If the half life of uranium-235 is #7.04 * 10^8# y and 12.5 g of uranium-235 remain after #2.82 * 10^9# y, how much of the radioactive isotope was in the original sample?
1. Quick Method.
Examiners and text - books often give nice numbers where the answer drops out easily.
In this case you count the number of 1/2 lives
Now multiply back from 12.5 by doubling it successively 4 times:
Initial mass =
1. General Method.
If the numbers are not so nice you need to use the general equation for radioactive decay:
We can get
Taking natural logs of both side of
We can use mass in grams instead of atoms so: