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
It doesn’t work that way for the same reason two half-lives are not a “full life”.
A “quarter life” would be about 0.415 half lives. An exact calculation needs the exponential function, but we can check things in small steps to verify: After some unknown time t, 0.1% will have decayed so 99.9% = 0.999 are left. After 2 t, 0.999^2 are left and so on. 0.999^288 = 0.7496 so 288 time steps are around the time a quarter has decayed. 0.999^693 = 0.4999 so that’s around the time half of it has decayed. 288/693 = 0.416
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