Chapter 18: Radioactivity And Nuclear Transformation Presented 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
Activity 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 = 3.7x10 10 Bq(dps) = 2.22x10 12 dpm
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 (T 1/2 or T p1/2 ) 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 halflives are related by: N = N 0 /2 n [18-5], where N 0 is the initial number of radioactive atoms, and n is the number of half-lives that have elapsed. The decay constant and physical half-life are closely related: = ln2/t p1/2 = 0.693/T p1/2 [18-6]
Example: Tc-99m ( =0.1151 hr -1 ), Physical Half-Life = 6 hours (0.25 days) 100
Fundamental Decay Equation N t = N 0 e - t or A t = A 0 e - t [18-7] --------------------------------------------------------- N t = number of radioactive atoms at time t A t = activity at time t N 0 = initial number of radioactive atoms A 0 = initial activity e = base of natural logarithm = 2.718 = decay constant = ln2/t p1/2 = 0.693/T p1/2 t = time
A t = A 0 e - t ln(a t )= ln(a 0 ) - λt ln(a t /A 0 ) = 1 - λt
18.2 Nuclear Transformation Spontaneous 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)
Alpha Decay Spontaneous emission of an alpha particle (helium A A 4 4 2 nucleus): Z X Z 2Y 2He transition_ energy [18-8] Alpha decay typically occurs with heavy nuclides (A>150) It is not used in medical imaging: < 100 m in tissue
Beta-Minus (Negatron) Decay Ejection of a beta particle ( - )/electron, and an antineutrino: A Z X A Z 1 Y energy 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.
Beta-Plus Decay (Positron Emission) Ejection of a positron ( + ), and a neutrino. Usually happens in light neutron-poor nucleus A A Z X Z 1 Y energy 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).
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 A A Z X e Z 1Y energy 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.
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 Am Z X A Z X (energy)
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) 32 15 P 9 F 18 32 16 43Tc 18 8 99 M 99 43 S O Tc 86 Rn 220 81Tl 201 216 84 201 80 Po Hg