Rad Onc Physics: Nuclear Decay

Nucleus

Protons + Neutrons

Atomic Number (Z)

Number of protons (uniquely determines the chemical identity of the element)

Atomic Mass (A)

# protons + # neutrons

Neutron Number (N)

A - Z

Nomenclature

Isotopes

nuclides with the same number of protons

Isotones

nuclides with the same number of neutrons

Isobars

nuclides with the same atomic mass (A)

Isomers

nuclides in different excited/metastable states

Radioactive decay results in the production of what 2 types of radiation?

Particulate (protons, electrons) and Electromagnetic (X-rays, 𝛄-rays)

Radioactive Decay

A process by which an unstable nucleus transforms into a more stable one by emitting particles and/or photons and energy

Unstable Nucleus

Parent

"more" Stable Nucleus

Daughter

Energy Released

Transition Energy (Q)

Decay equation for Beta- emission

- Neutron converted into Proton + Electron

- Z+1 results in isobar formation

Isomeric Transition (IT)

Decay of metastable (isomeric) state to ground state with the emission of a 𝛄-ray

Internal Conversion (IC)

Transition energy transferred to an orbiting electron (usually in k-shell)

Conversion electron emitted with energy equal to

[𝛄-ray energy - binding energy of the k-shell]

Decay Equation for Isomeric Transition (IT)

Nucleus goes from higher energy state to ground state

Decay Equation for Internal Conversion (IC)

Nucleus interacts with orbital electron

X-Rays and possible Auger electrons accompany

Decay Equation for Electron Capture (EC) and (EC, 𝛄)

Orbital electron captured by the nucleus

Z-1 results in Isobar formation

For (EC): Only radiation emitted is neutrino (v)

Decay Equation for Positron Emission (β+) and (β+, 𝛄)

Proton converted into neutron and positron

Z-1 results in Isobar formation

ALWAYS 1.02 MeV from annihilation interaction

A pair of _______ MeV photons are emitted at _______ degrees to each other

0.511; 180

Decay Equation for Alpha Emission (⍺) and (⍺, 𝛄)

Atomic Number (Z) must be greater than or equal to 140

Alpha Particle is a Helium nucleus

May or may not be accompanied by gamma

Nuclear Fission Equation

The Decay Constant (ƛ)

Fraction of the atoms undergoing radioactive decay per unit time (during a time period that is so short only a small fraction decay during the time interval)

For a sample of N radioactive atoms, the average decay rate (decays per time), dN/dT is given by:

Law of Decay

N(t) = number of atoms at time t

N(0) = number of atoms at time 0

𝜆 = decay constant

****can sub N with A (activity)

A(t) = activity at time t

A(0) = activity at time 0

True or False: Decay is an exponential function of time

True

True or False: Activity is an exponential function of time

True

Half Life (T^1/2)

The time required for the activity to decay to 50% of its initial value

Average Life or Mean Life

Important concept in permanent brachy implants

Physical Half Life

Biological Half Life

Disappearance with time of a radioactive biochemical substance in a biological system, can be described as ƛ(biol) similar to radioactive decay

Effective Half Life

Disappearance with time of a radioactive biochemical substance in a biological system, both by radioactive decay and biological elimination

ƛ(eff) = ƛ(phys) + ƛ(biol)

Curie (Ci)

1 Ci = 3.7 x 10^10

Disintegrations per second

Originally defined as:

1 Ci = 1gram(226)Ra

Becquerel (Bq)

1 Bq = 1 disintegration per second = 27 x 10^-12 Ci

Conversion Factors

1mCi = 37 megaBq (MBq)

1MBq = 27 μCi

Equilibrium

A roughly constant relationship between the activity of the Parent (which is radioactive) and the activity of the Daughter (which is also radioactive)

What does the type of equilibrium depend on?

The ratio of the parent and daughter half-lives

Secular Equilibrium

T(1/2) parent >>> T(1/2) daughter (seems ∞)

ƛ daughter >>> ƛ parent

Transient Equilibrium

T(1/2) parent > T(1/2) daughter (5, 10, 20)

ƛ daughter > ƛ parent

No Equilibrium

T(1/2) daughter > T(1/2) parent

ƛ daughter < ƛ parent

Commonly used brachytherapy sources

Radium, Radon, Cobalt, Cesium, Iridium, Gold, Iodine, Palladium

When was Radium (226Ra) discovered?

1898, first source utilized

What is the half life of Radium 226?

