What is the reason radioactive decay is measured in half-life’s instead of just using the elements “full-life”?

Question

Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?

In: 910

Answer 1

Try thinking of it this way:

When talking about a radioactive element, there is a X% chance that a specific atom will decay in the next minute. For all intents and purposes, this is a completely random and unpredictable event.

The half-life value is then spit out from this. For example, Let’s assume a radio-active element has a 1/6 chance of decaying in 1 minute. We can simulate this by rolling a die. If you have a large block of this element with 1,000 atoms in it, then we can roll a die 1,000 times to simulate which will decay and which wont. Every time we roll a 1, that atom decays, all other rolls, nothing happens.

After 1 minute we will have ~167 atoms that have decayed and 833 that haven’t. In the next minute we only roll the die for the 833 remaining that can still decay. After the second minute we have 694 atoms left. After the 3rd minute: 579, and after the 4th: 482. This means the half-life is somewhere around 4 minutes. Because we have fewer original atoms at the end of each minute fewer atoms will decay. If you graph the values it will look like a curve getting ever smaller, but not quite hitting zero.

Since we are only rolling the die again for the atoms remaining and each one has a chance of decaying or not, we will continue to get smaller and smaller numbers. In the above example with 1,000 atoms it would actually take about 43 minutes before we likely didn’t have any of the original atoms left. This is with a pretty quick half-life and an extremely small number of atoms. In the real world half-lives are typically longer and you will have a sample with something like 10^20+ atoms in it so there is likely to always be some of the original still there.

In theory you could calculate an elements quarter-life, tenth-life, or two-thirds-life. Half-life is just the easier to grasp and understand. Full-life isn’t really a thing since mathematically you never actually get to 0 atoms left, you just keep getting closer to it.