It takes a very long time for uranium to decay into lead. Who even lived that long to observe this? If this is not how they determine the half life, then in what method do they use to determine the half life? I think it has to do with calculations. |

As was pointed out, the formula describing decay is very well understood. As time passes, the amount of material that is left given by the formula

A=A_{0}2^{-t/h},

where A_{0} is the amount of the radioactive material that you start with.

A little bit of calculus, and we find that the number of decays you measure in a given amount of time, say in a second or a minute, is given by

decays per unit of time = A_{0} ln 2 /h 2^{-t/h}

If the half life, h, is very long, then 2^{-t/h} stays close to 1 during the length of time of the experiment, and so

decays per unit of time = A_{0} ln 2 /h

So one can measure the half life of a material just by measuring the amount of the material tha tone has, and measuring the number of decays that occur during a short amount of time.

Of course, there are practical issues in making these measurements, but as an undergraduate, I measured half lives of various radioactive materials, some of which have half-lives of millions of years.

*Edited by Chiroptera, : Removed some minus signs.*

*Edited by Chiroptera, : Forgot the base of the exponent, heh.*

*Edited by Chiroptera, : Oops. Meant to write 2 instead of e.*

*Edited by Chiroptera, : *sigh* Will I ever get this right? Serves me right for trying to mix College Algebra with Calculus.*