Transcript FRCRIII - hullrad Radiation Physics

Interactions of EM
Radiation with Matter
Manos Papadopoulos
Nuclear Medicine Department
Castle Hill Hospital
Hull & East Yorkshire Hospitals NHS Trust
ELECTROMAGNETIC RADIATION
 Light is electromagnetic radiation
 a form of energy
 Has both electric and magnetic components
 Characterised by
 wavelength (λ)
 frequency (ν)
WAVE CHARACTERISTICS
 Wavelength (λ): The distance between two
consecutive peaks in the wave
WAVE CHARACTERISTICS
 Frequency (ν): The number of waves (or cycles)
per unit time
WAVE CHARACTERISTICS
 The product of wavelength (λ) and frequency (ν)
is constant
PARTICLE CHARACTERISTICS
 Particle-like properties
 Photons or quanta
 Ε = hν = hc/λ
where h is Planck’s constant
 For a typical diagnostic X-ray
 λ = 2·10-11 m  photon energy is 62 keV
ELECTROMAGNETIC SPECTRUM
ELECTROMAGNETIC SPECTRUM
Name
 (m)
 (Hz)
Interesting Facts
Radio/TV
10-1 – 10-4
109 – 104
Low “” are reflected
from earth’s atmosphere
Microwaves
10-3 – 10-1
1011 – 109
Cellular phones, Radar
Infrared
10-7 – 10-3
1014 – 109
“Heat” radiation
–
7.5·1014 –
4.3·1014
~ 1/40 of total spectrum
Visible
4·10-7
7·10-7
Ultraviolet
10-8 – 7x10-7
1016 – 1014
“Burning rays” of sun
X-rays
10-11 – 10-8
1019 – 1016
tissue damage, ionisation
Gamma rays
<10-11
>1019
tissue damage, ionisation
GENERAL PROPERTIES
 Intensity (I) of a beam of radiation
 rate of flow of energy per unit area (A) perpendicular to
the beam
 Reduction in intensity by
 the inverse square law
 attenuation by interaction with matter
INVERSE SQUARE LAW
 The intensity of a beam of radiation decreases as the inverse of
the square of the distance (r) from that source
E
I
4r 2
where E is the rate of energy emission of the source
 Applies to all radiations under defined conditions

for a point source

in the absence of attenuation
INVERSE SQUARE LAW
PHOTON ATTENUATION
 The removal of photons from a beam of photons
 as it passes through matter
 Attenuation is caused by
 absorption
 scattering

of primary beam
ATTENUATION COEFFICIENT

Linear Attenuation Coefficient (μ) is defined as

the fraction of photons removed from a beam of X- or γ- rays per
unit thickness
 
n
1

cm
N  x

n: number of photons removed from the beam
N: number of photons incident on the material
Δx: thickness of the material (cm)
ATTENUATION COEFFICIENT
Linear attenuation coefficients (in cm-1) for a range of materials at γ-ray energies of 100-, 200- and 300 keV
Absorber
100 keV
200 keV
500 keV
Air
0.000195
0.000159
0.000112
Water
0.167
0.136
0.097
Carbon
0.335
0.274
0.196
Aluminium
0.435
0.324
0.227
Iron
2.72
1.09
0.655
Copper
3.8
1.309
0.73
Lead
59.7
10.15
1.64
PHOTON ATTENUATION
N  N 0  e x
HALF-VALUE LAYER
 The half-value layer (HVL) is defined as:

the thickness of material required to reduce the intensity of a beam to
one half of its initial value
 μ and HVL are related as follows:
ln 2 0.693


HVL HVL
 HVL is a function of

photon energy

attenuating material

geometry
HALF-VALUE THICKNESS
INTERACTIONS WITH MATTER
 Rayleigh scattering
 Compton scattering
 Photoelectric effect
 Pair production
RAYLEIGH SCATTERING
 Incident photon interacts with and excites an atom
 Atom is excited  emission of a photon
 Emitted photon
 same energy
 different direction  scattered photon
RAYLEIGH SCATTERING
RAYLEIGH SCATTERING
RAYLEIGH SCATTERING
RAYLEIGH SCATTERING

Electrons are not ejected


no ionisation
In medical imaging

detection of scattered photons

impairs image quality

Scattering angle increases as the photon energy decreases

Occurs with very low-energetic diagnostic X-rays

Low probability of occurrence in diagnostic energies

~ 12% of interactions at 30 keV

~ 5% of interactions above 70 keV
COMPTON SCATTERING
 Inelastic scattering
 Photon interacts with an outer-shell (valence) electron
 scattered photon – reduced energy
 Compton electron
 Through conservation of energy:
E 0  Esc  Ee 
COMPTON SCATTERING
Esc 
E0
 E 
1   02   1  cos  
 mc 
   00  Esc  E0 and Ee  0
E0
2E
1  02
mc
2 E0
 Esc  E0 
mc 2
2
E0
   180 0  Esc(min) 
and Ee (max)
COMPTON SCATTERING
 Compton electron loses its kinetic energy through
 excitation and ionisation of surrounding atoms
 Scattered photon may traverse the medium
 without interaction or
 may undergo subsequent interactions
 Scattered photons detected by image receptor
 image quality is impaired
COMPTON SCATTERING
 Incident photon energy increases
 scattered photons

 Compton electrons
scattered more towards the forward direction
 For higher energy incident photons
 majority of energy transferred to scattered electron
 Probability of a Compton interaction
 increases with the incident photon energy (E)
 is independent of atomic number (Z)
PHOTOELECTRIC EFFECT
 Photon interacts with orbital
electron
 Electron absorbs all of photon energy
 Electron is ejected
 now called a photoelectron
 Through conservation of energy
E e   Eo  Eb
PHOTOELECTRIC EFFECT
PHOTOELECTRIC EFFECT
 The incident photon energy must be
 ≥ to the binding energy of the ejected electron
 Following a photoelectric interaction
 the atom is ionised
 a vacancy is created  electron cascade
 Characteristic X-rays or Auger electrons
 Probability of a photoelectric interaction
 decreases with increasing photon energy (E)
 increases with atomic number (Z)
PAIR PRODUCTION
 X- or γ-ray photon interacts with electric field of nucleus
 energy of photon transformed into an electron-positron pair
 Pair production has a threshold energy
 equal to 1.022 MeV - the rest mass energies of the β-particles
 The beta particles lose their kinetic energy via
 excitation and ionisation
 When the positron comes to rest
 interacts with an electron  annihilation radiation
PAIR PRODUCTION
DOMINANT REGIONS
SUMMARY I

Light is electromagnetic radiation



energy propagated as a pair of electric and magnetic fields
Duality of light

wave-properties

particle-properties
Reduction in intensity by

the inverse square law

attenuation by interaction with matter
SUMMARY II

Interactions of photons with matter

Rayleigh scattering
 incident photon excites the entirety of the atom

Compton scattering
 part of the incident photon’s electron absorbed by free electron

Photoelectric effect
 all of incident electron absorbed by inner-shell electron

Pair production
 X- or γ-ray photon interacts with electric field of nucleus
 electron – positron pair created
THE END
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