Dumb question about radioactive decay.

[Ranb]

I am arguing with a guy who says that total activity of a sample of a heavy element like uranium 235 increases over time due to the shorter half life of the daughter products. How do I calculate the activity in curies at any given time to show that the total activity of the parent and daughter products in the sample goes down? Thanks.

Ranb

[Graham Jackman]

Since they have shorter half-lives, they cannot accumulate to any significant degree and will reach a steady state, where there rate of decay equals the rate of production. Any naturally occurring sample should be in steady state, unless purified. Since the rate of production depends on the rate of decay of U235, the steady state radioactivity must fall as the amount of U235 falls. This assumes there are no interactions between U235 and daughter products resulting in enhanced decay reactions.

[Ranb]

Thanks for the reply. Enhanced decay reactions is a new one for me, I will have to look that up sometime. Would these enhanced decay reactions happen in enriched U-235 reactor fuel and U-238 depleted uranium munitions?

Ranb

[ben m]

I am arguing with a guy who says that total activity of a sample of a heavy element like uranium 235 increases over time due to the shorter half life of the daughter products. How do I calculate the activity in curies at any given time to show that the total activity of the parent and daughter products in the sample goes down? Thanks.

I suspect I know what confused your correspondent. If you start with, e.g., 10^17 atoms of 238U (that's about 600 micrograms), you'll get about one 238U decay per second---the daughter is 234Th. If you were to start with 600 micrograms of 234Th, however, you'd be seeing 40 billion decays per second. In this sense, the 238U daughters are "more radioactive" than their parent, and that's probably the sort of thing your correspondent is thinking of.

The error is that 600ug of 238U doesn't actually give you 600ug of 234Th. It gives you about 1 femtogram (10^-15 g) of 234Th at any given time. 1 femtogram of 234Th has the *same* radioactivity (same decay rate) as 600ug of 238U. That's what the equilibrium demands. So, no, a pile of 238U does not decay into an equal pile of something horribly dangerous---it decays into an equal pile of its stable endpoint, (what, 208Pb?) with miniscule amounts of the horribly dangerous stuff as intermediaries.

[Graham Jackman]

Thanks for the reply. Enhanced decay reactions is a new one for me, I will have to look that up sometime. Would these enhanced decay reactions happen in enriched U-235 reactor fuel and U-238 depleted uranium munitions?

Ranb
I'm thinking more of enhanced fission reactions that occur as you approach a critical mass, but there may be other options. Certainly they can occur in enriched uranium, where the object is to induce the capture of neutrons to accelerate the decay rate. Very unlikely in depleted uranium

[DRBUZZ0]

I am arguing with a guy who says that total activity of a sample of a heavy element like uranium 235 increases over time due to the shorter half life of the daughter products. How do I calculate the activity in curies at any given time to show that the total activity of the parent and daughter products in the sample goes down? Thanks.

Ranb


Actually he is right in the short term at least. Yes, given enough time the activity will go down, but with something as short lived as uranium the daughter products contribute more to the radioactivity than the uranium itself.

The uranium ore is more radioactive than the uranium metal because it contains these daughter products such as radium-226, bismuth-214, lead-210, polonium-210, thorium-234 etc etc.. When the uranium is refined these daughters are removed and the uranium metal is concentrated. So if you have a chunk of uranium metal it will indeed slowly revert back to the higher radioactivity of the uranium-baring ore which exists in nature as the products build up in it. Once in equilibrium the proportions of the original material to daughter products are stable.

In many radioactive substances this is negligible because it happens so quickly, but uranium has a very long half life and it also has a very long decay chain which complicates things

The term for the point where the decay curve has stabilized with the daughters is called "secular equilibrium" and just about all samples from nature will be in a state of equilibrium. However, if you get thorium nitrate or uranyl acetate or something from a chemical supplier or if you have refined uranium metal it will not initially be in this state.

The time to equilibrium in uranium can also be complicated by the fact that one of the decay chain produces is radon, an inert gas which depending on the geology and other factors may be partially dispersed from the original sample before it gets a chance to decay.

You can look up the secular equilibrium for various materials like uranium.

I do not know offhand what it is for U-235, but if you want to be technical about it and include all the daughters it's probably a considerable amount of time.

With U-238 it increases in radioactivity for a couple of months as it goes into equilibrium with palladium and thorium because those are short lived but then the next step in the decay process is U-234, which has a halflife of a quarter of a million years.

I'll try to find you some more information for the whole uranium-series decay chain.

But in any case, it's not that big a concern as far as becoming "more radioactive" since it only reverts to the natural state anyway.

[DRBUZZ0]

Thanks for the reply. Enhanced decay reactions is a new one for me, I will have to look that up sometime. Would these enhanced decay reactions happen in enriched U-235 reactor fuel and U-238 depleted uranium munitions?

Ranb

All radioactive materials decay at a constant rate. Would there be any reactions in uranium? Not really. At least not if it's in a nuclear reactor or something. A chunk of natural or depleted uranium may experience the odd spontaneity fission from time to time and that may produce a neutron which is captured by another atom. Or you might have a random cosmic ray come along and produce a neutron which is captured or causes one or two fissions.

This is extremely rare. Extremely. So much so it doesn't really have any real affect on the overall decay rate. It's just a handful of atoms really.