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Study Guide for Radiologic Physics for Radiation Oncology
This exam tests your knowledge of the principles of physics underlying the practice of radiation oncology. Included are questions on:
Useful constants and conversions:
| Fundamental Charge |
1.602 x 10-19 |
| electron rest mass |
9.109 x 10-31kg = 0.000558 amu |
| electron rest energy |
0.511 MeV |
| proton rest mass |
1.673 x 10-27kg = 1.0727 amu |
|
935.798 MeV |
| neutron rest mass |
1.675 x 10-27kg = 1.00866 amu |
|
941.011 MeV |
| amu |
1/12 C-12 mass = 1.660 x 10-27kg |
| Planck's Constant |
6.62 x 10-34Joules/second |
| eV (electron volt) |
kinetic energy acquired by accelerating 1 electron across 1 volt potential |
|
1.602 x 10 -19 Joule |
| Approximate Tungsten Binding Energies |
K-Shell 69500 eV |
|
L-Shel 11000 eV |
|
M-Shell 2500 eV |
| Permittivity of free space (ε0) |
8.8854 x 10-12C/(V-m) |
| Permiability of a vacuum (μ0) |
4πx10-7(V-Sec)/(Amp-m) |
Useful formulae:
| f=c/&lambda |
frequency (sec-1 = 3x108m/sec / wavelength (m) |
| E=h&nu |
energy = 6.625 x 10-34j-sec x &nu (frequency sec-1) |
| E=hc/&lambda |
|
| c = 1 / (ε0μ0)1/2 |
Light speed in free space =~ 3 x 108m/s |
| A=kN0 |
dN/dt = -kN0 |
| N=N0e-kt | N=N0e(ln(2) ⁄ t1/2)t |
| Ta=1/k = 1.44T1/2 | Average Life |
Unit Conversions:
| Phyical Quantity |
Symbol |
SI Units |
Common Units |
Conversion Factors |
| Length |
l |
m |
nm |
|
| Mass |
m |
kg |
1 MeV/c2 |
1 MeV/c2=1.78x10-30kg |
| Time |
t |
s |
|
|
| Current |
I |
A |
|
|
| Charge |
Q |
C |
|
|
| Force |
F |
N |
|
1 N = 1 kg-m-sec-1 |
| Momentum |
p |
N-s |
|
1 N-s = 1 kg-m/s |
| Energy |
E |
J |
eV |
1 eV = 1.602 x 10-19J |
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- basic physics
- instruments and measurements
- dosimetry
- radioactivity (radionuclides and physics of therapeutically employed radionuclides)
- protection and safety
Categories for Radiologic Physics for Radiation Oncology
Atomic and Nuclear Structure
- Bohr model of the atom
 | The classic Bohr model is the planetary model consisting of a central nucleus and planetary electrons in orbit around the nucleus. |
- Coulombic force and electron binding energy
The fundamental charge on a electron is -1.602x10-19coulombs. For protons, the charge is positive and the number of protons equals electrons in electrically balanced atoms
- Electron orbits (energy levels)
Discrete orbital energies (quanta) result in specific orbital patterns, with discrete energy transitions rather than continuous transitions. The orbital electrons are restricted to integral multiples of h/2&pi.
h is Planck's Constant = 6.602 x 10-34 Joule-second. Energy is conserved when electrons remain in a quantum orbit.
- Electron transitions—absorption and emission of energy
Electron transitions cause discrete spectral lines or energy transitions. K,L, M, N shell electron state transitions cause characteristic x-ray emission or absorption. Typical transistion energies for tungsten K series is 69.5 KeV, for L 11.0 KeV, for M 2.5 keV.
- Characteristic radiation and the Auger effect
Characteristic X-rays are emitted when an electron moves from a higher orbital energy level to another lower (ie closer) orbital. Since energy is conserved in these transitions, energy will be absorbed at a characteristic value if an electron moves to a lower energy orbit and emitted if the electron transitions to a higher energy orbit. For a K to L transition, the electon moves from a lower energy orbital to a higher energy orbital and will absorb energy equal to the difference in energy levels. For tungsten, this is 69.5 KeV - 11.0 KeV = 58.5 KeV. If the opposite occurs, and the electon drops to a vacancy in the K shell from the M shell, a characteristic x-ray of energy 58.5 keV will be emitted.