≈ 1600 years

What is the average 𝛾-ray energy of Radium 226?

0.83 MeV (830keV)

Original Rx regimens of Radium 226

Only specified Radium, Interstitial and Intracavitary treatments

Construction of Radium 226

Radium Sulfate or Chloride, mixed with inert filler, sealed in Gold foil and then sealed in Platinum needle to prevent leakage of Radon Gas

Radium Prescription

mg-hrs to give the desired dose

Leakage of Radon Gas is a significant hazard if what is broken?

Source (needle)

Radium Exposure rate constant equation

𝚃 (exposure rate constant) = 8.25 R-㎠/mCi-hr for a platinum needle 0.5mm thick

Cesium (137Cs)

Byproduct material from reactors

Cesium 137 half life

30 years, most correct activity 2%/year

Cesium 137 𝛾-ray energy

0.622 MeV (662keV)

Cesium 137 Rx regimens

Replacement for radium, Interstitial and Intracavitary treatments

Cesium 137 construction

Insoluable powders or microspheres labeled with 137Cs and double encapsulated in stainless-steel needles or tubes

Cesium 137 prescription

mg-hrs Radium equivalent to give the desired dose.

Grew out of original Radium data.

Later changed to rad (cGy) and mCi

Cobalt (60Co)

Manufactured in reactors, rarely used now

Cobalt 60 half life

5.26 years, must correct activity ≈1%/month

Cobalt 60 𝛾-ray energies

1.17 MeV and 1.33 MeV

Cobalt 60 Rx regimens

Replacement for Radium, Intracavitary treatments

Cobalt 60 Construction

usually fabricated in a wire that is encapsulated in a sheath of platinum iridium or stainless steel

Iridium (192Ir)

Lower energy: less personnel shielding

Iridium 192 half life

73.8 days

Iridium 192 average 𝛾-ray energy

0.38 MeV (380keV)

Iridium 192 Rx regimens

Replacement for Radium, Interstitial (ribbons, LDR, HDR), Intracavitary (HDR)

Iridium 192 Construction

Usually fabricated in the form of thin flexible wires than can be cut to desired lengths

Gold (198Au)

Lower energy: Less personnel shielding

Gold 198 half life

2.7 days

Gold 198 𝛾-ray energy

0.412 MeV (412keV)

Gold 198 Rx regiments

Replacement for Radon seeds, permanent implants (brain, etc)

Iodine (125I)

Lower energy: less personnel shielding

Most commonly used LDR source

Iodine 125 Half Life

59.4 days (TG 43)

Iodine 125 Average energy

0.028 MeV (28 keV)

Iodine 125 Rx regimens

Permanent Implants (i.e prostate), Temporary (i.e Eye Plaques)

Iodine 125 Construction

0.05mm titanium tube welded at both ends to form a cylindrical capsule; differing vendor designs of the active portion

Iodine 125 Lower Energy

Less personnel shielding

Palladium (103Pd)

Lower energy: less personnel shielding

Palladium 103 Half Life

17 days (Decays faster than iodine, delivers dose faster)

Palladium 103 average energy

0.021 MeV (21keV)

Palladium 103 Rx regimens

Permanent Implants (i.e prostate), Interstitial (ribbons), Permanent

Palladium 103 Construction

Laser welded titanium tube containing 2 graphite pellets plated with 103Pd

Radioactive Decay Source Strength Specification

1. Activity (Curie, Bq)

2. Exposure Rate (R/time, or X)

3. Equivalent Mass of Radium (mg-Ra equivalents)

4. Air Kerma Strength (μGy-㎡/hr)

Exposure Rate

Exposure Rate Constant (𝛤)

Unique to each radionuclide

Relates the activity of a nuclide's emitted photons to the Exposure Rate

Exposure Rate Constant Equation

𝛤 = (Ẋ * d^2)/A

Measured at a specified distance perpendicular to seed axis (std. is 1m)

Assumes the nuclide to be a point source

Units of 𝛤 = (R-㎠)/mCi-hr) or R-㎡)/Ci-hr)

Exposure Rate Constant (𝛤) depends upon?

1. Isotope (energy, # photons/decay)

2. Encapsulation (stainless steel, platinum, etc)

mg-Radium Equivalent Equation

A(Ra) = A x 𝛤/𝛤(Ra)

Can also use the equation pictures:

*****Cs may be substituted for other elements

Total dose equation

D = Ḋ x time