Radioactive Decay Modes

Nuclide Relationships

Isotopes
Atoms having the same number of protons (Z) but different number of neutrons (N) are isotopes.

Isobars
Atoms having the same mass number (A) are isobars.

Isotones
Atoms having the same number of neutrons (N) but a different number of protons (Z) are isotones.

Isomers
Atoms of the same element (same Z and N) but which are in different excited states are isomers.

Alpha Decay

Alpha decay is the emission of a helium nucleus (2 protons and 2 neutrons) which is referred to as an alpha (α) particle.

  • Primarily occurs in heavy (Z > 82) atoms
  • Alpha particle is emitted at discrete energies in the range of 5-10MeV
    • Allowed energies are specific to the emitting nuclei.

Beta Decay

Beta- (Electron) Decay

Beta--) decay converts a neutron into a proton, an electron, and an anti-neutrino.

  • Occurs in radionuclides with high neutron-to-proton ratio (i.e. lying above the line of stability)
  • A neutron is converted to a proton, the electron is required to conserve charge and the anti-neutrino is needed to conserve Lepton number
  • Continuous energy spectrum
    • Energy shared between electron and anti-neutrino

Beta+ (Positron) Decay

Beta++) decay converts a proton into a neutron, a positron (anti-electron), and a neutrino.

  • Occurs in radionuclides with low neutron-to-proton ratio (i.e. lying below the line of stability)
  • A proton is converted to a neutron, the positron is required to conserve charge and the neutrino is needed to conserve Lepton number
  • Continuous energy spectrum
    • Energy shared between positron and neutrino

Electron Capture

During electron capture, an electron is captured by the nucleus which converts a proton into a neutron.

  • Occurs in radionuclides with low neutron-to-proton ratio (i.e. lying below the line of stability)
  • The captured electron is usually from the inner orbital shell and leaves a vacancy.

Key Point: Beta+ decay and Electron Capture are competing processes. That is, they are both able to convert a proton into a neutron producing isobars.

Internal Conversion

Internal conversion allows an excited nuclear state to lower its energy to a ground state via the emission of a gamma-ray or orbital electron. If an orbital electron is ejected, characteristic x-rays and/or Auger electrons may be emitted as well.

Photodisintegration

photodisintegration

Photodisintegration occurs when a high energy photon interacts with an atomic nucleus and imparts sufficient energy to cause the nucleus to loose one or more nucleons.

  • Threshold energy (minimum required energy) for photodisintegration is around 10MeV for most nuclei
    • Beryllium and deuterium are notable exceptions with threshold energies around 2MeV

Nuclear Fission

Fission is the term for nuclear disintegration of high Z nuclei.

  • May be spontaneous or induced by neutron bombardment
  • In neutron induced fission, the neutron is absorbed by the nucleus making it unstable. The nucleus subsequently decays.

Nuclear Fusion

Fusion is the process of combining two low atomic number elements into a larger atomic number element.

Common fusion reactions include: 

Deuterium/Deuterium Fusion

Deuterium/Tritium Fusion

Deuterium/Helium Fusion

D-t-fusion

Decay Statistics

Activity

Definition

Activity is the rate of radioactive decay measured as the number of disintegrations per unit of time. Mathematically, activity may be defined as in the below equation where ΔN/Δt is the change in number of radioactive atoms (N) per unit time.

Key Point: The unit of Curie, 3.7E10 dps, is approximately the activity of 1 gram of Radium-226.

Equation

Units

Activity is measured in Curie (Ci), becquerel (Bq), or disintegrations per second (dps).

Decay Constant (λ)

The decay constant (λ) is the fraction of atoms of a radionuclide which decay in a given time.

Given the decay constant and the number of initial atoms of a radionuclide, the number of atoms remaining may be calculated as in the below equation.

Half-Life (T1/2)

Half life is the time required for half of the atoms of a radioactive sample to decay.

Decay rate is often expressed in terms of half lives as it provides a quick way to determine remaining activity using the below equation where are the number of half-lives elapsed.

Effective Biological Half-Life

Biological half life is defined as the time required to remove half of a substance from the body. For the case of the radionuclides, the effective biological half-life is a function of both biological processes and radioactive decay.

