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A single atom doesn't have a state of matter. Radon-222 decays lead to a couple of short-living (half life under an hour) nuclei in the decay chain until it becomes lead-214 lead-210 with a half life of 22 years. As bulk matter all these decay products are solid but you don't get macroscopic amounts of them. As individual atoms they can stay in the air or get captured by some liquid or solid surface - including dust particles.

An isolated lead atom in the air is just a very heavy atom that bounces around randomly just like all other atoms and molecules.

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Would the individual lead atom very quickly oxidize or otherwise react with something else in the atmosphere?

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Yes and no. That totally depends. Chemical reactions are actually really unlikely to happen, as the right particle has to hit another appropriate particle under just the correct angle with the right energy (collision theory). Those prerequisites make chemical reactions pretty much a numbers game. It’s entirely possible for the lead atom to just bounce around for a really long time and work it’s way to the ground.

In the air, Pb most likely to react with oxygen, so like 20% of the entire air mixture. Now think about a single Pb atom as a grey ball (albeit a rather big and heavy one) in a big room with 10000 (most gases consist of surprisingly low amounts of molecules) other balls. Only 21%, so 2100, of them are reactive oxygen, which is evenly distributed and well mixed with other ones in the room. Now, the heavy big ball bounces around and hits mostly nitrogen, which doesn’t do anything. If it hits oxygen, it needs to fulfill all the above conditions to actually oxidise instead of just bouncing off of it.

Basically, looking at an individual atom, its pretty unlikely it’d react with anything. Looking at bulk atoms, as they practically never are singled out, reactions are way more likely to happen.

The decay process leads the daughter isotope to be charged. This causes it to become affixed to dust in the air. This is also where the real hazard from radon comes from: the decay products becoming trapped in your lungs and irradiating them through several decay cycles.

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Randomly like others? What about prevailing gravity force for such heavy particles?

Doesn't play a big role over the size of a room. Random air currents and even diffusion are more important. If you release a heavy atom in the middle of a room it's slightly more likely to hit the ground first instead of the ceiling but the difference is just something like 0.1% or less.

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So 7x mass nearly doesn't matter.

How far radon will go via diffusion until it decays in h.l. 3.8 days? Its products are to be bound faster, I suppose.

> How far radon will go via diffusion until it decays in h.l. 3.8 days?

Many meters (as rms). Random air currents are the dominant effect unless you have an extremely calm room.

The scale height for nitrogen and oxygen is ~8 km, something with 7 times the mass still has ~1 km, so in perfect equilibrium you would expect the concentration to change by ~0.2% over the height of a room. In practice you never achieve such a perfect equilibrium unless you completely seal the room, keep its temperature completely constant and wait for a very long time.

So how many atoms do you need to be able talk about states of matter?

As far as I'm aware, "arbitrarily many"

If this one introductory thermodynamics course I did last semester is any indication

I disagree. For one, a single lead atom is basically a radical so there is no energy barrier to overcome on its side for the reaction to occur (since it has no metallic bond to other Pb atoms). This means the likelihood of a reaction with all other collision parameters being the same is increased by orders of magnitude

Second, things move hella fast at room temp and the mean free path length at STP is very small. This means that it will have collided with air molecules a whole lot before it reaches any surface. I don't remember the numbers off the top of my head for some shoddy napkin math but I'm very confident that if we account for both these factors, Pb will have reacted with oxygen with a very high likelihood before touching a surface unless it formed like, right next to it.

(orgchemist not physics one here) that sounds about right. If you start adding atoms, going 2, 3 etc there is no clear number when it suddenly behaves like a macroscopic solid. As with everything in science, "solid" is just a concept/model and there is no one 100% clear way to define when a set of particles switches from non-solid to solid

my thought process is: if we add Pb atoms and they stick together, then at what number do we consider it a solid particle? You wouldn't count alkane vapour where the molecules consist of dozens of atoms a solid (or liquid), right? In essence they are chemically bonded and stay together, so why would 20 or 30 Pb atoms together be considered differently? So what is it, 100, 200? It is pretty arbitrary

and it's not like if it's, say, 200 then at 199 it's not a solid and at 200 suddenly it is and behaves totally differently

Pretty much my line of thinking, yeah.

