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Q & A: why radioactive half-lives?

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Most recent answer: 09/29/2014
hi I wonder why do we calculate half life of radioactive elemnts and not their full life? thankx
- Muneeba Gul (age 17)
Kohat Pakistan

Great question. The radioactive decays are a purely random quantum process. There's no way to predict exactly when any particle will decay. You can just give the probability that it will decay in a time interval, if it hasn't already decayed. Since the particles don't change until they decay, that probability doesn't change. That means that if, for example,  on average half the particles will decay in the first year, half of the remaining particles will decay in the second year, leaving 1/4 of the original ones. Then another half decay the the next year, etc. The average fractions remaining go 1/2, 1/4, 1/8, 1/16,... but never reach zero.

For a particular sample with a finite number of particles, at some point the very last particle will decay. When that will be depends on how many particles you start with plus the random chance of when they happen to decay. The half-life doesn't depend on the starting number.

Mike W.


(published on 09/25/2014)

Follow-Up #1: radioactive full-life

But if we were to take like 1 nanogram of Tc96 and count how many days it takes to fully decay into Mo96, and repeat the experiment many times, we would come up with an average. Couldn't we use that average to say that on average Tc96 will fully decay into X days.
- Anonymous

You could do that, but you'd get a different lifetime if you started with 2 ng or 2kg, etc. The half-life is independent of sample size.

Mike W.

(published on 09/29/2014)

Follow-up on this answer.