Near equilibrium in 30 days. Use the half-life of Rn to find equilibrium. Is the source sealed?

point source is instaled in small box in HpGe detector this box is colsed and gluen by isolation glue

That should do it.

Dear Joseph,

could you please specify your statement. First, what is near equilibrium (error bars), second how did you evaluate the 30 days? Ten half lifes of radon?

I used the secular equilibrium equation as recommended by H. L. Krieger. No error bars provided but the results are

I was hoping for an algorithm. I´ve tried one in my textbooks and think 99% of saturation is equlibrium. I´m sorry, HL Krieger is not available for me. I append my approach.

No algorithm, other than placing your Zerfallsgesetz eqn 4.44 in EXCEL.

The other H Krieger is

Krieger, H.L.; Whittaker, E.L. Prescribed procedures for measurement of radioactivity in drinking water. Cincinnati, OH 45268; U.S. Environmental Protection Agency EPA-600/4- 80-032; 1980. Lieberman,

Yes he does use the same equation.

Here is the equation, A is activity, 3.8 is radon half-life in days, and D is days.

dr / Joseph, many thanks

i know this equation and agree with u about radon gas and raduim source already i have this case but if i want to measure Rn progeny related to Ra activity with gamma if i have emenation fraction nearly 20% is that mean at any time of measurmen Rn progeny have activity 80% of Ra activity if the source open?

and if the source sealed we can use ur eqution for equlibruim yes?

If 20% of the radon leaves the source, then, yes, the 80% remaining will produce progeny. The progeny concentration will be 80% of the radium concentration.

A down vote for providing information?

I think you have to wait at least ten times halve life time of it 

First, at 3.82 days, the Rn-222 is the longest & thus the rate-determining half-life in the secular equilibrium of Ra-226> Bi-214 chain.

Applying this in the lab, we wait for 20 days after the sample is sealed in a container. This is ~5 half-lives of the Rn-222 (~97% of equilibrium). The counting & measurement uncertainties are typically large enough so that the ~3% loss is in the measurement noise.

Also, remember that your point source would have to be in a sealed container or the gaseous Rn-222 would escape & you would 'never' reach equilibrium.

I hope that this helps

20 days for your Ra-226 sealed in a container is good enough. However, due to a leakage and back diffusion of Radon, a Plastic or PP container is not the best choice.   

There is no separate effect called back diffusion. The diffusion constant accounts for atomic motion in all directions. The erroneous concept of back diffusion started showing up in the 1980s. It is an unnecessary factor for emanation calculation.

It is correct that a sealed radon source reaches about 97% equilibrium in 20 days. It is not good practice to assume counting error will mask the 3% loss. It is necessary to eliminate systematic error when known. That said, if the source started off, say, at 85% equilibration, then the error is much less than 3%. Best practice is to count the sample when sealed, then again in 20 - 30 days. Account for all known errors.

oops- I didn't see the page 1 answers- sorry for my repetition.

Concerning precision: we are an environmental lab & in general, most of our customers are concerned about activity relative to established limits. Typical errors due to sampling & total uncertainty are much greater than the 3% max assumption for the secular equilibrium.  I acknowledge that your precision & data quality needs may vary from ours depending on your use.

Thanks Dr. Jospeh for the errors. For enviromental samples (low level), and concerning precision it is neccesary to take into account the leakage or diffussion. Here is some EX

www.sciencedirect.com/science/article/pii/S1687850714000594

link.springer.com/article/10.1007/s10661-013-3210-7

"Back diffusion" is a term applying to the "closed can" method measuring the emanation rate. The Rn (or thoron) levels in the can increase so that the concentration gradient is diminished. We solved the time dependent diffusion equation and published it in 1983 (PJDallimore and RF Holub, "General Time-Dependent Solutions for Radon Diffusion From Samples Containing Radium", RI 8765, US Bureau of Mines). I can send you this publication if you give me your e-mail address. My e-mail is [email protected]. Elsevier considers RG as infringing on copyright laws.

