A useful thought experiment: Suppose you have a whole bunch of quarters. Every hour, you flip them all, and any quarters which land tails, you take away. The next hour, whatever quarters you have left, you flip again, and so on. Every time you flip your coins, about half of them will come up tails, so you’ll lose about half of your quarters every hour. Your quarters then have a half-life of one hour.
This analogy is a bit oversimplified, of course. In a radioactive sample, the atoms are not all decaying exactly on the hour, all at the same time. For a better approximation, you could use dice instead of coins. Suppose instead that you roll a bunch of six-sided dice once every 15 minutes and 47 seconds, and any die that comes up 1, you remove. At any given roll, a particular die is less likely to “decay”, but the rolls come more often. The net result is the same: In the long run, you’ll lose about half of your dice every hour. Or suppose you use 20-sided dice, and roll them once every 4:26. Again, you’ll lose about half of them each hour, in the long run. If you take this to the extreme, you have the way that atoms behave: An atom can decay at any time at all, and there’s no way to predict when any given atom will do so, but in the long run, for every half life, about half of them will have decayed.
