AIR SAMPLING EQUATION

7/5/2011
Air Sampling Equations

Which equations are used in air sampling depend the manner in which the air sample is analyzed.There are two types of sample analysis:

1. Nuclide Specific (isotopic)2. Gross Beta or Alpha
Two Types of Air Sample Analysis

1. Nuclide Specific Measurement

Individual nuclides (e.g. Cs-137) are quantified on 

collection media, either by gamma spectroscopy ugermanium detector, or by radiochemistry.

2. Gross Beta and/or Alpha Measurement

Usually performed on an air filter using a gas-flow 

proportional counter, beta/alpha scintillator, GM or detector. In some cases, the collected material migan impactor plate instead of an air filter.
Nuclide Specific (Isotopic

Analyses of Air Samples Analyses of Air Samples
Collected Activity at End of Sampli

When an individual nuclide (e.g. Cs-137) in an air is quantified, it is possible to correct for the decay sampling.

A

0 activity of the nuclide at the end of sampling (e

C concentration of radionuclide in air (e.g., uCi/mF sampling flow rate (e.g., ml/min)E

c efficiency of collection

8 decay constant of radionuclide (e.g., min-1

)

t 

s sampling time (e.g., min) 
Collected Activity at the End of Samplin

when the Sampling Time ( t

s) is longer t

half-lives of the Radionuclide

Thi i th i ti it f lid th t This is the maximum acti

vity o

f a nuclide th

a

t can 

collected. It is known as the saturation or equilibriuactivity. At equilibrium, the activity being collected time is equal to the amount of activity decaying petime.Some people say that equilibrium/saturation is achwhen sampling has continued for seven or ten halrather than five half lives.
d Activity (A0)

Equilibrium 

activity

Collected

Sampling Time (t

s

)

ca. five 

half-lives
Collected Activity at the End of Samplin

when the Sampling Time ( t

s) is longer t

half-lives of the Radionuclide

If th h lf If the 

h

alf-lif f lid i h li l 

life o

f a nuclide is one 

hour, sampling lo

four hours won’t increase the activity of the collectmaterial by very much.What can be done to increase the collected activitSample using a higher flow rate.
ctivity (A)

Collected Activity at Start of Count

Between the end of sampling and the staanalysis, the activity of the sample decre

Activity at En

Sampling (A

Collected Ac

Time 

Sampling

ts 

Activity at S

of Count (A

Wait

td

Count

tc
Collected Activity at Start of Count

A activity of the nuclide at the start of the an

(e.g., uCi) 

t 

d time between the end of sampling and the 

the count (e.g., min) 
Airborne Concentration

This is the key equation because it calculates the interest: the concentration of the radionuclide in thThis equation assumes one thing: that the concenthe air does not change during the sampling perioIf the concentration changes during the sampling pand the radionuclide half-life is short compared to sampling period, the equation doesn’t work.
Sun. Mon. Tues. Wed. Thurs. Fri. 

Continuous release during sampling period – the equation gives the correct average concentration

Release only during first day of sampling period equation underestimates the average concentra

the sampling period

Sun. Mon. Tues. Wed. Thurs. Fri. 

Sun. Mon. Tues. Wed. Thurs. Fri. 

the sampling period

Release only during last day of sampling period –the equation overestimates the average concentration during the sampling period
Half-life is Much Longer Than Sampling 

When the half-life of the radionuclide being collectmuch longer than the sampling time, the previous complicated equation simplifies. In this situation we haven’t sampled nearly long enreach the saturation (equilibrium) activity.As such, the collected activity increases linearly wsampling time. In addition, the activity of the collecsample will not decrease after sampling (or during the sample is being counted.In practice, this is usually the case and the followinsimplified equations are more commonly employethe complicated equation. 
d Activity (A

0

)

Half-life is Much Longer Than Sampling 

Collected

Sampling Time (ts)
y

Half-life is Much Longer Than Sampling 

Activit

Time

Sampling Wait Count
When we calculate a concentration (e.g., uCi/ml) 

Half-life is Much Longer Than Sampling 

dividing the sample activity with the volume (V) of sampled, we are assuming that the radionuclide hwas relatively long that there was no significant dactivity during sampling.The use of the above equation instead of the longgeneral equation can lead to mistakes if the radiois short-lived.
If we use this simplified equation with a radionuclid

decays significantly during sampling, we will undethe concentration of the nuclide.For example we would underestimate the concenHalf-life is Much Longer Than Sampling For example, we would underestimate the concen

I-131 (8 d) by 4% if the sampling period were one by 25% if the sampling period were one week.