?? are you saying lead can be a (very low partial pressure) gas at STP?

With lead alone almost all atoms would hit the wall and freeze out in milliseconds, although theoretically the vapor pressure is not zero. With other gases you can have lead in there for a while outside of equilibrium.

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Gas, liquid, solid — it’s mostly about how close molecules/atoms are to each other (if you abstract enough from interatom interactions). Gaseous state means that everything is so far away and moves so quickly in random, it doesn’t feel any kind of interaction from outside. For it to happen you either need to reduce the distance (increase pressure) or to take away some energy from particles (cool down), so they could “talk” to each other. It’s called condensation and unless it happens to radon, you can easily think of atoms of lead separated from it as single atoms, it’s unlikely that they will condense together by themselves which will allow you to think of it as liquid/solid. Otherwise, you can think of it as a really expanded gas diffused into radon. Depends on what you’re trying to achieve and which processes to describe.

Well, all you’re saying is right. But it’s also pretty unlikely to really find a single Pb atom flying around. There’d be a gradient originating from the source, with most heavy Pb atoms actually chilling at the source and not wanting to really move (think elastic impact) as all the other atoms/molecules colliding with it have way less mass. Only the most energetic ones escape (we’re overlooking any kinds of wind here for simplicity, just focusing on the thermal energy). So Pb will most likely see other Pb and form more inert clusters before even noticing any other molecules flying around. Those clusters will get oxidised on the surface eventually, but definitely not instantly or „quickly“ (however uncertain that term might be).

Now, in a realistic scenario, with wind working it’s magic and mixing everything, you’re probably right to disagree. That’s why my answer was „yes and no“. Realistically, it’d probably get oxidised at some point. Even a radical reacting with another radical needs to (Pb and O2/O•) fulfil certain strict geometrical conditions in order to pair the lone electrons. Those conditions can only be achieved randomly and under a certain energy threshold, which is why radicals in gas phase can be (but definitely don’t have to) pretty stable. I aimed to explain the reasons why this isn’t really a straightforward case.

Again. So basically, it’s pretty unlikely that a single Pb gets quickly oxidised. It will happen to some atoms though. It’s way more likely for Pb to form bigger clusters, which are more probable to hit (or rather be hit by) oxygen to react on their surface.

Edit: I’m all for napkin math though. I’ll try to remember to do it later.

Every element and compound can be, it's just that for most solids the partial pressure is so low as to be negligible.

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Not necessarily milliseconds. It can take minutes for an atom of gad in STP atmosphere to bumble its way to a room's wall.

The first sentence was discussing a scenario where we only have the lead atoms (at their extremely low density) and nothing else. I added the remaining gases back in the second sentence.

you are right. it will instantly react with oxygen radicals which are freely available from photo dissociation of O3 and NO2.

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"Even [diatomic radical reactions] must fulfil strict geometrical (sic) conditions in order to pair lone electrons" I don't agree with. There is genuinely only 1 geometric paramater, i.e. the distance between the two atoms, unless you are implying Born-Oppenheimer doesn't apply or relativistic effects are necessary (which, they are, but for which your bouncing ball model doesn't account). Even the angle between their velocities does not matter following from Newtonian relativity.

I also believe your "energy threshold" (Eyering transition state Gibbs free energy?) is being imagined as far too high. Ground state monoatomic oxygen and lead must overcome only Pauli repulsion in the formation of the transition state, which will be on the same order of magnitude as Coulombic benefit entering the transition state, so I posit ca. 10% of bond enthalpy as the maximum barrier? Which for even the strongest diatomic leaves us with 90 kJ/mol, which for an ordinary reaction proceeds unmonitorably quickly at room temperature, for a more reasonable guess of 20 kJ/mol we need an argon matrix to observe these using IR spectroscopy. Reaction with triplet and heaven forbid singlet dioxygen will likely have larger barriers. Do I think these barriers will be large enough to stop reaction with a radon daughter lead? No not at all. Even under your assumptions.

