chapter 4 hrtd - nrc: home page · 2012. 12. 5. · a laboratory chemically separates out 50 mci of...
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Chapter 4
Series Decay and Equilibrium
Neutron Activation
HRTDHuman ResourcesTraining & Development
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SERIES DECAY
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ANDEQUILIBRIUM
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Objectives
Explain the concept of radioactive series decay
Calculate the ingrowth of activity of a radioactive decay product from a parent radionuclide, given
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y p p , gelapsed time and initial amount of parent
Define the terms secular equilibrium and transientequilibrium
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90Sr → 90Y → 90Zr
Example of Serial Decay
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Note: Also see MISC-31
T1/2 = 28 y
T1/2 = 64 h
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Rate of Change of Daughter = (Production of Daughter) – (Decay of Daughter)
dN
Serial Decay Equation
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= λP NP - λD NDdND
dt
Assumes the branching ratio is 1
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ND(t) = (e-λ t - e-λ t)P DλP NP
λD - λP
0
Serial Decay Equation
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Recall that λP N0P = A0
P = initial activity of Parent at time t = 0.
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The General Equation forRadioactive Series Decay
0
λDND(t) = (e-λ t - e-λ t)P D
λD - λP
λDλPNP
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D P
Activity of Daughter at time t
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Types of Radioactive Equilibrium
Secular Half-life of parent much greater than (> 100 times) that of decay product
Transient Half life of parent only greater than
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Transient Half-life of parent only greater than that of decay product (> 10 times)
No Equilibrium Half-life of parent less than that of decay product
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Secular Equilibrium
T1/2 = 3.8 d
Ra-226
Rn-222
T1/2 = 1,600 y
ARn (t) = A0Ra (1 - e-λt )
Rn-222
Time (Rn-222 T1/2 units)
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Buildup of a Decay Product underSecular Equilibrium Conditions
AD(t) = (1 - e-λ t)DAP0
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AD(t) (1 e )AP
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Behavior of the Secular Equilibrium Equation
Time t
(in half-lives of daughter, D)
AP (dps)
(constant)
( 1 – e-λD
t) AD (t)
(dps)
0 1000 0 0
1 1000 0.5 500
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2 1000 0.75 750
3 1000 0.875 875
4 1000 0.937 937
5 1000 0.969 969
6 1000 0.984 984
7 1000 0.992 992
8 1000 0.996 996
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Secular Equilibrium
λPNP = λDND
A = A
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AP = AD
Note: Total activity in the sample =
AT = AP + AD = 2 AP
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Transient Equilibrium
Transient Equilibrium between Pd-100 and Rh-100
Activity of Parent
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Act
ivit
y
Time (in Daughter Half-Lives)
Activity of Parent
Activity of Daughter
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Equation forTransient Equilibrium
λDND = λ λ
λD λP NP
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D D λD - λP
Note: This equation is only valid once transient equilibrium is reached
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Transient Equilibrium
AD =AP λD
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AD λD - λP
Note: This equation is only valid once transient equilibrium is reached
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Time for decay product (D) to reach maximum activity
lnλD
Transient Equilibrium
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tmD = λD - λP
ln λP
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No Equilibrium
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No Equilibrium (e.g. Ce-146 → Pr-146)
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Moly-Tech Production
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Tc-99 T1/2 = 212,000 yrs
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Moly-TechProduction
ve A
ctiv
ity
Rel
ativ
Time (Days)
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A laboratory chemically separates out 50 mCi of pure Sr-90 to use for research purposes. The Sr-90 is then stored in a vial for 48 hours prior to being used. What is the activity of Y-90 in the sample vial at that time?