Sampling Time (t

S) Underestimate of Conce

the same as the radionuclide’s half-life 28%

1⁄2 the radionuclide’s half-life 15%

1/10 the radionuclide’s half-life 3%1/20 the radionuclide’s half-life 1.7%
The collection efficiency of filters for particulates is 

specified by the manufacturer.This efficiency is specified for 0.3 um particles. Th“worst case” scenario because the collection efficibe greater for particles smaller than 0.3 um and palarger than 0.3 um.Determining the Collection Efficiencylarger than 0.3 um.In general, the higher the velocity of the air across filter, the higher the collection efficiency. For some (e.g., many membrane filters), this effect is small. other filters (e.g., cellulose filters) velocity can havsignificant impact on collection efficiency.In many “real-world” situations, the collection efficwill be close to 1.0 (i.e., 100%). 
The collection efficiency of adsorber cartridges (e.

charcoal) are usually specified by the manufactureform of a curve (see next slide) that shows efficienfunction of flow rate.In the case of charcoal, the collection efficiency is specified for methyl iodide. This is a

“worst case

” s

Determining the Collection Efficiencyspecified for methyl iodide. This is

a worst case s

because the collection efficiency will be greater foelemental iodine.The higher the flow rate through the adsorber, the the collection efficiency.When adsorber cartridges are produced “in-housecollection efficiency will have to be determined.
Determining the Collection Efficiency

Charcoal Collection Efficiency vs Sampling Flo

1.00.9

30 x 50 sieve

Iodine

Collection 

Efficiency

Sampling Flow Rate (cfm)

0.8 10 x 16 sieve

0 5.0
The collection efficiency of adsorber cartridges an

absorber solutions can be determined by analyzinactivities collected in several identical collection deoperated in series. In the simplest case, two collecdevices would be employed.This method assumes that the collection efficiency Determining the Collection EfficiencyThis method assumes that the collection efficiency 

same for the different devices, something that migbe true if there are different chemical or physical fothe contaminant being sampled.
E is the collection efficiency

A1 is the measured activity in the first collection deA

2 is the measured activity in the second collection 

Determining the Collection Efficiency

A1 A

2

Bubblers

A1 

Adsorber Car
Gross Beta or Alpha Analyse

Air Samples Air Samples
Two Problems with Gross Alpha an

Measurements

1. In most cases, we cannot account for any decay 

sample activity because we don’t know the half-nuclide or nuclides in the sample. An exception a situation where the alpha or beta activity can o

due to a specific nuclide (in addition to the radon due to

a specific nuclide (in addition to the radon 

thoron decay products). 

2. We only want to report the gross alpha/beta 

concentrations in the air of the licensed materialmany of the gross alpha and beta counts are dunaturally occurring radon and thoron decay prod
Alphas or betas from 

radon (Rn-222) decay products: Po-218, Pb214, Bi-214, Po-214 (30 min effective half-life)

Alphas or betas from 

licensed material

Alphas or bthoron (Rnproducts: P212, Bi-212208 (10.6 hhalf-life)

Problems with Gross Alpha and BeMeasurements

min effective half-life) half-life)
Radon-222 Decay Products 

Po-218 (3 min)

Alpha

Radon-220 Decay 

Po-216 (0.1 

Alpha

Problems with Gross Alpha and BeMeasurements

Pb-214 (27 min)

Beta

Bi-214 (20 min)

Beta

Po-214 ( 164 us)

Alpha

Pb-212 (10.6 

Beta

Bi-212 (60 m

Beta Alp

Po-212 ( 0.3 us) T

Alpha B
There are several ways to account for the contribu

radon and thoron decay products to the gross alphbeta counts:

1 Wait a long time

Problems with Gross Alpha and BeMeasurements

. Wait

a long time

2. The two-count method3. Annular impactor4. First count factor method

None of these methods are completely satisfactory
Correcting for Radon and Thoron Decay P

Contribution to Gross Alpha or Beta Coun1. Wait a long time.If we wait seven days after sampling to perform the alpha or beta count on the filter, the radon and thorodecay products will have decayed away.The count then reflects the activity of the “licensed material.”What we refer to as “licensed material” also includecontributions from long-lived natural material (NORMClearly, waiting seven days after sampling would noacceptable if the licensed material were short-lived. 
2. Two Count Method

This method involves counting the filter twice.The first count (C1) is approximately 4 hours after saCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta CounThe second count (C2) is approximately10 – 20 hou

sampling.The time between the first and second count ()t) is 

two half-lives of the thoron decay products. 
2. Two Count Method

The first count is due to the “licensed material” plus decay products. Since the first count was four or so after sampling, the radon (Rn-222) decay products (half life) would have decayed awayCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun

-life) would have decayed away.

