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?

1 Answer
Jul 12, 2016

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.