Bob,

Have not talked to you for many years. 

I do not understand what you are saying about back diffusion. I have RI 8765. Nothing about back diffusion. I agree that concentrations increase and diminish the concentration gradient. It does not matter if it is a closed can, open bucket, or a source on horse back, concentration gradients determine the net movement. 

What does a Bureau of Mines report have to do with Elsevier?

Please explain your position of back diffusion.

Joe

@Jack Burn

I have tried to explain to investigators that good enough is perfect as long as you define good enough. Not giving the best possible answer, i.e., explaining all the uncertainty is not good enough. Nearly all my work is at environmental levels. I acknowledge that sampling errors usually, if not always, dominate all other errors. Nevertheless, by not accounting for equilibrium in analyses is sufficient to have it discounted by EPA and a court of law. One cannot dismiss a known error because it is small. It becomes a wedge to demonstrate incompetence. I have had several data sets discounted because the analysis laboratory was cavalier about uncertainty propagation. In all cases, the reason for discounting was frivolous.

I'm so happy about this discussion

I completely agree with the above answers. In my experience 30 days equilibration time and two/three times measurement will give you correct measurement.

@Hao Cong Le

One of the references listed in the articles you listed is by C. Samuelsson, March 1990. He states explicitly that the can method should not include back diffusion.

I agree, it's not diffusing "back", as I said above, the gradient (the difference between the concentration in the rock (pores), and the concentration in the closed can) is diminishing and therefore the flow is less, according to the first Fick's law. How big this diminishment is depends on how big the volume in the closed can is with respect to the volume in the pores. 

All right, everthing is fine. What I want to say is the notice of leakage or diffusion.

Thanks Joseph and Robert for discussions.

Thanks, Bob. I was not sure from your answer. I thought you might be saying it was valid for the closed-can method.

Hao Cong Le

If I have a problem with leakage, I fix it. I have studied many materials for radon emmantion. I select a volume I can seal and and use fittings appropriate to necessary equipment. Leakage should be negligible.

It's good to hear from you again Joseph with some materials for negligation of Rn leakage. When some one want to measure Ra-226 in environmental (soil) sample using Bi (609 kev) with HpGe (marinelli beaker), what is a good material for this geometry (marinelli beaker) to negligible the leakage? Thanks @ Joseph L Alvarez and I highly appreciate your discussions.

Glass or metal containers are best using glass to glass and metal to metal seals. Most high density plastics are good enough. You can improve plastics by coating with wax or epoxy. Anything that will hold helium will hold radon. You can also make marinelli beakers of tedlar or mylar. Use cardboard to maintain the shape. Indeed, you can a make a cardboard container and impregnate it with wax.

Test your materials and techniques by placing a radon source in the container and follow the growth curve. Negligible leaking is good enough, using your definition of negligible.

Fantastic and fruitful discussion. It is important to assure the radon leakages of the container with the soil sample.

Some thoughts on uncertainty. I have attached a file that addresses the discussion on uncertainty.

30 days to achieve equilibrium between Ra-226 and Rn-222 and few hours from Rn-222 to Bi

Okay thanks @ Joseph L Alvarez.

it is very important to know that U-235 has gamma peak (185.7 keV) 

it is very important to know that U-235 has gamma peak (185.7 keV) 

Sorry I didn't know this discussion had continued... I thought it's been solved. It is the best to seal it 100% (the can), as Joseph suggested, yet a leak can be detected and quantified. Not sealing the sample means the emanation rate changes depending on pressure, temperature, humidity, making the results erroneous. 

What is more interesting is to find out why the emanation rates of Rn (3.8 d half-life) and Tn (55 seconds) are comparable from samples of sizes suitable for measurements (200 to 500 cm3). Is it an anomaly? To find out one would have to scale up the size, say twice or more times, derive the diffusion coefficient using our equations in the two papers available on RG, and see if they are the same. If not, then we don't understand the transport of these atoms in solid matrices. Anomaly discovered. 

greater than 7 half life.