Question about half life

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Question about half life

Postby Vellyr » Sun Apr 03, 2011 10:43 am UTC

This is going to sound really dumb to those of you who are familiar with the topic, but I don't understand how things can have half lives of thousands of years. I think that maybe my idea of what radioactivity actually is might be flawed.

By my current logic, if something is giving off alpha or beta particles it's radioactive, and those particles are the radioactivity. So if a chunk of say, plutonium-239 is shooting out alpha particles, each time it shoots out a particle, it comes closer to becoming a stable element. So my question is, how can that chunk of plutonium still be over half plutonium and still be very radioactive after it's been shooting out particles for 4000 years? Like if I have two Pu atoms, are they not radioactive until thousands of years pass and one decays? Basically it seems like long-lived isotopes would have to decay slower and therefore emit less ionizing radiation per unit time than fast-decaying species like tritium, otherwise they would run out of particles to emit since they only have a few dozen more nucleons.

But people seem to treat them as just as dangerous as anything else radioactive, so why is this? How do they sustain their radioactivity for so long?

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Re: Question about half life

Postby Roĝer » Sun Apr 03, 2011 10:57 am UTC

Just as you guessed, an isotope with a very long half-life will be less radioactive per unit of time. But that still may be in some way dangerous, so in practice long-lived radioisotopes are a bigger problem.
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Re: Question about half life

Postby firechicago » Sun Apr 03, 2011 12:27 pm UTC

You're right that long-lived isotopes give off proportionately less radiation, but they still give off plenty of radiation to give you radiation sickness if you spend too much time around them. And they can be especially nasty if they are swallowed or breathed in. If the radioactive material makes it into your body then it only takes vanishingly tiny amounts to make you very very ill.

And the real tricky question is how to store this stuff. If you've got an isotope with a half-life of one year, all you need to do is lock it up in a lead box for a couple decades. And after ten years it will be giving out less radiation an equal amount of an isotope with a half life of 1,000 years. Lots of human institutions are capable of keeping track of something important for a few decades. But what if that lead box needs to be kept closed for not 30, but 30,000 years? There aren't any human institutions older than a couple thousand years.

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Re: Question about half life

Postby Zamfir » Sun Apr 03, 2011 12:46 pm UTC

You're absolutely right that materials with longer half-lives have less events per time period, for the same amount of material. That's why quantities of a radioactive material are often indicated in Becquerel. A Becquerel is one decay per second. So for materials with long-half-lives, you need more atoms to get the same amount of Bq.

In general, you see a balance in danger: short-lived isotopes are less dangerous because they disappear fast, very-long lived isotopes are less dangerous because you need a lot of material before they start to matter. The most dangerous isotopes are the ones with a half-live comparable with the time-scale you are interested in.

So minutes to hours when you are working around a reactor, days to months when you care about dose to people in the environment, years to decades when you are thinking about contaminated land that might be unusable for living or agriculture, up to centuries when it's about waste disposal. Isotopes with half-lives longer than thousands of years are often more dangerous simply as poisonous heavy metal than as radioactive material.

Plutonium is a bit of an outlier: with a half-life of 24000 years, it's not very radioactive, or particularly dangerous per gram compared to other reactor-produced isotopes. But it is produced by a different process than most isotopes in a reactor core, so there is usually much more of it.

The main isotopes to worry about are usually isotopes of Iodine and Cesium. Those do spread reasonably well, and they are chemically more likely to get fixed in human bodies. Iodine-131 has a half-life of 8 days, just long enough to be spread over larger distance but short enough to produce a lot of radioactivity per gram. Most radiation readings around Fukushima are dominated by I-131. Cs-137 has a half-life of 30 years, making it the prime worry when you are thinking about long-term health risks.

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Re: Question about half life

Postby Jakell » Mon Apr 04, 2011 5:11 am UTC

When things decay depends on the stability of the nucleus. Radioactive elements have a small chance (some not so small) of decaying at any single moment in time, so watching one or a few atoms of a radioactive substance won't get you a really good count of the half-life. Usually, you have millions or quadrillions or more of the atoms, in which case treating them with statistics is your best bet. You can real easily measure the radioactivity with a Geiger Counter and see when the radioactivity has decreased by half. The exact reasons for the nucleus undergoing radioactive decay has to do with the balance between the Strong Nuclear force, the weak nuclear force, and the electromagnetic force between all the protons and neutrons within the nucleus. Generally, the Strong force tried to keep all the nucleons together, while the positive charges on the protons tries to split the atoms apart. If you have too many or too few, the nucleus will decay through one of several methods, into eventually a stable element.

Whether or not things are radioactive depends on the chance that their nucleus will break down, wither by expelling alpha, beta, or gamma radiation (a helium nucleus, (anti) electron, or a gamma ray respectively). If you are talking about a individual atom of Uranium238 (since I'm familiar with it), it is radioactive since at any moment it could shoot out an alpha particle, and cease being uranium. The product is now more radioactive, with the chance to eject a beta particle to further the cycle. If you gave it enough time, the atom would progress through the decay chain until it hit lead206 at which time it would be stable, and no longer radioactive. This Decay Chain, which details how the elements break down into the daughter products, and at what rates. U238, for example, starts with a half-life of 4.5 billion years. It then decays into Th234 which only has a half-life of 24 days, which then decays into Pa234, which with a half-life of a minute decays into U234 with a half-life of 250,000 years. The material starts out relatively benign, but as it decays it becomes more radioactive with time. This series actually goes through a fairly long decay chain, ending finally with lead 206.
Generally, though, you have a large number of radioactive atoms, in one kilogram of U238, you have about 2.5*10^24 atoms, and an initial activity of 11 million counts per second. So, in 4.5 billion years, you would only have about half of the U238 left (so a base count of 5.5 million counts per second), but the rest would have worked it's way through the decay chain with some as different radioactive isotopes of astatine, bismuth, lead, polonium, protactinium, radium, radon, thallium, thorium, and other forms of uranium all providing their own radioactivity. All of these elements would be here, but until all the initial U238 has completely turned into Pb206, the sample will still be radioactive. In 9 billion years, only a quarter of the original U238 would remain, in 18 billion years a sixteenth would remain, ect... all while flushing the other atoms through the decay chain. You can do some sweet modeling of this, and see that the activity of our originally pure U238 sample would increase slightly in the first million years, and slowly decrease over the next hundreds of billions of years.

It's actually quite neat, in our Modern Physics lab, we take a sample of Uranium 238 in a container, and extract from it Radon Gas. By measuring the radioactivity of the sample of gas, you can see that the activity nearly triples(!!) in the first five minutes as the pure radon decays into far more radioactive substances. Soon, though, it levels off as the amount of material becoming more radioactive gets offset by the material decaying to less radioactive materials, and eventually the activity of the sample becomes indistinguishable from the background radiation as the Radon is almost completely converted into less radioactive materials. (insert joke about full-life consequences)
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