Saying it will only occur when it forms larger clusters is frankly laughable. The ionisation energy goes up, the Gibbs free enegy of the transition state goes up, and frankly the chance of interacting with oxygen goes down, not up when forming a cluster. The total reactive lead surface area goes down rapidly with cluster size as core atoms become inaccessible, and on forming a cluster the volume goes down from overlapping atomic radii. On small clusters the cluster radius is a similar fraction of the mean free path as the atomic radius of a lead atom is of the mean free path, so forming a Pb(0) tetramer roughly quarters your reaction time. Lead metal sheets oxidises slowly, and can readily be chemically forced back to metal, however fine lead powder can ignite simply by throwing it through air.

Your assumption that lead clusters are forming in preference to reaction with oxygen is only true if your amount of parent radon is decaying much faster than it is diffusing or you have far more radon than oxygen. This is not true, as isolable radon (222Rn) has a half life of almost 4 days. Under any reasonable conditions this is much slower than diffusion and all radon will be well mixed with the surrounding air.

I would be frankly shocked to see any metallic lead deposition at all. I tried to read about experimental evidence for this however daughter isotope measurement is only performed by radiation measurments rather than any chemical means so the identity of the material is never stated (comprehensive article by Yamamoto et al. in J. Environ. Radioactivity).

If the scenario only takes the presence of lead into account, there's still a decent probability of lead vapor existing. You figure the vapor pressure of mercury is so well documented by experiments where ullage develops in a container filled in such a manner where no material other than mercury could be present; the same should be true of all materials subject to vacuum.

Or, put another way, your suggestion that lead would "freeze out" as soon as it hits the wall of its container suggests you could hit absolute vacuum (and thus absolute zero temperature) by simply waiting.

Which is what makes it so hazardous to our lungs. Essentially it becomes a tiny particulate, and is also an alpha-emitter, which means that most of the radioactive energy is deposited in the small air sacs of the lung - hence, cancer risk.

I already mentioned that, too...

> With lead alone almost all atoms would hit the wall and freeze out in milliseconds, although theoretically the vapor pressure is not zero.

The vapor pressure of lead at room temperature is absurdly small. Something below 10^(-20) Pa extrapolating from this graph.

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Radon-222 decays via several steps, a decay chain leading to non-radioactive, Lead-210. A lot of the radon decay products, Lead-214 and Bismuth-214, ends up coating dust particles and sold surfaces, a phenomena called Radon Daughter Plate Out. So the daughter atoms aren't usually free floating in the air, but usually more than 90% ends up sticking to dust particles and solid surfaces.

>A small fraction of radon progeny, typically 0.1 or less, remains unattached and in dynamic equilibrium with attached particles. Generally, dustier atmospheres are associated with smaller values of unattached fraction and higher concentrations of radon due to additional radiation emission from dust.

This is the decay chain for Uranium-238, which includes Radon-222

Radon-222 initially decays to Polonium-218, via emitting a positively charged Alpha particle. The resulting Polonium-218 atom, with a half life of 3.1 minutes, is electrically charged and it is attracted to charged dust particles and sold surfaces where it quickly decays to Lead-214 and Bismuth-214, formimg a radioactive coating, a major source of radiation exposure from indoor Radon gas.

These two isotopes, in comparison to other isotopes of the randon decay chain, have relatively long combined half life of just over 20 minutes.

Radon Plate Out can be demonstrated using a balloon. If you have a building or better still, a basement with a slight radon problem, and leave an electrically charged balloon in the room for an hour or so, then measure it with a Geiger Counter, you'll often find the balloon becomes radioactive due a coating of Lead-214 and Bismuth-214, from attracting Polonium-218 directly and radioactive dust particles.

https://youtu.be/C_P-euxMGSA

The Plate Out on glass is very sticky, I keep a Radium dial WWII compass safely sealed in an air tight jar. The inside of the jar gets coated with radon plate out, rubbing the glass with a wet tissue removes some of the contamination, the tissue gets contaminated, but most of the activity is stays stubbornly stuck to the glass.

It's possible some of plate out might have formed some sort of electrostatic bond, perhaps Van Der Waals force.

I can also measure the decay of the contamination:

https://imgur.com/XpibmUV

The isotopes have an average half life of just over 20 minutes, so it's decay noticed quite quickly (using a Radiascan 701a connected to logging software on my PC).

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3 x 10^-14 3.67 x 10^-12 Pa, actually, but I take your point.