If sufficient energy is absorbed to completely eject the electron from an inner orbit, an energy instability is created and the void will be quickly filled by an outer shell electron. This will release additional characteristic x-rays which may be emitted or absorbed by other orbital electrons, raising their energy levels. If enough energy is absorbed, a process calledAuger emissionmay occur. Energy may be transferred to other atomic electrons causing multible electrons to be ejected leaving a highly unstable atom.
- Nuclear structure
- Nucleons —protons and neutrons
Nuclear particles consist of quarks. The quarks are theoretical particles which make up baryons. Neutrons and protons are baryons made up of combinations of up and down quarks.
Sample Fermionic Hadrons
Baryons ( ) and Anti-baryon ( )
|
| Symbol |
Name |
Quark
Content |
Electric
Charge |
Mass
(GeV/c2) |
Spin |
|
p |
proton |
uud |
1 |
0.938 |
1/2 |
|
p-bar |
anti-proton |
u-bar u-bar d-bar" |
-1 |
0.938 |
1/2 |
|
n |
neutron |
udd |
0 |
0.940 |
1/2 |
| λ |
lambda |
uds |
0 |
1.116 |
1/2 |
|
ω |
omega |
sss |
-1 |
1.672 |
3/2 |
|
π+ |
pion |
u d-bar |
+1 |
0.140 | "
0 |
There is a mass difference between a proton (charge +1) and a neutron (charge 0).
n (UDD) --> p (UUD) + β + anti-&nue
There are discrete nuclear energy levels and when nuclear particles confined to a nucleus are raised to an excited state, they will attempt to return to their ground state. In the process, they will give off electromagnetic and particle radiation. 60Co will decay by emitting a 1.48 MeV &beta particle to an intermediate energy level. This energy level is still excited but will decay further to a stable level by emission of a 1.33 MeV &gamma ray. In a second decay path 60Co will decay by emission of a 0.32 MeV &beta and a subsequent 1.17MeV &gamma, followed by a second 1.33 Mev &gamma.
In both cases, a neutron will lose the electron (&beta) and transform into a proton and a neutrino. A neutrino is a nearly massless and chargeless particle. Then end product will be 60Ni which is stable.
- Nuclear force
There are four known natural field forces. Energy used to bind the nucleus together (protons, neutrons)
include mass defect where mass is converted to energy to bind particles. These internuclear forces are:
- Strong Nuclear force &mdash short range force acting on x < 10-34m
- electromagnetic force &mdash much weaker than strong nuclear force. This force acts only between particles carrying a charge and can be attractive or repulsive. It can act over long distances.
- Weak Nuclear force — responsible for radioactive decay and neutrino interactions. The weak nuclear force is responsible for β decay. The electroweak force is a constituent force of the weak nuclear force, as it is of the electromagnetic force.
- gravitational force &mdash very weak force operating over long (ie infinite) distances.
- E = mc2 and nuclear binding energy
Nuclear binding energy is around 28-30 MeV
- Factors affecting nuclear stability
- Neutron-to-proton ratio
For stability, in light atoms the ratio of n:p is approximately 1:1. For heavier atoms, the ratio increases to approximately 1.5:1.
- Average binding energy per nucleon
For 58Fe, average binding energy/nucleon is around 8 MeV
- Pairing of similar nucleons in the nucleus
- Nuclear nomenclature
- The four isos (isotopes, isotones, isobars, isomers)
- Isotopes have the same atomic number -- different number of neutrons
- Isomers have the same number of neutrons and protons but different nuclear energy levels
- Isotones have the same number of neutrons but different mass and Z
- Isobars have the same mass but different numbers of neutrons and protons.
- Shorthand representation of isotopes
Radioactive Decay
Radiactive decay is the process by which an unstable uncleous is transformed into a stable nucleus. There may be a series of intermediate unstable nuclei as the decay/transformation process continues until a stable nuceleus is reached.
- Modes of radioactive decay
- Beta (ß)
Beta decay is characterized by the emission of a electron or a positron.
A neutron decays into a proton (gain of Z), an electron (emitted) and an antineutrino
- ß- (negative beta, negatron)
- ß+ (positive beta, positron)
- Electron capture
An inner shell electron (K-electron) is captured by the nucleus. A proton is converted into a neutron and an electron neutrino.
