Physics Flashcards
Equation for maximum number of electrons for each shell.
2n^2
K=2(1)^2=2
L=8
M=18
Number of substrates for each shell.
2n-1
A: atomic mass
P+N
Z
Number of protons
N
Number of neutrons
Isotopes
Same number of protons, Z
Isotopes
Same number of neutrons,N
Isobars
Same number of atomic mass, A
Line of stability
Low z number –>p:n is 1:1
High z number –> p:n is 1:1.5
Radioactive element seeks stability, this transition is called mode of decay
Modes of decay
b- decay b+ decay Electron capture Isomeric transition/internal conversion Alpha decay
b- decay
n –> p + e- + v + energy
V =neutrino, behaves like a particle with no mass and is not critical to imaging consideration
Daughter has an extra proton
Z+1 and N-1
Atomic mass same
B- particle is of no use in imaging and may contribute to increase radiation dose
b+ decay
P –> n + e+ + v + energy
b+ particle (positively charged electron) will be attracted to and collide with a free negatively charged electron –> annihilation of both particles –> conversion of mass to energy state, E=mc2
Annihilation produce 2 photons, 511 keV, emitted 180 degree from each other. This is what is registered into an image in positron imaging, PET
Z-1
N+1
Atomic mass same
Electron capture
P + e- –> n + v + energy
Vacancy left by captured electron would be filled by an outer shell electron and lead to cascade of an electron to fill vacancy, will lead to emission of characteristic X-ray and Auger electrons
201Tl - characteristic X-rays that are imaged
Z-1
N+1
Atomic mass same
Isometric transitions and internal conversions
Excited state/metastable state exist for very short periods, less than 10^-12 sec, but may exist for hours, this lead to release of energy in form of radiation without changing p to n ratio. This is called isometric transition and results in electromagnetic emissions called gamma rays; same as X-rays but differ from origin, which is from nucleus
There is also a competing process called internal conversion
Ex. 99mTc –> 99Tc; isometric transition is 87% and rest are internal conversion
Alpha decay
Occur in unstable nuclei with high atomic masses
Alpha particle consists of 2 protons and 2 neutrons, helium nucleus; travels shirt distance given high charge and heavy mass.
No application in imaging
Z-2
N-2
A-4
B- decay of 99Mo yields 99Tc, which then decays to 99mTc by isometric transition/internal conversion
Sample of 99Mo will always have same proportion of 99mTc and 99Tc.
Since both parents are decaying, would reach equilibrium based on half lives.
This is employed by both technetium and rubidium generators
Parent-daughter equilibrium
Transient equilibrium
When parent half-life is marginally longer than daughter, amount of daughter in mixture will reach a maximum over a period of time.
Elapsed time will be multiple if half lives if daughter.
Equilibrium is reached after relatively few daughter half lives have passed
Basis of 99Mo-99mTc generators; four 99mTc half lives
Secular equilibrium
Half life of parent is markedly longer than that of daughter.
Since parent is decreasing so slowly relative to daughter, mixture appears to have half life of parent
Basis of 82Sr-82Rb generators used in PET imaging
82Sr 25 days
82Rb 1.2 min.
Many half lives of daughter must pass before equilibrium is reached
Number of decays for a given time equation
N(t) = N(0) e^-decay constant x time
N(t) is number of unstable nuclei remaining after elapsed time
Decay factor
e^-(decay constant x t)
Half life and decay constant relationship
T1/2= 0.693/decay constant
Unit of activity, A
Same equation as nuclear decay
Particles interactions with matter
Alpha or beta particles interact with matter through collisions, resulting in excitation, ionization, or bremsstrahlung.
Excitation
Low energy, electron is energized but does not exceed binding energy; increased energy is dissipated generally as heat radiation.
Ionization
Higher energy interaction
Incident particle transfers enough energy to exceed binding energy of electron; ion pair formed, an energized free electron and a positive ion.