Source Half-Life
Radium-226 1622 years
Iridium-192 73.8 days
Cobalt-60 5.3 years
Cesium-137 30 years
Gold-198 2.7 days
Iridium-192 73.83 days
Iodine-125 59.4 days
Palladium-103 16.99 days

Mean Life (Tmean)

Mean life is the average lifetime for the decay of radionuclide atoms.

Mean life can be used to quickly compute the total number of decays over the lifetime of the sample, which is equal to the initial number of atoms in the sample, N0.

Mean life is also useful as it allows simple calculation of cumulative dose from a permanent implant given an initial dose rate.

Radioactive Equilibrium

The product of decay for many radionuclides is another radioactive product with a distinct half life. In such radioactive decays, the original radionuclide is referred to as the parent and all subsequent radionuclide products are called daughters.  If the half life of the parent is shorter than the daughters, no equilibrium will be reached between the parent and daughters. However, if the half life of the parent is longer than the daughters, an equilibrium in concentration of the parent and daughter will be established. Under conditions of equilibrium, the activity of the daughter nuclides will be governed by the disintegration rate of the parent.

Transient Equilibrium
[T1/2(parent) > T1/2(daughter)]

  • TD is half-life of daughter
  • TP is half-life of parent
  • BR is branching ratio, the fraction of decays yielding the desired daughter nuclide
Transient equilibrium is established as U-234 undergoes alpha decay to Th-230.

Once transient equilibrium has been achieved, the ratio of activity between the daughter and parent (AD/AP) is:

Maximum Daughter Activity

Maximum daughter activity is reached at time tmax.

Secular Equilibrium
[T1/2(parent) >> T1/2(daughter)]

Once secular equilibrium is achieved, the activity of the daughter is equal to the activity of the parent.

Example of secular equilibrium. Radium-226 (half life ~ 1,622 years) decays to Radon-222 (half life ~ 3.8 days).

Common Radionuclides In Medicine

Brachytherapy Sources

NuclideHalf-lifePhoton Energy
(MeV)
HVL
(mm Lead)
Exposure Rate Constant
(R-cm2/mCi-hr)
192Ir73.8 days0.38 average2.54.69
226Ra1,600 years0.83 average12.08.25
222Rn3.83 days0.83 average12.010.15
60Co5.26 years1.17, 1.3311.013.07
137Cs30.0 years0.6625.53.26
198Au2.7 days0.4122.52.38
125I59.4 days0.028 average0.0251.46
103Pd17.0 days0.021 average0.0081.48

PET Nuclides

NuclideHalf-life
(minutes)
Positron
Maximum Energy
(MeV)
Dose rate constant
(μSv m2/MBq)
18F109.80.630.143
11C20.40.960.148
13N10.01.190.148
15O2.01.720.148
64Cu7620.650.029
68Ga68.31.90.134
82Rb1.273.350.159
124I60481.54, 2.170.185
Data taken from AAPM TG-108

A Closer Look At Medical Nuclides

Ir-192

Iridium-192 (192Ir) is the most common isotope used in high dose rate (HDR) brachytherapy. It is a man-made isotope produced by neutron bombardment of Iridium-191. (192Ir) decays primarily through β- decay to an excited state of Platinum-192 which is stable. Approximately 5% of decays occur via electron capture yielding an excited state of Osmium-192 which is also stable. It is regarded as superior to cobalt-60 and cesium-137 due to its higher specific activity which allows for smaller source sizes. One disadvantage to (192Ir) is its short half life (73.83 days) which results in a loss of activity of approximately 1% per day. This necessitates source changes every 3-4 months.

  • Half-life: 73.83 days
  • Activity loss per day (quick estimate): 1%/day
  • Decay modes
    • 95.6% β- decay to excited state of 192Pt
    • 4.4% Electron capture to excited states of 192Os
  • Exposure rate constant
  • Air kerma rate constant
  • Photon energy
    • 0.136-1.06 (0.38 average) MeV
  • Half-value layer (mm lead): 2.5mm

IR-192 decay scheme

Knowledge Test

1. Select all likely decay methods of a radionuclide with a low neutron-to-proton ratio.

Question 1 of 3

2. An I-125 seed (half life = 59.4 days) delivers an initial dose rate of 2.4cGy/hr to its reference point. What is the cumulative dose delivered after  30 days?

Question 2 of 3

3. Approximately how many half lives are required to reduce activity by 99%?

Question 3 of 3


 

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