The K shell vacancy is filled from an outer shell with the generation of a characteristic x-ray or Auger electrons.
- Alpha (α)
An alpha decay involves the emission of a He nucleus. The Z is reduced by 2 and the mass is reduced by 4. Alpha decay usually takes place in heavier atoms with Z>82.
- Other decay processes
- Gamma rays
A nucleus produced by beta decay generally has an excited nucleus. The excess nucelar energy is emitted via energetic photons or γ-rays. This will reduce the nuclear energy to a ground state which is more stable. 60Co to 60Ni by beta emission leaves an excess energy which is emitted by two γ-rays of energy 1.17 and 1.33 MeV.
- Internal conversion
Internal conversion results from nuclear energy being transferred to a K-shell electron. The excess energy will cause the K-shell electron to be ejected with the excess energy - binding energy of the orbital. The vacant K-shell orbital will be filled from an outer shell with the emission of characteristic x-rays or Auger electrons.
- Decay schemes
- Construction and interpretation
- Examples for each decay mode
- Mathematics of radioactive decay
- Units (SI Units)
| Quantity |
Definition |
SI Units |
English Units |
Conversion |
| Exposure |
X=ΔQ/Δmair |
2.58x10-4C/kgair |
1 R = 1 esu/cm3airSTP |
1 R = 2.58x10-4C/kgair |
| Absorbed Dose |
D = ΔEab/Δm |
1 Gy = 1 J/kg |
1 rad = 100 ergs/g |
1 Gy = 100 rads |
| Equivalent Dose |
H=Q · D |
1 Sv |
1 rem |
1 Sv = 100 rem |
| Activity |
A = λN |
1 Bq = 1 dps |
1 Ci = 3.7 x 1010d/s |
1 Ci = 3.7 x 1010 Bq |
- Exponential decay equation
- Half-life
| A=λN |
| N=N0eλkt |
| T1/2=ln(2)/λ |
- Decay constant
Mean life, average life, and effective half life
Average life ( =1.44·T1/2)
The effective half life is the final half life of an unsealed source based on the two complementing half lives: biological elimination time and the physical decay time.


,
Where λe is the effective half life and λpλbare the physical and biological half lifes, respectively.

Mean life time τ is the mean time an element in a radioisotope lasts before decay.
- Simple dose calculation for implants
- Radioactive equilibrium
Radioactive equilibrium describes the state of radioactivity when there are two or more competing decay processes ongoing. A parent radionuclide decays to a "transient" daughter radionuclide which may then decay further to a "transient" granddaughter radionuclide until finally a stable offspring is reached. The transiency of the intermediate decay products may be long or short relative to each other. The relative lengths of the transiency of intermediate decay products determines the type of equilibrium which will be reached.
If the decay half life of the parent radionuclide is longer than the daughter radionuclide, then equilibrium will be attained. The ratio of parent:daughter radionuclides will approach a constant. The apparent activity of the daughter radionuclide will be governed by - a.) its rate of generation from the parent
- b.) its rate of decay.
Transient equilibrium occurs when the parent half life is slightly longer than the daughter half life. Secular equilibrium occurs when the parent half life is much longer than the daughter half life.
The above equations describe the activity of the daughter nuclide, given the decay constants of the parent and the daughter. The maximum activity of the daughter nuclide is given by

| For λd > λp (daughter half life shorter than parent): |
 |
| For λp > λd this equation reduces to |
 |
| For λd >> λp (or daughter half life very short compared to the parent half life): |
 |
- Secular equilibrium
Radium decays to radon with a half life of 1602 years. Radon decays to Polonium with a half life of 3.82 days and Polonium decays to lead which is stable with a half life of 3 minutes. This is an example of secular equilibrium.
Radium series decay table.
- Radium needles
- 90Sr applicators
- Transient equilibrium
- Nuclear medicine generators
Molybdenum (T1/2=66h) decays to 99*Tc which is used in nuclear medicine. The Mo generator decays producing Tc with a half life of 6 hours. The generator is "milked" of its Tc which is then used to prepare biologic agents used in nuclear medicine.
- Counting statistics
Naturally occurring radioisotopes
Manmade radioisotopes
Manmade isotopes are generally produced as byproducts of nuclear reactor processes. These materials are regulated in the US by the US Nuclear Regulatory Commission.
