Is there something special about the halfway point? Does the decay happen at a steady pace or exponentially?
In: 910
Lets say you have 100 coins and you flip them. Every time you get a tails that coin is removed and then you repeat until you get rid of all the coins. On the first flip you would expect to remove about 50 coins. Let’s assume it was actually 50 so now there are 50 left. If you flip again you wouldn’t expect to get 50 tails because the coins don’t care what happened last, every time you flip a coin it’s 50/50 that you get heads or tails. Instead you would probably get around 25 tails and so on.
With decay you can think of it in the same way, if you observe for a second there is some probability that a given nucleus will decay and in the next second it has the same probability. Most of the time that probability is very small over a second time scale (or even a year time scale) so it’s easier to just talk about how long it takes half of the nuclei to decay. In reality a lot of the time I’m working on something to do with decay the first thing I do is turn it back into that probability because the math is just simpler.
It’s also worth noting the number of nuclei we deal with. For that original situation I proposed with only 100 coins you wouldn’t be that surprised if you get a lot more or less than 50 tails. It probably wouldn’t be 90 tails but something like 60-70 isn’t that unreasonable. When you’re talking about a radioactive decay though the number of nuclei gets to the scale of 10^23 and at that point getting to that half value is going to be really consistent. There are so many trials that your odds of getting a really unexpected result plummets to the point of being basically impossible.
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