Question

Radiometric dating is the workhorse of absolute dating. If you had a sample with a radioactive component with a half-life of 5000 years and an initial concentration of one part per million, how much would be present after 5000 years? After 10,000 years? After 50,000 years? When does the radioactive material completely disappear?

Answer 1

The amount left over after T years where P is initial amount is $P( \frac{1}{2})^{ \frac{t}{5000} }$
it halves each time so after t times of the 5000 years have elapsed, the amount is now (1/2)^t of the original amount

find how many half lives

10000/5000=2
(1/2)^2=1/4
1/4 of original amount after 10000 years

after 50000 years
50000/5000=10
(1/2)^10=1/1024
1/1024 of original amount after 50000 years


it dissapears when it attains an amount you deem is nigligible, so if you had 1 mol of subsutance, you might say it dissapears when it gets to 10^-23 or about 6.02 molecules