Question

A sample of U-238 initially contained `1.3x10^18` atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today?

Answer 1

`N(t) =1.5xx10^17`

Explanation:

We can find the number of atoms remaining from an original sample using the half-life formula:

`N(t) = N(0) (1/2)^(t/t_(1//2))`

where
`t_(1//2)` is the half-life of U-238 which is `4.468xx10^9` years (`4.468` billion years) and `N(0)` is the original number of atoms in the sample

Plugging in our numbers we get:

`N(t) = 1.3 xx 10^18 (1/2)^((13.8 xx 10^9)/(4.468xx10^9))=1.5xx10^17`

Checking to see if this makes sense, we are left with about `12%` of the original sample and our time was approximately `3` half-lives. Exactly 3 half-lives would be:

`1/2*1/2*1/2 = 1/8 = 0.125 = 12.5%`

Therefore our answer does make sense.