Radioactive things spit out radiation, but that decreases over time because they’re breaking down – spitting out parts of themselves – in order to do that. Half-life is how long it takes for the radiation to decrease by half. After multiple half-lifes, the object may not be totally inert but close enough, because of the effect of halving repeatedly.
100 / 2 = 50
50 / 2 = 25
25 / 2 = 12.5
12.5 / 2 = 6.25
6.25 / 2 = 3.125
3.125 / 2 = 1.5625
As you can see from the progression, 50 radiation drops to 1.6 radiation over only 5 half-times. The time progression is linear, but the change in radiation is exponential. This makes it relatively easy to date things (as in carbon dating) because the numbers are so different from one period to the next.
Related, nuclear waste with a short half-life is often left to sit for 10 half-lives, after which the radiation is so low as to be close enough to inert, and it can be disposed of normally. (following the example above, by 10 half-lives, it has gone from 50 down to 0.049).
But different isotopes have different half-lives, so while some decay quickly, others take a long long time. Generally lighter things have less stuff to spit out, and therefore shorter half-lives, than heavy things, which have more stuff to spit out.
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