If you regard "finding the lead atom" I might agree, but "ionized(?) lead atom finds oxygen in air" would be one in five collisions.

How likely to hit those though? Really low, right?

What I'm gathering is that in normal air it would mostly cling on to dust particles, in dust-free air it would be an extremely low-partial-pressure gaseous component, and in pure form (say, a container of pure radon that decays) nearly all of it would attach to container walls, leaving an extremely low-pressure lead gas behind.

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Right.

To add to the already-excellent analysis already posted, I have to quibble about:

>There’d be a gradient originating from the source...

Exactly what "source" are you envisioning here? We're talking about radon gas mixed freely in the atmosphere. Any decay products would be distributed randomly and diffusely, as there is no monolithic source from which to originate.

Yes, Po-218, Lead-214 and Bismuth-214 are electrically charged, as a result they tend to stick to dust particles and solid surfaces that are negatively charged, a phenomena called Radon Daughter Plate Out. Indoor air contains mostly (>90%) attached progeny, stuck to dust particles. Attached (Po-218, Lead-214 and Bismuth-214) progeny are responsible for most of the radiation dose from indoor radon.

Vogiannis, E.G. and Nikolopoulos, D., 2015. Radon sources and associated risk in terms of exposure and dose. Frontiers in public health, 2, p.207.

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FYI. have a radium dial compass sealed inside an air tight jar, safely stored in an unoccupied room. It's highly radioactive, back then Zinc sulfide phosphor wasn't particularly sensitive so they compensated by adding extra radium.

Anyway, the interior of the jar gets coated with radon daughter plate out:

https://imgur.com/XpibmUV

This is the decay I measured, due to Bismuth-214 and Lead-214 decay.

Anyways, the contamination stubbornly adhers to the glass. I tried rubbing it off with tissues, dampened with water and alcohol. I estimate I can remove about 25% of the contamination, by measuring the radioactivity on the tissue, most remains stuck to the glass.

Radon Plate Out occurs because the decay products (218Po, 214Pb and 214Bi) are electrically charged, they are attracted to dust and surfaces that are slightly charged.

So does that mean my basement with it's slight radon problem is entirely covered in radioactive particles? How do you even clean that out and make the space usable / liveable after taking radon mitigation steps?

Now I'm thinking about this room with 100ppm lead in the atmosphere, and how fast the neighborhood test scores are dropping.

Where did that value come from?

Assuming a straight line going through (0.6, 4.6) and (1.36, -4) we reach 1000K/(293K) = 3.41 at -21.65 which means 10^(-21.6) Pa. The extrapolation that far out will come with a large uncertainty of course.

Having high radon levels in a basement area, a little above the recommended levels, shouldn't be a problem as you don't spend much time there, unlike a bedroom or living room.

Also, if you have a clothes drier in your basement and a Geiger Counter, a fun experiment involves measuring the radioactivity of the lint caught in the dust trap. It can sometimes be extraordinarily radioactive.

https://youtu.be/1s8wYJybizc

It doesn't work for me, as my clothes dryer is in a well ventilated room.

Also, the most effective way for society to reduce the risk of lung cancer from indoor radon exposure is to reduce rates of tobacco smoking.

Most people who get radon linked lung cancer are current and former smokers, as smoking reduces the lung's capacity to repair DNA damage caused by ionizing radiation. Smokers are almost 9 times more likely to develop radon linked lung cancer than never-smokers.

>The BEIR VI model also purports a significant synergism between radon exposure and smoking in lung cancer risk. On the basis of BEIR VI, the EPA estimates that, at a radon level of 4 pCi/L, the lifetime risk of radoninduced lung cancer death for never-smokers is 7 per 1000, compared with 62 per 1000 for ever-smokers.

Lantz, P.M., Mendez, D. and Philbert, M.A., 2013. Radon, smoking, and lung cancer: the need to refocus radon control policy. American journal of public health, 103(3), pp.443-447.

There are billions per second over all, the individual lead atom isn't hitting an individual oxygen radical a billion times a second.

If you've already taken radon mitigation steps, you're good. The big danger from radon is inhalation, you really don't want any radioactive decay to occur inside your body. The radioactive dust can likely be removed through simple cleaning activities, and isn't that dangerous if it remains outside your body. Radon's decay chain exclusively produces alpha and beta particles, which your skin can easily block.