Bremsstrahlung
High energy interaction
More typical of high energy particles interacting with high Z number matter
Incident particle penetrates the electron cloud and interacts with charged field of the nucleus and trajectory of incident particle is markedly changed, resulting in decreased in velocity, energy loss produced photons of X-rays called bremsstrahlung (German for “breaking radiation”)
LET
Linear energy transfer
Alpha particle has high let (high charge and heavy mass)
Beta low let (little charge and low mass)
Photon interactions with matter
Photoelectric absorption
Compton scatter
Pair production
Photoelectric absorption
Photo transfers all of its energy to an inner shell electron
Photon is completely absorbed and electron, called a photoelectron is ejected
Energy of photoelectron is equal to photon energy less its binding energy. Energy of photon converted from electromagnetic energy to kinetic energy.
Vacancy left by the ejected electron is quickly filled by an outer shell electron; characteristic X-rays and auger electrons are then emitted.
Compton scatter
Photon interacts with an outer shell electron; photon is not completely absorbed, unlike photoelectric absorption.
Transfers a portion of its energy to the electron, called Compton electron, which is subsequently ejected.
Most probable interaction in imaging of 201Tl (Hg X-rays) and 99mTc gamma rays in tissues.
Source of image degradation, but can be identified by their lower energy values.
Pair production
High energy photons may completely avoid interacting with orbital electrons and interact in the magnetic field of the nucleus. Resulting in creation of a pair of election, one positive and one negative. Positive one combines with a negative electron, creating two 511 kEV photon; energy of the incident photon must be at least two times the mass energy equivalency of an electron (511 keV) or 1.022 MeV. Energy in this range are not used for imaging.
Attentuation
Affected by thickness of absorber, along with photon energy and atomic number.
Thickness of absorber increases, fraction of transmitted photon will decrease.
Linear attentuation coefficient, my
I(x) = I(0)e^-mux
If thickness reduces beam intensity by 50%, imaging effect would be a reduction in count density of 50% as well.
Half value thickness
HVT =0.693/mu
201Tl HVT in tissue(h2o)
38mm
99mTc HVT
46mm
82Rb HVT
73mm
1 gray (Gy)
Absorbed dose equal to 1 J of radiation energy absorbed by 1 kg of matter (1J/kg)
1 rad
Dose of radiation that imparts 100 erg to 1 g of matter.
Conversion of gray to Rad
1 gray = 100 rad
Roentgen (R)
Amount of electric charge produced by radiation in a unit mass of air
1 rad ~ 1.07 R
Exposure rates common to nuclear medicine range from 0.1 to 10 mR/h.
Survey meter
Gas radiation detector I
Film dosimeters
Radiation interacts with photographic film and resulting film exposure can be used quantitatively to estimate dose
TLDs
Radiation induction of defects in crystals.
On heating, gives off light proportional to the absorbed dose.
Stochastic effects
Induction of genetic mutations in offspring and the induction of malignant rumors
All or nothing
With increasing dose, probability of a stochastic effect increases
Non-stochastic effect (deterministic)
Do not occur below a certain dose
E.g. Lymphopenia, azoospermia, erythema, epilation, pancytopenia, cataract
Encountered from 25 rad to 200 rad
At higher dosages, systemic manifestations occur, acute radiation poisoning; fatigue, nausea, vomiting
At very high dose, death
Less common
Sv to Rem conversion
1Sv =100 mrem
201Tl Cl critical organ
Testes/kidneys
99mTc sestamibi critical organ
Upper large intestine
99m Tc tetrofosmin critical organ
Upper large intestine
99m Tc-labeled RBCs critical organs
Spleen
82Rb chloride critical organ
Kidneys
18FDG critical organ
Urinary bladder wall
Radiation protection methods
Distance
Shielding
Time
Occupational exposure of adult radiation workers
5 rem, 0.05 Sv effective dose
50 R.E.M., 0.5 Sv dose equivalent to any organ other than lens of eyes in 1 year
Natural resources public average exposure
0.3 rem/year
Higher altitude, Denver Colorado, 1 rem/year
Limit dose for public
Less than 0.1 rem (1mSv) per year
ALARA
As low as reasonably achievable
Patients injected with 99mTc will emit detectable levels of radiation for?
24-48 hrs
Patients injected with 201Tl will emit detectable levels of radiation for?
2-4 weeks
