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RADIATION
Effective half-life
Effective half-life, τe, is the combined radioactive and
biological half-life.
1 1 1
= +
τ τ τ
e
where
r
τr = radioactive half-life
τb = biological half-life
b
Half-Life
–0.693 t/τ
N = Noe , where
No = original number of atoms,
N = final number of atoms,
t = time, and
τ = half-life.
Flux at distance 2 = (Flux at distance 1) (r1/r2) 2
The half-life of a biologically degraded contaminant
assuming a first-order rate constant is given by.
0.693
t 1 =
2 k
k = rate constant (time -1 )
t1/2 = half-life (time)
SAMPLING AND MONITORING
Data Quality Objectives (DQO) for Sampling Soils and Solids
151
Ionizing Radiation Equations
Daughter Product Activity
λ1N10
−λ1t −λ2t
N2= ( e −e
)
λ −λ
2 1
where λ1, 2 = decay constants (time –1 )
ENVIRONMENTAL ENGINEERING (continued)
N10 = initial activity of parent nuclei
t = time
Daughter Product Maximum Activity Time
1n λ2 −1nλ1 t′
=
λ2 −λ1
Inverse Square Law
( R2
)
( )
1
2
=
1
2
2
I
I R
where I1, 2 = Radiation intensity at locations l and 2
R1, 2 = Distance from the source at locations l and 2
Confidence
Minimum Detectable Relative
Investigation Type Level (1–α) (%) Power (1–β) (%)
Difference (%)
Preliminary site investigation 70–80 90–95 10–30
Emergency clean-up 80–90 90–95 10–20
Planned removal and
remedial response operations
90–95 90–95 10–20
EPA Document "EPA/600/8–89/046" Soil Sampling Quality Assurance User's Guide, Chapter 7.
Confidence level: 1– (Probability of a Type I Error) = 1 – α = size probability of not making a Type I error
Power = 1– (Probability of a Type II error) = 1 – β = probability of not making a Type II error.
CV = (100 * s)/ x
CV = coefficient of variation
s = standard deviation of sample
x = sample average
Minimum Detectable Relative Difference = Relative increase over background [100 (µs –µB)/ µB] to be detectable with a
probability (1–β)