 x 1012 Hz

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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 n (direct relationship)
• "count" of photons per unit time
• f E

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Mathematics

• E µ f
• E h f
• h Plancks 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

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Example

• What is the energy (keV) of an x-ray photon with
  a frequency of 1.6 x 1019 Hz?
• E ?? 1.6x1019Hz f h 4.15 x 10-15
  eVs
• E h f
• 4.15 x 10-15 eVs 1.6 x 1019 Hz
• 6.64 x 104 eV
• 6.64 x 104 eV / 103 ev/keV
• 6.64 x101keV 66 keV

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Example 2

• What is the energy in MeV of an x-ray photon with
  a frequency of 2.85 x 1021 Hz?
• E ?? 2.85x1021Hz f h 4.15 x 10-15
  eVs
• E h f
• 4.15 x 10-15 eVs 2.85 x 1021 Hz
• 11.8275 x 106 eV
• 11.8275 x 106 eV / 106 ev/MeV
• 11.8 MeV

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Wave Particle Theories Combined

• l n inverse relationship n l
• E n direct relationship n E
• E l should have ??? .
• inverse relationship l E

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Combination of Wave Practical Theories

• combine formulas c l n E h n
• solve wave wave equation for frequency n c / l
• insert solution in quantum formula

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Shortcut Formulae

• EeV hc/l 12.4x10-7eVm / lm
• by incorporating changes in prefixes you can
  arrive at the following shortcut formulae

nm 10-9m
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Example

• What is the l of an 85 keV x-ray photon?
• l ?? 85 keV energy need h c
• EeV hc
• lm
• lm 4.15 x 10-15eVs 3 x 108m/s
• EeV
• 12.4x10-7eVm
• 85 x 103 eV
• 0.1458823529412 x 10-10m
• .15 x 10-10m or .15A

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Shortcut method

• l ?? 85 keV energy
• shortcut h c
• EkeV 12.4 / lA
• lA 12.4 / EkeV
• 12.4 / 85
• 0.1458823529412
• .15 A

EkeV 1.24 / lnm lnm 1.24 / EkeV
1.24/85 0.01458823529412 .015 nm



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Example 2

• What is the energy of a .062nm x-ray photon?
• keV ?? .062 nm lnm shortcut h c for
  nm
• EkeV 1.24 / lnm
• 1.24 / .062 nm
• 20 keV

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Matter and Energy

• Relativity Formula

• Enables calculation of matter equivalence for any
  photon
• Must convert E in keV to E in J
• 1 J 6.24x1018eV

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Relativity problem example

• What is the matter equivalence of a 86keV x-ray
  photon?
• ? mass E 86keV c 3x108 m/s

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Relativity problem example

• How many electron-volts are contained in .25kg of
  matter?
• ? E m .25 kg c 3x108 m/s