I find that pretty interesting, but I imagine that especially the upper atmosphere, with high levels of ionizing radiation and radicals floating around, doesn't resemble inside of a jar, not to mention the distance the daughter nuclides must travel before deposition is vastly increased for atmospheric radon decay products.

Air is fairly diffuse, as in there aren't nearly as many atoms per unit volume as with a liquid, so the atom will stay suspended until it encounters another element or compound with which it can react chemically and has an interaction with that other element/compound of a long enough duration that the interaction can proceed. Smacking into an O2 molecule "might" result in the formation of PbO but not if the collision is too forceful, too weak, or not adequately direct. Eventually, over time, thermodynamics say that the metallic lead in air will undergo an oxidation-reduction reaction and make some sort of base salt such as lead carbonate or lead oxide. However, it does take some time for that to happen on a statistical basis (never goes to total completion, really).

Even then, though, the new compound will tend to stay suspended until it absorbs onto some larger solid or dissolves into some larger liquid mass (like droplets in a cloud). It will then go wherever that larger mass ends up going.

If air is still (no movement at all), there will be a slow downward migration because of density differences, but even the slightest air movement will be enough to keep the atoms or tinier particulates in suspension.

Mostly though, the atom will bounce around in the gas, as part of the gas phase, until it gets lucky and reacts with some other participant in the chaotic dance, making a new molecule.

Even metallic lead has a vapor pressure, the presence of some atoms that will leave the solid and enter the air just by random energy pulses, so the drive to "rain" out of the air just by density isn't all that powerful. That is, in a closed space, if you leave a bar of lead out on a tabletop, some of that lead will escape the solid and enter the air. Not a lot because lead isn't all that volatile, but you cannot prevent all loss at the interface (surface of contact between air and solid).

I don't know what the average residence time (median duration that the atom would exist in suspension before descending to the ground) of a lead atom in air would be. Not likely a value measured in seconds or minutes. Even household dust has mean residence times longer than that, and that stuff is destined to fall fairly rapidly by comparison to a lone atom, if only the air would stay still long enough.

>How do you even clean that out and make the space usable / liveable after taking radon mitigation steps?

If you've taken radon mitigation steps (such as barriers against radon infiltration from the ground, overpressure in the building or increased basement ventilation from non-radon air sources) then the remaining already deposited decay products on surfaces in the basement should be negligible. Just vacuum the place.

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Commercial tobacco is also fertilized with mined phosphate fertilizers that are naturally Rick in uranium decay series elements, including Po-210. It also turns out that the tobacco plant has an unusually high affinity (uptake factor) for polonium, and the leaves become enriched in polonium. Smoking those leaves is the most effective exposure pathway: inhalation. Put all that together and voilà: cancer.

Radon Daughters stick to dust at ground level and that dust is carried into the higher atmosphere by rising air currents, they can rain out when there's heavy rain, thunderstorms particularly, a phenomena called Radon Washout.

It was discovered by accident in the 1960s. A nuclear worker walked though puddles in a car park on the way to work, and he set off the alarms as he arrived, since that's backwards they were intrigued, and they discovered that atmospheric dust is coated with radon daughters which can get concentrated in electrically charged thunderstorms, and rain out as Radon Washout.

Radon Washout can sometimes be intensely radioactive, and there's a paper that estimated that a few percent of skin cancers might be linked to Radon Washout, beta radiation from Lead-214 and Bismuth-214 decay is able to penetrate the outer layers of the skin and deposit a radiation dose to living skin cells, a risk increased for people who work outdoors. This might be speculative, nevertheless, it illustrates just how radioactive rain can be sometimes be when weather conditions are just right.

I measured it myself a few times. Got readings up to 2 microsieverts per hour, nothing spectacular.

Styro, B.I. and Stelingis, K.I., 1978. On the value of flow of long-lived radon-222 decay products into atmosphere with the dust of natural and anthropogenic origin. In Chemical and radioactive pollution of the atmosphere and hydrosphere. V. 4.

Edit: Also, >90% of indoor radon daughters are bound to dust, very little is unbound, free floating.

How many grains of sand do you need before it can be called a heap?