The second count is also due to the “licensed materlong lived naturally occurring airborne radionuclides thoron (Rn-220) decay products. However, the thorodecay products have decreased in activity. 
2. Two Count Method

The corrected first count (CC1) represents the first c

due to the “licensed material” without any contributthoron or radon decay products.

Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun

8 is the decay constant of the “licensed material” 

0.0654 is the decay constant for thoron decay pro
In many situations, the “licensed material” is long-l

the equation simplifies somewhat to:

Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun

2. Two Count Method

The next figure summarizes what is going on.We are only interested in the “licensed material”, bactual measurements (counts) are of the total acti
Alpha or Beta 

Counts on Filter 

Total A

Licen

C1

C

Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun

2. Two Count Method

Time 

Sampling

)t ca. 4 hrs

Cc1
3. Annular Impactor

The annular impactor only collects particles with d

1 um. The assumption is that the naturally occurring rado

Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun

p yg

thoron decay products are attached to airborne pathat are smaller than 1 um while “licensed materiatypically associated with airborne particulates largum.These assumptions are usually correct, although aof licensed material would be smaller than 1 um.
3. Annular Impactor

With a typical design, air enters the relatively large the bottom of the annular impactor. As the airstream moves upwards, it increases in velocity because the channel through which the air is travelling decreaseCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Counchannel through which the air is travelling decrease

cross section. At the top of the unit the airstream makes a 180 turnsignificant momentum of the larger particulates (i.e.licensed material) prevents them from making the 1As a result, they impact onto the collection plate/pla
3. Annular Impactor

There might be a fine film of oil applied to the collecplate/planchet in order to retain the impacted particlAlternatively a glass fiber filter might be glued to theCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta CounAlternatively, a glass fiber filter might be glued to the

planchet - this will act as a substrate that will hold o

impacted particles.The small particulates (i.e., radon and thoron decay products) have less momentum. As such, they make 180 degree turn and are not collected.
3. Annular Impactor

Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun
Correcting for Radon and Thoron Decay P

Contribution to Gross Alpha or Beta Coun3. Annular Impactor
4. First Count Factor

This is a “quick and dirty” method to determine if thebeen a release resulting in airborne alpha or beta acIt can also estimate the alpha or beta contribution frCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta CounIt can also estimate the alpha or beta contribution fr

released material.It involves sampling particulates for a standardized a specific flow rate, waiting for a specific period and counting for a specific period. The times and flow raalways be the same.
4. First Count Factor

The filter is analyzed for beta and alpha activity. The “First Count Factor” is the beta to alpha ratio”Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta CounBefore the method can be used, the beta to alpha rato radon decay products must be determined in the absence of licensed material.
4. First Count Factor

Before the method can be used, the beta to alpha rato radon decay products must be determined in the absence of licensed material.Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta CounThe typical back ground beta to alpha ratio due to radecay products might be in the 1.8 to 2.5 range. If the filter is counted immediately after sampling so Po-218 hasn’t had time to decay very much, the ratibe closer to 1.
4. First Count Factor

As an example, lets imagine that the beta to alpha rto radon decay products was observed to range from 2.5 and that the average ratio (') was 2.Correcting for Radon and Thoron Decay PContribution to Gross Alpha or Beta CounThen, if a beta to alpha ratio above 2.5 is seen in thworkplace, it suggests that there has been a release beta emitter.If a ratio is subsequently observed below 1.8, it wousuggest that an alpha emitter was released.
4. First Count Factor

The observed ratio might be outside the range of ranormally associated with radon decay products, but might be due to radon decay products with no contrfrom licensed materialCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Counfrom licensed material. 

To evaluate this possibility, the beta and alpha counbe repeated 30 minutes later. If the counts drop in hcan conclude that they were only due to radon decaproducts.If the counts do not drop in half, they were due to “limaterial.” 
4. First Count Factor

If there was an alpha release, the alpha activity due released alpha emitter can be calculated with this eCorrecting for Radon and Thoron Decay PContribution to Gross Alpha or Beta Coun

If there was a beta release, the alpha activity due to released beta emitter can be calculated with this eq
Appendix

Measuring the Activity at the Measuring the Activity at the 

of the Count
Count Rate at Start of Count

With short-lived nuclides, the count rate is higher at start of the count than at the end. The following equcorrects for any decrease in count rate during the ctime. It calculates the count rate at the start of the c

N net counts during the count timet

c count time (e.g., min)
Measured Activity at Start of Count

The activity of short-lived nuclides is higher at the sthe count than at the end. The following equation cfor any decrease in sample activity of short-lived nduring the count time. It calculates the activity at ththe count.

N net counts during the count timeE

D detector efficiency (e.g., counts/gamm

I intensity/yield/abundance of radiation 

gammas/decay) 

t

c count time (e.g., min)