Science, Maths & Technology

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The science of nuclear energy

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# 2.3.1 Half-life

Figure 13

When quantifying the risk posed by a particular isotope, it’s important to consider the amount of time that it will remain radioactive and its activity during this time. Both of these quantities relate to the half-life of the isotope.

Last week, we defined activity as a measure of the number of particles (alpha, beta or gamma) that are emitted in a given time. As the particles are emitted, the isotope is said to decay and changes into an isotope of another element.

Let’s consider the alpha emission that you looked at last week:

emits an α particle and decays to .

If there are a certain number of uranium-238 atoms in a particular sample, the half-life is the time taken for half of these radioactive atoms to decay. After another half-life, half of the remaining atoms will decay and so on.

Imagine you were given 1200 atoms of uranium (in reality it would be a much larger number). After one half-life, half the uranium atoms will have decayed into thorium, so you will only have 600 uranium atoms left. After another half-life, another half will have decayed so you will have 300 uranium atoms, after another half-life you will have 150 uranium atoms. After four half-lives you would be left with 75 atoms of uranium and 1125 atoms of thorium.

Now, in fact, the half-life of uranium is 4.5 billion years so you would have to watch your atoms for a long time to see them decay! Half-lives can vary from billions of years to nanoseconds. Some half-lives are shown in Figure 14.

Figure 14 The main decay chain for uranium-238; other radioisotopes similarly have their own characteristic decay chains

If an isotope has a short half-life, it will decay quickly, and emit more particles in a given time than an isotope with a longer half-life. So isotopes with shorter half-lives have higher activity than those with longer half-lives. The activity of all isotopes will diminish over time as the number of atoms that are present decay away. It is worth noting that, unlike chemical reactions, the rate at which radioactive isotopes decay at any particular moment cannot be changed; heating them, subjecting them to high or low pressures, or to any other physical process, does not alter the half-life.

Both the high rates of decay, or activities, of radioisotopes with short half-lives and the longer life span of those with long half-lives have an impact on the disposal of radioactive waste. Some products of fission have half-lives of the order of hours or days, while others have half-lives of thousands of years or more. This requires both short- and very long-term planning when considering what to do with the waste.

Next, you’ll look in more detail at the different sorts of radioactive waste produced.