# Q & A: why radioactive half-lives?

Q:
hi I wonder why do we calculate half life of radioactive elemnts and not their full life? thankx
- Muneeba Gul (age 17)
Kohat Pakistan
A:

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)