These products are produced when a stable parent isotope is bombarded by the neutron flux (φ) in the reactor core. Each isotope has a specific neutron interaction probability, known as a cross section (σ) measured in barns ( 10-28 m2 = 10 -24cm2) that is a function of the neutron energy, and the nuclear composition of the parent element. There may be subsequent decay with to a granddaughter isotope upon activation.
- Fission
- Nuclear bombardment
Decay schemes and properties for therapeutic isotopes
| Element |
Isotope |
Energy (MeV) |
Half-Life |
HVL-Lead (mm) |
Exposure Rate Constant Γδ |
Source Form |
Clinical Application |
| Obsolete Sealed Sources of Historical Significance |
|
|
|
|
|
| Radium |
226Ra |
0.83 (average) |
1,626 y |
16 |
8.25 R-cm2/mg-hr |
Tubes and needles |
LDR intracavitary and interstitial |
| Radon |
222Rn |
0.83 (average) |
3.83 d |
16 |
8.25 |
Gas encapsulated in gold tubing |
Permanent interstitial Temporary molds |
| Currently Used Sealed Sources |
|
|
|
|
|
| Cesium |
137Cs |
0.662 |
30 y |
3.28 |
|
Tubes and needles |
LDR intracavitary and interstitial |
| Cesium |
131Cs |
0.030 |
9.69 d |
0.030 |
0.64 R-cm2/mCi-hr |
Seeds |
LDR permanent implants |
| Iridium |
192Ir |
0.397 (average) |
73.8 d |
6 |
4.69 |
Seeds in nylon ribbon; Metal wires Encapsulated source on cable |
LDR temporary interstitial Intravascular brachytherapy; Cardiac HDR interstitial and intracavitary Intravascular brachytherapy: peripheral |
| Cobalt |
60Co |
1.25 |
5.26 y |
11 |
13.07 |
Encapsulated spheres |
HDR intracavitary |
| Iodine |
125I |
0.028 |
59.6 d |
0.025 |
1.45 |
Seeds |
Permanent interstitial |
| Palladium |
103Pd |
0.020 |
17 d |
0.013 |
1.48 |
Seeds |
Permanent interstitial |
| Gold |
198Au |
0.412 |
2.7 d |
6 |
2.35 |
Seeds |
Permanent interstitial |
| Strontium/Yttrium |
90Sr–90Y |
2.24 βmax |
28.9 y |
— |
|
Plaque |
Treatment of superficial ocular lesions |
| |
|
|
|
|
|
Seeds |
Intravascular brachytherapy |
| Developmental Sealed Sources |
|
|
|
|
|
| Americium |
241Am |
0.060 |
432 y |
0.12 |
0.12 |
Tubes |
LDR intracavitary |
| Ytterbium |
169Yb |
0.093 |
32 d |
0.48 |
1.80 |
Seeds |
HDR interstitial |
| Californium |
252Cf |
2.4 (average) neutron |
2.65 y |
— |
— |
Tubes |
High-LET LDR intracavitary |
| Samarium |
145Sm |
0.043 |
340 d |
0.060 |
0.885 |
Seeds |
LDR temporary interstitial |
Properties and Production of Particulate and Electromagnetic Radiation
- Particulate radiation
- Mass, charge
- Relativistic energy equation
- Electromagnetic radiation
- Wave-particle duality
- Wave equations
- Electromagnetic spectrum
- Production of radiation
- Principles
- Radioactive decay
- X-ray tube
- Linear accelerators
- Operational theory of wave guides
- Standing wave guides
- Traveling wave guides
- Bending magnet systems
- Flattening filters
- Electron scattering foils
- Electron cones
- Targets
- Factors affecting
- Beam energy
- Entrance dose
- Depth of maximum dose
- Beam uniformity
- Dose rate
- Monitor chamber
- Collimation systems
- Primary and secondary collimators
- Coupled and independent jaws (including virtual wedges)
- Multileaf collimators
- Other collimation systems (e.g., stereotactic systems)
- Radiation and light fields (including field size definition)
- Mechanical and operational features
- Cyclotron
- Microtron
- Cobalt units
- Therapeutic x-ray (<300 kVp)
Interactions of Electromagnetic Radiation with Matter
- Coherent scatter
Coherent or Rayleigh scatter is a completely elastic photon scatter. The
incident photon has insufficient energy to remove an electron and the photon is scattered to a new path.
