Chapter 18: Radioactivity And Nuclear Transformation. Presented by Mingxiong Huang, Ph.D.,

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1 Chapter 18: Radioactivity And Nuclear Transformation Presented by Mingxiong Huang, Ph.D.,

2 18.1 Radionuclide Decay Terms and Relationships Activity Decay Constant Physical Half-Life Fundamental Decay Equation Example of the Decay Equation

3 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

4 Different Units for Radioactivity

5 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 ( = hr -1 ), Mo-99 ( =0.252 day -1 ). Relation between Activity and decay constant: A = N [18-4]

6 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]

7 Example: Tc-99m ( = hr -1 ), Physical Half-Life = 6 hours (0.25 days) 100

9 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 = = decay constant = ln2/t p1/2 = 0.693/T p1/2 t = time

11 A t = A 0 e - t ln(a t )= ln(a 0 ) - λt ln(a t /A 0 ) = 1 - λt

12 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

13 Alpha Decay Spontaneous emission of an alpha particle (helium A A 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

isobatric ( A doesn t change) and occurs with radionuclides

14 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.

15 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).

16 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

17 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.

18 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)

19 Decay Schemes

20 Example: Alpha Decay

21 Example: Simple Beta-minus Decay

22 Example, Complicated Beta-minus Decay

23 Example, Isomeric Transition

24 Example: Electron Capture and Beta-plus decay

25 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) P 9 F Tc M S O Tc 86 Rn Tl Po Hg

Some nuclei are unstable Become stable by ejecting excess energy and often a particle in the process Types of radiation particle - particle

Some nuclei are unstable Become stable by ejecting excess energy and often a particle in the process Types of radiation particle - particle Radioactivity George Starkschall, Ph.D. Lecture Objectives Identify methods for making radioactive isotopes Recognize the various types of radioactive decay Interpret an energy level diagram for radioactive