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That's interesting. I always wondered where the Polonium-210 came from. I have a radioactive apatite from Brazil. In this case it contains radioactive thorium, but yes apatite (phosphate ore) can also contain uranium.

Most commenters here are referring to the decay of radon in air, but it also occurs in solids and water, like rocks and groundwater. In radiological risk assessment for radioactive waste, we are interested in what happens to the radon parent, radium, when it decays to radon.

A radium atom will generally exist as part of a crystal matrix or as a radical or compound dissolved in groundwater, and when it decays to radon its physical form depends on whether the recoil from the emitted alpha is strong enough to knock the newly formed radon atom out of the crystal matrix or out of the water into the air or from one crystal into another or into the water. The probability of radon escaping the solid phase and going into a fluid phase, being air or water, is called the escape to production ratio, Nielsen and Sundquist. I study this as part of radiological risk assessment because once the new atom is in air or water it is available for transport. If the radon does not escape the crystal, it will soon decay to polonium and other progeny, and likely stay put. Note also that radon has an affinity for water as well, so in balance, some radon will be in the air and some in the water.

Uranium decays to thorium decays to radium decays to radon, and so on. So any or that contains uranium will contain this huge suite of decay products as well.

What's especially interesting to me about tobacco is that it selectively removes polonium from all the others and puts it in the hapless smoker.

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Wow, so it's biologically concentrating Po-210 like how Chernobyl mushrooms concentrate Cesium-137, or radioactive galena...

This will interest you. Here's a sample of radioactive galena I have from the Kateřina Coal Mine, Radvanice, Czech Republic.

https://youtu.be/Ju8c6LtA5ZE

Here's a close up photo...

https://www.mindat.org/photo-1144820.html

It looks like a bismuth specimen, due to its odd formation process, deposition from hot gas.

The Kateřina Coal Mine was a bizarre combination of a coal and uranium mine, that caught fire in the 1960s or 70s. Fumes from the burning coal seams deposited galena in cracks, which ended up contaminated with radioactive Lead-210, half life 22 years.

The specimen was likely collected in the 1990. The entire site was rehabilitated about 15 years ago, it's now a nice green park. Big difference from the hell scape of a burning radioactive coal mine.

Yes, bioconcentration.

That's amazing about the burning coal mine forming galena from the lead. Nature is incredible.

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Another writer responded with mean free path and velocity for particles. Given that dust, that is other larger masses than individual oxygen atoms, will the electrically charge particle be much more likely to first bound with oxygen and then with dust?

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There is no way that it is more likely to find other lead atoms, which are only there at trace amounts as decay products, before it interacts with trillions upon trillions of other gas molecules... many of which are reactive.

However, there are a lot more more oxygen atoms to collide with. Given mean free path and velocity at standard temperature and pressure, I think the random movement of the Pb atom is more likely to react with oxygen before finding the dust particle. Another response calculated the Pb O reaction to occur with in a second.

A shovel full?

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Yeah, my furnace filter gets slightly radioactive after a few months. Very minor but it’s detectable above background level.

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Do the decay products even form isolated atoms?

When the radon nucleus splits, do its electrons stick with the smaller nucleuses?

I'd have thought they are ions, which would be likely to bind to molecules in the air before collecting enough free electrons to become an atom.

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I've heard an entertaining argument that the answer to your rhetorical question is zero. If there's a heap of sand and someone takes away one grain, there's still a heap of sand. If we repeat this many times, we have a heap of only one grain of sand, then remove that grain and have a heap of sand with no grains of sand left in it.

Agreed with the others in that it is somewhat arbitrary as in the is no fixed number and it may vary with the element or molecule in question. But we usually consider it when the aggregate of atoms is relatively stable and has bulk properties of the solid. A gas or clump of atoms even of the same type likely will not behave as a solid of the same constituents.

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Radon decays with alpha particles, which are just bare helium nuclei, two neutrons and two protons

So the electrons will tend to stay with the new Po-218 atom, giving it a nice -2 charge, which will encourage it to attach itself to whatever random dust it passes by.

Once the alpha particle slows down, it will pick up some electrons from somewhere eventually too.

Sounds like something to be cautious of, but I've read that the risk is way overblown.

