Chapter 18: Radioactivity And Nuclear TransformationPresented by Mingxiong Huang,

Ph.D., mxhuang@ucsd.edu

18.1 Radionuclide Decay Terms and Relationships

• Activity• Decay Constant• Physical Half-Life• Fundamental Decay Equation• Example of the Decay Equation

• What is “Activity”? The quantity of radioactive materials, expressed as the number of radioactive atoms undergoing nuclear transformation per unit time, is called “Activity”.

• A = -dN/dt, [18-1] where “A” is the Activity, “N” is the total number of radioactive atoms, “t” is the time, negative sign indicates that the number of radioactive atoms decrease with time.

• Units for “A”: a) curies (Ci), b) disintegrations per second (dps), also called becquerel (Bq), c) disintegrations per minute (dpm)

• 1Ci = 3.7x1010 Bq(dps) = 2.22x1012 dpm

Activity

Different Units for Radioactivity

Decay Constant

• dN/dt N [18-2]• More precisely: dN/dt = -N [18-3] where is called the “decay constant”, which is characteristic of each radionuclide.

• Examples: Tc-99m ( =0.1151 hr-1), Mo-99 ( =0.252 day-1).

• Relation between Activity and decay constant: A = N [18-4]

Physical Half-Life• Physical half-life (T1/2 or Tp1/2) is defined as the

time required for the number of radioactive atoms in a sample to decrease by one half.

• The number of radioactive atoms remaining in the sample (N) and the number of elapsed half-lives are related by: N = N0/2n [18-5], where N0is the initial number of radioactive atoms, and nis the number of half-lives that have elapsed.

• The decay constant and physical half-life are closely related: = ln2/Tp1/2 = 0.693/Tp1/2 [18-6]

Example: Tc-99m ( =0.1151 hr-1), Physical Half-Life = 6 hours (0.25 days)

100

Fundamental Decay Equation Nt = N0e-t or At = A0e-t [18-7]---------------------------------------------------------Nt = number of radioactive atoms at time tAt = activity at time tN0 = initial number of radioactive atoms A0 = initial activitye = base of natural logarithm = 2.718… = decay constant = ln2/Tp1/2 = 0.693/Tp1/2t = time

At = A0e-t

ln(At) = ln(A0) - λt

ln(At/A0) = 1 - λt

18.2 Nuclear TransformationSpontaneous transformation (radioactive decay) will end if the daughter nucleus is stable. If the daughter nucleus is not stable, the process will continue until a stable nuclide is reached. Most of the decays are in one or more of the following ways:

• Alpha Decay• Beta-Minus (Negatron/Electron) Decay• Beta-Plus (Positron) Decay• Electron Capture• Isomeric Transition (Gamma ray emission,

internal conversion)

• Spontaneous emission of an alpha particle (helium nucleus): [18-8]

• Alpha decay typically occurs with heavy nuclides (A>150)

• It is not used in medical imaging: < 100 m in tissue

Alpha Decay

energytransitionHeYX AZAZ _

242

42

Beta-Minus (Negatron) Decay• Ejection of a beta particle (-)/electron, and an antineutrino:•

• It is isobatric (“A” doesn’t change) and occurs with radionuclides that have an excess number of neutrons. The decay decreases the N/Z ratio.

energyYX AZAZ

1

Beta-Plus Decay (Positron Emission)

• Ejection of a positron (+), and a neutrino. Usually happens in light neutron-poor nucleus

•

• It is isobaric and occurs with “neutron-poor” light radionuclides. The decay increases the N/Z ratio

• The positron will meet with an electron and convert into oppositely directed 511-keV annihilation photons

• The transition energy between the parent and daughter nuclide must be greater than or equal to 1.02MeV (2 x 511 kev).

energyYX AZAZ

1

Annihilation Radiation and Positron Emission Tomography (PET)

Electron Capture Decay• Nucleus captures an orbital (usually K- or L-

shell) electron, usually happens in heavy neutron-deficient nucleus

• It is isobaric and results in an increase in N/Z ratio.

• Neutron-poor heavy radionuclides below 1.02Mev threshold can only decay with Electron Capture, not positron emission.

energyYeX AZAZ

1

Isomeric Transition (Gamma Ray emission)

• Often during radioactive decay (++, -, +, capture), a daughter is formed in an excited (unstable) state. Gamma rays are emitted as the daughter nucleus undergoes an internal rearrangement or transitions from the excited state to a lower-energy state.

• N/Z stays the same

)(energyXX AZAmZ

Decay Schemes

Example: Alpha Decay

Example: Simple Beta-minus Decay

Example, Complicated Beta-minus Decay

Example, Isomeric Transition

Example: Electron Capture and Beta-plus decay

Questions

• 1) Indium’s half life is 2.81 days, what is its decay constant? (a) 0.12 day-1; (b) 0.25 day-1; (c) 0.50 day-1; (d) 0.75 day-1

• 2) Nuclear Transformation may take any of the following ways, EXCEPT: (a) alpha decay; (b) beta-minus decay; (c) beta-plus decay; (d) Rayleigh scattering; (e) electron capture; (f) isomeric transition

• Identify the way of decay:• 3)• 4)• 5)• 6)• 7)

SP 32163215

PoRn 2168422086

OF 188189

HgTl 2018020181

TcTcM 994399

43