Why exactly do radioactive elements decay in half every set amount of time? What is happening on an atomic scale?
In: Physics
Imagine you start with a million coins. You flip all of them, and only keep the ones that came up ‘heads’. Then you flip again, and so on. After one flip, you’ll have about half of your original coins remaining. After another, you halve the number of coins again, etc. until there are zero coins left.
Now let’s repeat the experiment but let’s use loaded coins instead of regular ones. These coins come up heads an average of 99 every 100 times. Starting with a million of these coins, it will take a lot longer to get to 0.5 million: about 69 flips. But guess what: it will take another 69 flips to halve that number again and get to 0.25 million. And another 69 to get to 0.125 million, and so on. So even though the probabilities are no longer 50:50, there is still a set (average) time that it takes for the number of remaining coins to be reduced by half. This “coin half-life” is a convenient way to describe the speed of the coin discarding process. However, note that we could equally use the probability of heads or tails (0.99 or 0.01) to convey the same information. One determines the other: if you know the probabilities, you can work out the half-life, and vice versa.
It is worth emphasizing that these are all averages. It will not take exactly 69 flips to have 0.5 million coins left, every time you run this experiment. It is, after all, random. But if you repeat the experiment many times, the average number of flips required will be 69.
Radioactive decay is just like a biased coin toss. In any given period of time (say, a nanosecond), each nucleus of your radioactive material (say, Uranium-235) has some fixed probability of decaying. It is useful to know the speed of decay of different elements, and you could use probabilities for this. However, note that unlike the coin tosses in my example, the universe doesn’t run in discrete time steps*. So if you want to quantify the probability that an atom will decay, you need to specify the time window that you’re talking about (e.g. “each second, a rubsebium-331 atom has a 0.001 probability of decaying”). So now you have to use two numbers to describe the speed of decay: a time window and a probability. Whereas, using the half-life, you can convey the same information using just a single number: the time it takes (on average) for 50% of atoms in a given sample of your material to decay.** It’s also arguably a more easily interpretable format, if you want to get an idea of how quickly something decays. If you tell me the half life of an element, it’s reasonably easy to get a feel for how long it will take before most of a sample of this stuff will be decayed away. Whereas, if you told me the “nanoseconddecayprobability” of that same element, I’d be hard-pressed to convert that to a similar intuition.
(*Actually, there are some theories that speculate time might be discrete, but this isn’t certain, and in any case we don’t treat or experience time that way.)
(**To be fair, this is sort of cheating because there is actually another number involved, namely 50%. It’s just that this second number has been agreed upon beforehand, so you don’t need to say it every time. But we could equally have decided on a standard time window to report decay-probabilities instead, e.g. “the nanoseconddecayprobability of rubsebium-331 is 0.001”.)
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