Problem
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END OFSERIES DECAY
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SERIES DECAYAND
EQUILIBRIUM
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Parent T1/2 = 60 min Daughter T1/2 = 1 min
0 1000 0 0 01 990 10 10 0 + 10 = 102 980 10 20 5 + 10 = 153 970 10 30 7.5 + 10 = 17.54 960 10 40 8.7 + 10 = 18.75 950 10 50 9.3 + 10 = 19.36 940 10 60 9 7 10 19 7
Residual Parent atoms Daughter atoms Total Daughter atomsTime Parent transformed received from (remaining after 1 min(min) atoms in 1 min parent + new ones from parent)
6 940 10 60 9.7 + 10 = 19.77 930 10 70 9.8 + 10 = 19.88 920 10 80 9.9 + 10 = 19.99 910 10 90 9.9 + 10 = 19.9
10 900 10 100 10 + 10 = 20*11 890 10 110 10 + 10 = 20\ \ \ \ \
60 500 10 500 10 + 10 = 20
* at this point both the daughter and parent are decaying at the same rate (10 atoms per minute) although the daughter only has 20 total atoms while the parent has hundreds. This will continue until the parent and the daughter both decay to 0 together.
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NEUTRON
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ACTIVATION
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Objectives
Explain neutron activation and discuss real world applications of the phenomenon
Explain each term given the activation equation and
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p g qgive the equation for maximum (saturation) activity
Calculate the amount of radioactivity produced in a specified time period given the activation equation and the maximum activity that could be produced
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Neutron capture in
Neutron Capture
slow neutron
gamma
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sodium-23:
23Na(n,γ)24NaReaction
gamma rays
n + 23Na 24Na + γ
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Applications of Neutron Activation
Production of medical and industrial isotopes (e.g. Co-60, Ir-192, Mo-99, etc.)
Accident dosimetry (e.g. Na-24 in blood)
Forensic medicine (Napoleon’s hair)
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Forensic medicine (Napoleon s hair)
Activation analysis to measure trace elements
Activated cobalt (Co-60) in reactor coolant system components is the primary source of radiation exposure to plant workers. Activation products at reactors can also increase public exposure (e.g. N-16 in steam in BWRs)
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Determination of fast neutron radiation component at Hiroshima:
Accelerator mass spectrometry of 63Ni (half-life = 100 years) produced by fast neutron activation of
Applications of Neutron Activation
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100 years) produced by fast neutron activation of copper in building materials
Reaction is 63Cu(n, p)63Ni
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Terminology
Cross section - probability of neutron interacting with a target atom, denoted by σ, given in units of barns (1 barn = 10-24 cm2 )
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Target - number of atoms being irradiated by neutrons, denoted by n0
Neutron flux φ - neutrons incident on a unit area per unit time (e.g. n cm-2 s-1)
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Activation Rate
Activation Rate = φσn0
φ = neutrons/cm2 . S
σ = cm2/neutron . atomφ
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σ = cm /neutron atom
n0 = number of target atoms
Assumptions:
φ remains constant
n0 remains constant
φ
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= φσn0 - λNdNdt
Activation Equation
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φ 0dt
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N(t) = φσn0(1 - e-λt)
Activation Equation
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( ) φ 0 λ
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λN(t) = A(t) = φσn0 (1 - e-λt)
Activation Equation
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λN(t) A(t) φσn0 (1 e )
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Buildup to Maximum (i.e. Saturation)Activity as a Function of
Neutron Bombardment Time
Number of Elapsed Half-Lives of
Activation Product(1 - e-λt)
1 0.50
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2 0.75
3 0.87
4 0.94
5 0.97
6 0.98
7 0.99
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A(∞) = φσn0
Saturation Activity
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A( ) φσn0
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Buildup of Activation Productsin a Target Material
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SimultaneousProduction and Decay
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Saturation
Saturation activity is a function of neutron flux, cross section, and number of target atoms
Ni-63 (T1/2 = 96 yr)
atoms
Time to reach saturation activity is a function of product half-life
Co-58 (T1/2 = 71 days)
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END OF
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NEUTRONACTIVATION
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END OF
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CHAPTER 4