T=t/n
T is the half life
t is the amount of time that has passed
n is the amount of half lives that have passed
If you take a chunk of pure radioactive material and let it decay for 1 year, then find that 25% of it is has decayed they you know that only half a half life has passed so…
T=1(year)÷.5(half life’s passed)
T=2 years
To calculate uranium you have to use incredibly small number, large samples, and way to count atoms. But it’s doable, and now you can change the equation to t=n•T to find out how old something is.
Nuclear decay is a first-order reaction. Viz. The rate of the reaction is directly proportional to the amount of material. When a nucleus decays, it releases decay products and energy particles, and we can count the number of decay particles using a Geiger counter against time.
The real scientific problem here is getting a pure enough sample in the first place i.e. the amount of uranium 238, for example, in a particular sample. That has been solved by clever chemistry and isotope separation.
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