Coherent scatter predominates at low energy and high Z material. The incident photons are scattered through small angles.
Coherent scatter mass energy transfer coefficient is σR/ρ.
- Photoelectric effect
Photoelectron effect occurs when an incoming photon has sufficient energy to eject an inner shell electron. The incident photon is completely absorbed. The inner shell vacancy is then filled by a higher orbital electron which will then release its energy either via characteristic x-ray emission or in the alternative the production of Auger electrons. The probability of a compton interaction is proportional to Z3. The probability of a photo-electron interaction is proportional to 1/E3. The angular distribution of electrons is 90° relative to the incident photon with low energy photons. The angular distribution decreases as incident photon energy increases. The photoelectric mass energy transfer coefficient is τ/ρ
- Compton effect
Compton events are inelastic interactions with the incident photon interacting with a "free" or orbital electron. The electron is scattered, increasing its energy. Part of the photon energy is lost to the scattered electron and the photon itself is scattered. There are several possibilities of the outcome of this interaction.
| Knock on collision | This interaction is a direct hit. The knock on collision back scatters the incident photon and the electron is forward scattered. The electron in this case will recieve the maximum energy and the back-scattered photon will have minimum energy. |
| Grazing Hit | The electron will be scattered at 90° and the photon will continue forward with no energy loss. |
| Photon Side Scatter | The photon will scatter through 90 degrees and the electron angle will be a function of hν0/m0c2 |
- Pair production
- Photonuclear disintegration
- Relative probabilities of interactions in human tissues
- Energy dependence
- Atomic number dependence
- Electron density dependence
Interactions of Particulate Radiation with Matter
- Formalism
- W value
- Specific ionization
- Linear energy transfer
- Range
- Stopping power
- Types of interactions
- Heavy vs light particles
- Charged vs uncharged particles
- Elastic collisions
- Inelastic collisions
- Heavy charged particles
- Inelastic collisions with electrons
- Depth dose characteristics ( Bragg peak)
- Light charged particles
- Elastic and inelastic collisions with electrons
- Inelastic collisions with nuclei
- Neutrons
- Elastic collisions with hydrogen nuclei
- Depth dose characteristics vs charged particles and photons
- Biological implications of particle therapy
Quantification and Measurement of Dose (including SI units)
- Exposure (air kerma)
- Absorbed dose (kerma)
- Dose equivalent
- RBE dose
- Calculation of absorbed dose from exposure (e.g., f factor)
- Bragg-Gray cavity theory
- Gas-filled detectors
- Principles of operation
- Uses
- Ion chambers
- Types
- Exposure measurement
- As a Bragg-Gray cavity
- Correction factors (e.g., temperature and pressure)
- Calibration of photon and electron beams (e.g., TG 21 and TG 25)
- Thermoluminescent dosimetry
- Calorimetry
- Film
- Chemical dosimetry
- Solid state diodes
- Scintillation detectors
- Measurement techniques
Characteristics of Photon Beams
- Mathematics of exponential attenuation
- Half-value thickness
- Attenuation coefficients (linear, mass, partial, total)
- Narrow beam vs broad beam geometry
- Monoenergetic vs heteroenergetic
- Parallel vs diverging beams
- Beam quality for heteroenergetic beams
X-ray beams with a few specific exceptions are composed of a more or less continuous spectrum of energy. These beams generally have a peak energy and a mean energy making them difficult to characterize directly. For kilovoltage radiation, the energy is generally specified as kVp or peak kilovoltage. A spectrum of energies ranging from zero to kVp are created by bremsstrahlung emission. This spectrum has low energy radiation that does not contribute to imaging or depth dose, but does contribute to skin dose and is frequently filtered off with copper or aluminum foils. A measure of the quality of the beam is the half value thickness of an absorber in the beam path. The half value layer is the measure of the thickness of an absorber needed to reduce the beam energy by 1/2.
- Energy distribution of accelerated electron beam
- Filtration
- Geometry
- Effective energy
- Energy spectra
Dosimetry of Photon Beams in a Homogeneous Water Phantom
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