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
David B.
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.

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