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Isolated metal atoms are actually very reactive compared to metal atoms bound in a bulk solid phase. It wouldn't surprise me if a lead atom would spontaneously react with gases in the atmosphere.

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You can test your furnace air filter after it has been collecting dust for a while, with a Geiger counter with the right probe.
Even if you don’t have a radon problem, you will detect a slightly higher decay count compared to background.

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Wait... But if there is a gravity a single atom in perfect vacuum will gradually lose (kinetic) energy and will "fall" on surface?

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Consider water vapour in the form of humidity. We say water is a liquid but the liquid phase can only exist if there is enough of it in vapour phase to begin to condense out.

The same is true for lead with the difference been that it requires a lot less lead in vapour phase before it starts to condense out.

I want to add that the decay products are almost always charged particles and thus interact with stuff right away, even if it just be static attraction.

A single lead atom (or ion) still moves so fast that it's going to collide with some random side of the room with almost equal probability in vacuum. If the wall has the same temperature and the atom doesn't get stuck there then it has no reason to lose kinetic energy over time, although its energy will vary randomly from each collision. In practice lead atoms tend to stick to something pretty quickly at room temperature.

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Po-218, Lead-214 and bismuth-214 are singly ionized ions. Since they are singly ionized, reactions with oxygen are not favoured, they are instead predicted to hydrolyse with hydroxyl radicals and with trace Volatile Organic Compounds (VOCs) that often contaminate air, indoor air in particular.

Also, you must consider the effects of the radiation and kinetic recoil of the ions, their velocity, c. 10-13 million mph for Po-218 ions after they emit an Alpha particles at 7% the speed of light. Lead-214 and Bismuth-214 also form in ionization trails, generated by Beta particles. As a result, chemical reactions, and thus neutralization of the ions, take place with hydroxyl radicals generated from ionized water vapour, and also, likely NO₂.

The reaction products of radon progeny grow and form ultrafine particles, 1.2 to 2 nanometres in diameter, these likely consist of 5 to 8 molecules of water and a few molecules of VOCs. These stick to dust or settle on solid surfaces, i.e. radon progeny plate out.

>The chemical and physical properties of 218Po immediately following its formation from 222Rn decay are important in determining its behavior in indoor atmospheres and play a major part in determining its potential health effects. In 88% of the decays, a singly charged, positive ion of 218Po is obtained at the end of its recoil path. > >These ions can interact with water vapor or other volatile organic compounds (VOCs) that may exist in indoor air. > >The ions can be neutralized by 3 different mechanisms, small-ion recombination, electron transfer, and electron scavenging. In typical indoor air, the ion will be rapidly neutralized by transfer of electrons from lower ionization potential gases such as NO2. > >The neutral molecule can then become incorporated in ultrafine particles formed by the radiolytic processes in the recoil path. These particles will typically be formed by the presence of the air ions produced by the passage of the emitted α-particle through ion-induced nucleation. > >In addition these energetic ions can react with water molecules to produce hydroxyl radicals. > >Thus, the decay of the radon nucleus produces a variety of effects and can result in changes in the size of the radioactive species that includes the radon progeny.

Refs.:

Castleman Jr, A.W., 1991. Consideration of the chemistry of radon progeny. Environmental science & technology, 25(4), pp.730-735.

Hopke, P., 1996. The initial atmospheric behavior of radon decay products. Journal of Radioanalytical and Nuclear Chemistry, 203(2), pp.353-375.

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The radon progeny, Bi-214 and Pb-214 do not react with oxygen, except sometimes Po-218.

They start off are singly ionized ions (Po+, Pb+, Bi+). As a result, reactions with Volatile Organic Compounds (VOCs), which commonly contaminates air, especially indoor air, is favoured over oxygen. They also react with hydroxyl radicals, ionized water vapour that's formed in the ionization trail of their recoil path (Po-218 recoils at 13 million mph, after Radon-222 emits an Alpha particle travelling at 7% the speed of light).

These reactions form minute particles, 1.2 to 2 nm in diameter, likely consisting of clusters of 5 to 8 water molecules and a few molecules of VOCs surrounding a now neutral atom of Pb or Bi.

