For 1000k atoms I will have a 500k after 1 half life, and 250k after 2 half lives. But when I try to do the same with fractions something doesn’t add up. Because after “quarter life” i will have 750k atoms, but then I’ll have 562500 atoms, because of 750k multiplied by 0.75. So quarter life should be equal to 0.5 of half life, but half life doesn’t work that way. I am confused.
In: Physics
The problem here is that half-life is a non-linear decay, which means you can’t just add things up.
Imagine it like this: After a quarter-life, you have three quarters left. But if you now lose another quarter, in the next quarter-span, it is a quarter of those three quarters you started the second period with. A quarter of three quarters however is 3 / 16, which is slightly less than the quarter you lost in the first period.
The actual decay you get in a given period is always one quarter less than the decay you got in the last period.
To put it more simply: The decay you get is always depending on the amount at the start of each decay period. So it becomes less and less. For calculating the length of decay periods, this is somewhat factored in, so a half-life has a longer decay period than just double the quarter-life.
Case in point: The full-life period is not just double the half-life period. It is in fact infinitely long!
You calculate the half-life like this: T_half = 0.693 / K, where K is some speed constant of the stuff you are looking at.
Quarter life would be T_quarter = 0.287 / K.
Ignoring K, as that does not change for a given process, you can see that the relation of quarter life to half life is always 0.287 / 0.693 = 0.415, so the quarter life is always 41.5% of the half life value.
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