Whether or not Radon is a problem is completely unrelated to this issue. Radon occurs naturally, while DU does not. We do not have Radon cannons that pollute large areas (besides, its a gas and wouldn't hang around long enough to do any harm). Radon problems are not related in any particular way to being a soldier or serving in a combat zone.
The problem with DU and other heavy metal radioactives is that they bind in body and don't just go away over time. You can't chelate them out, or flush them out or anything like that, at least not easily.
Not to belittle the Radon problem, but DU is something under our control and created by us, and foisted on our own servicemen and servicewomen and on the populace of the countryside when we have war. Sure, it is effective in taking out enemy troops and hardware, but it doesn't go away after that.
The reason you cannot just look at the halflife is because, even though it is long, it still decays regularly in the body and is of a nature to cause severe damage to cells.
Just for some little numbers, assume someone has a minute piece of DU in their body, tucked away somewhere, with a mass of, say, 1 microgram. Hmmm, pretty small, right? Well, 1 microgram of U238 consists of about 5 million billion atoms. Now, assume someone breathed in some dust that was loaded with little bits of DU, so that maybe they absorb as much as a milligram total (1000 specks like the one above). This would not be unreasonable on a battlefield, or even in a field being plowed up long after the war is over. This leads to about 5 billion billion atoms. At the decay rate listed, the half life is about 1 billion billion seconds. Doing some quick averaging, it is clear that we would get about 2 decays per second over that period. Each of these decays is able to cause damage to a cell. Not all damage will lead to a cancer, of course. So, in one year, the body is hit with about 60 million such events, and so forth every year thereafter.
So, it is not insignificant or dismissible. It only takes one cancer to cause trouble. After 10 years, that person has had 600 million chances to have something happen that might lead to a cancer. (I did the math quickly, so it might be off by a little, but it should be in the ballpark.)
And remember, each of these decays yields a particle that has at least dozens of chances to interact with various cells on its way to being absorbed, and usually it is absorbed before it can leave the body.
Now, that is not the end of it. When U238 decays, albeit on that long time scale, it also generates other radioactive materials which decay again, some of them much faster. The chain is something like this (excuse the poor column alignment):
(from
http://www.health.state.ny.us/nysdoh/radon/chain.htm)
Symbol Element Radiation Half-Life Decay Product
U-238 Uranium-238 alpha 4,460,000,000 years Th-234
Th-234 Thorium-234 beta 24.1 days Pa-234
Pa-234 Protactinium-234 beta 1.17 minutes U-234
U-234 Uranium-234 alpha 247,000 years Th-230
Th-230 Thorium-230 alpha 80,000 years Ra-226
Ra-226 Radium-226 alpha 1,602 years Rn-222
Rn-222 Radon-222 alpha 3.82 days Po-218
Po-218 Polonium-218 alpha 3.05 minutes Pb-214
Pb-214 Lead-214 beta 27 minutes Bi-214
Bi-214 Bismuth-214 beta 19.7 minutes Po-214
Po-214 Polonium-214 alpha 1 microsecond Pb-210
Pb-210 Lead-210 beta 22.3 years Bi-210
Bi-210 Bismuth-210 beta 5.01 days Po-210
Po-210 Polonium-210 alpha 138.4 days Pb-206
Pb-206 Lead-206 none stable (none)
So, you see, you not only get that nasty alpha particle, but you get a lot more over time, somce fairly quickly.
A little more about DU follows, taken from:
http://van.hep.uiuc.edu/van/qa/section/Everything_Else/Health/20040520044230.htm** Start copy
Depleted uranium is almost entirely made up of U238, which has a much longer half-life than U235, and therefore the nuclei decay much more slowly and emit much less radiation per pound of the stuff than U235. U235 spontaneously decays fast enough to be useful in making nuclear fuel for reactors or for weapons. Naturally-occurring uranium is mostly U238, with a small amount of U235 mixed in. The U235 may be separated out to make nuclear fuel, and the remaining U238 is a waste product, which is mostly useless. It is a bit less radioactive than natural uranium. It is dense, hard, and not too expensive, and so putting U238 in ammunition instead of making bullets entirely out of the much softer metal lead, sounds like a good idea if you want to make bullets that can punch through armor.
U238 decays by emitting alpha particles (two protons and two neutrons stuck together), and by spontaneous fission. Alpha particles have a very limited range through air (a few millimeters), and do not penetrate even very thin layers of most materials. Larger nuclear fragments travel with even more difficulty. Handling bullets probably isn't hazardous as long as direct contact is minimized, and as long as grinding, dust, and powder is not made which could be ingested. Current opinion from the European Union and the State Department is that the radioctivity in depleted-uranium ammunition poses a negligible health effect for soldiers using the ammunition as long as proper handling procedures are followed. (But it is an active area of debate and further reports can come out saying otherwise).
The people living around spent bullets may not be so fortunate. The uranium in a bullet may vaporize and burn when it strikes an armored vehicle, producing fine dusts of uranium and uranium compounds. These are toxic (most heavy metals are poisonous), and can be ingested. Alpha particles don't travel very far, but if the uranium is ingested into someone's body, they don't have to travel anywhere to cause their damage. It is a separate debate entirely if the residents of a country where a war is fought with depleted uranium ammunition are at an elevated health risk. Certainly the presence of depleted uranium will not make anyone any healthier.
** End copy
You can see from this that actually firing and handling is (maybe) not so dangerous, but anyone who then enters the field where it was used is at very high risk, and that includes most of the soldiers who just fired the stuff.