That said, some Po-218 ions react to form Po oxide. This is shown by a double peak in measured particle size distribution of radon Po progeny particles; Po forms a double peak, smaller particles of PoOx of 0.5 - 1.5 nm and much lager particles (c. 15 nm) of a Po atom surrounded by SO2, water and VOC molecules much larger than Bi-214 and Pb-214 clusters.

Castleman Jr, A.W., 1991. Consideration of the chemistry of radon progeny. Environmental science & technology, 25(4), pp.730-735.

Hopke, P., 1996. The initial atmospheric behavior of radon decay products. Journal of Radioanalytical and Nuclear Chemistry, 203(2), pp.353-375.

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One important consideration is the fact that Lead-214 and Bismuth-214 are electrically charged, singly ionized ions. The other factor that needs to be taken into account is the fact that these reactions occur within an ionization trail that contains hydroxyl radicals and NO2 (the Alpha particles are ejected at 7-8% the speed of light, and the daughter atoms recoil at 10 to 13 million mph). And the final factor that make all this more complex that single atoms floating in nitrogen and oxygen is the fact that air isn't pure, but is often contaminated with volatile organic compounds, particularly indoor air, and SO2.

As a result Lead and bismuth oxide isn't formed. They form clusters of 5 to 8 water molecules and often a few molecules of VOCs. They were measured experimentally, and are 1.2 - 2 nanometers in diameter.

Po-218 is a little different, it can form larger clusters about 15 nm that additionally contain SO2 (if air contains a few ppm of SO2, common in urban and inner city environments), and water molecules. It can also form much smaller clusters of PoOx, 0.5 - 1 nm.

I think I've summarize what I read correctly.

Ref.:

Castleman Jr, A.W., 1991. Consideration of the chemistry of radon progeny. Environmental science & technology, 25(4), pp.730-735.

Hopke, P., 1996. The initial atmospheric behavior of radon decay products. Journal of Radioanalytical and Nuclear Chemistry, 203(2), pp.353-375.

He was correct. Lead oxide isn't formed.

There's several factors that need to be considered. The fact that the Lead-214 daughter is singly ionized so reactions with oxygen aren't favoured, that air is humid and is often contaminated with VOCs and SO2, especially indoor air, and the fact that these reactions take place within an ionization trail generated by the Alpha particle, that generates hydroxy radicals from atmospheric humidity and NO2 (the radon daughter atoms recoil at 10-13 million mph btw).

Instead, Lead-214 will most often form tiny clusters surrounded by 5 to 8 water molecules and likely often a few molecules of VOCs. They measured the size of the clusters, they average 1.2 - 2 nm in diameter. Po-218 is a little different, it forms larger 15 nm clusters additionally with SO2 (once air contains a few ppm of SO2) and as, well as much smaller clusters of PoOx 0.5 - 1 nm in diameter (the proportion of these clusters depends on what's in the air).

Castleman Jr, A.W., 1991. Consideration of the chemistry of radon progeny. Environmental science & technology, 25(4), pp.730-735.

Hopke, P., 1996. The initial atmospheric behavior of radon decay products. Journal of Radioanalytical and Nuclear Chemistry, 203(2), pp.353-375.

Lead-214 has a half life of 27 minutes, you're thinking of Lead-210.

Radon-222 -> Po-218 + Alpha (3.8 days)

Po-218 -> Pb-214 + Alpha (3.1 minutes)

Pb-214 -> Bi-214 + e^(-) (27 minutes)

Bi-214 -> Po-214 + e^(-) (19.7 minutes)

Po-218, Pb-214 and Bi-214 are the most important radon daughters, they are responsible for most of the (indirect) radiation dose from Radon-222.

Pb-214 and Bi-214 are also ions, singly ionized.

Also, the Po-214 daughter travelling at 13 million miles per hour, recoil from kicking out a Alpha particle at 8% the speed of light.

I would take source to be the largest point of entry, and point from where the radon gas diffuses out into say the basement. However, I see your point in that it's not like a heat source or lead atom generator that constantly acts like a "lead source"

From what I can see, the gas gets in via cracks/voids in the foundation so in theory you could take those points of entry as "sources"

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Yes, you're right with compelling literature. I should've looked into the actual conditions the daughter joins are formed under but I typed it at 1am. I get rilled up if I see poor reasoning and tend to go after it without consideration of context and probably should've stopped after the first paragraph.