Hello Stephan, interesting problem. Personally I would expect (particularly at higher Rn concentrations) that Rn would at least partially separate from the air and settles down. However, Brownian motion, convection and a presence of aerosols would play their role as well. I think there is not much literature about this phenomenon available or it is quite old (offline) and mainly focused on active deposits of Rn daughters.

Hello Stephan.

Additional information about the system are needed to answer your question. For example:

• is your "closed volume" something like standard room or something significantly higher?
• is there present any kind of active/passive/turbulent air mixing?
• are there some concentration gradients, is there some heat source?
• is the air-radon mixture in thermodynamic equilibrium?
• is there a radon source? (radon can emanate for example from wall materials)

If mixing processes of any kind are not present, if the air-radon mixture is in thermodynamic equilibrium, everywhere is the same temperature and there are no Rn sources on the walls, then something like sedimentation of 222Rn particles in uniform gravitational field will take place.

Radon half life is long enough so we are allowed to neglect radioactive decay, therefore only 2 equations has to be taken under account.

- Hydrostatic equilibrium: dP=-Rho.g.dz

- Ideal gas law: P=Rho.k.T/M

(P- pressure, Rho - density, g - near ground gravitational acceleration, z - height, M - weight of single gas particle)

Solution: Rho(z)=Rho0.e-Mgz/kT (Rho0 is Radon density on the ground)

So there will be slightly higher concentration of Rn near the ground than near the ceiling. Notice, that average particle of air is approximately 6-7 times lighter than 222Rn particle.

This phenomenon is negligible in a room with standard height. But if your "closed volume" height is several tenths meters or more, it should be taken under account.

Bye bye, J

Dear Ján and Jan,

thanks for your answers. I was fully aware that the answer to my question will start with "depends on ...". Thats why it is surely better to clearly define the boundary conditions and approach the question by looking on different scenarios.

First of all, my question regarding gravitational settlement of radon gas refers to a rather small volume, 1 - 10 m3 max. Lets for now define it as a cube of 1 m side length and call it a "Rn chamber" located at sea level. The gas in that chamber does not exchange mass neither energy with the outside world, there is no active mixing or heating occurring. All gas particles are at 298 K (in thermodynamic equilibrium), so there is no temperature gradient existing.

A first scenario resembles my initial question most closely - assume the gas in the chamber to be a homogenous mixture of air (N2 + O2) and radon. Would gravitational settling occur and would radon separate from air even at infinite time (lets neglect the decay of radon for convenience)? Jan Simon already gave very useful mathematical tools (thanks for that!) to estimate the concentration (density) gradient for such a scenario and it mostly answers my question. I admit i am surprised that

1) it seemingly does not depend on the other gas species in the mixture - would the gradient be the same for radon in He and radon in Xe?

2) it does also not depend on the Rn concentration,

3) it seems to happen quickly [< T1/2(Rn-222)] according to Jans reply.

It is interesting to note that the observations that Rn would behave like SF6 come from measurements using electronic dosimeters, which actually detect the decay products, not the Rn itself. As Jan Kozempel mentioned, the presence of aerosols and humidity play an important role in their settlement dynamics and there is already different physics involved. So these observations cannot be directly taken as being valid for the behaviour of radon gas itself.

I would like to draw a second scenario just cause i like asking myself these questions. With the same boundary conditions as above, consider now only air (N2 +O2) in that Rn chamber and a Ra point source in the center of the bottom plane, constantly emanating radon and helium gas into the chamber. What would be the vertical radon concentration profile at steady state condition [this time, considering Rn decay and the velocity of radon diffusion into the chamber + neglecting the recoil effect]? I just wonder how fast brownian motion would be at 298 K in homogenising that gas volume.

Probably not an easy one to solve, but i would love to continue this discussion.

Stephan

Hello Stephan.

This time my answer is getting more technical, requiring more formulas. Therefore I prepared a PDF for you. Please, find it attached below.

Let me know whether you are looking for analytical solution of advanced experimental setup or not.

Bye, JS

Hello Stephan.

I prepared a solution to the advanced radon problem setup you have drawn. You were right - it is not way too easy to solve it, but on the other hand still not too hard to get analytical formula.

If you don't like introducing math, just skip it to the solution on the last pages of attached file.

Let me know if you have found what you were looking for.

Cheers, JS

Hello Jan, Stephan,

I would suggest to introduce yet another parameter - the Temperature. Particularly, I would slightly complicate the situation with the (initial) condition of T(Rn source) = -196°C or 77 K, bearing in mind the Rn melting point of 202 K and boiling point of 211.5 K. (heat of fusion = 3.247 kJ/mol, heat of vaporization = 18.10 kJ/mol :)

Regards

Jan

Hello again,

i believe my question(s) have now been fully addressed. Jan Simon, many thanks for giving me your detailed answers based on the solid foundations of physics. I understood that for the boundary conditions mentioned above, brownian motion will dictate the distribution of radon in the described chamber and that gravitational settling will not (measurably) occur at room temperature.

For a constant radon emanation source located at the bottom of the chamber the situation might be different - although this is just theoretical gameplay. In reality, more factors will play a role such as active mixing, thermal gradients etc.

With regard to the comment of Jan (Kozempel) - thats a completely new discussion :) I would first challenge the validity of that numbers - i bet there is no experimental data on the melting and boiling point of pure Rn-222 ever reported, science limits itself here to extrapolation from the homologues. However, going down with the temperature is certainly an interesting mind game as well!

Hi Hana, I'm always fascinated by the rigorous approach of physicists filled with elegant equations that, at the end of the story, are difficult to solve and usually refer to ideal situations far from the real experimental conditions (usually, much more complex). As an experimental chemist it's quite sure that heavy-atomic-weight noble gases tend to concentrate at the bottom of the containing vessel. Chemists use this strategy to protect oxygen-sensitive substances from atmospheric air by flowing, for example, argon into the vessel: since argon has the tendency to accumulate at the bottom of the vessel this partially shields the sample from entering in contact with air oxygen that concentrates at the top. However, I'm skeptic that this procedure could be efficiently used to concentrate and remove microscopic amounts of radioactive radon due to ubiquitous thermal disorder. This process is temperature dependent, but it is quite obvious to figure out without the need of sophisticated equations. If your problem is to separate radioactive radon, I'm attaching here a patent that reports a method for separating radon from carbon dioxide (a very volatile gas). Hope this helps you for your problem. All the best, Adriano