# 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 Answer

#### Answer:

#### Explanation:

**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: