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
This is the difference between “linear decay” and “exponential decay”.
With linear decay, things work sort of like you’d expect. So you’ll lose a certain number of atoms per second. So if we have 500k atoms after 8 seconds, we’re losing 62,500 atoms per second. After 4 seconds we will indeed have 750k atoms. But this only really happens if we’re doing something like pouring atoms away. In this situation, after 16 seconds we’ll have nothing left at all.
Half life is exponential decay. We can’t model this in the same way. Instead after half the time we have √½ times as many atoms.
So if the half life is 8 second, initially we have 1000k atoms, and after 4 seconds we have √½ = 0.7071 times as many, or 707.1k atoms. After another 4 seconds we multiply again by 0.7071 and have 500k atoms as you expect.
The actual calculation for atoms remaining after a time is not really all that easily explained to a 5 year old, but I’ll put it here anyway, for time t,
Number of atoms remaining = Starting number of atoms *x* (0.5)^(t/half_life)
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