If we start with 60 atoms of uranium-238 how many would remain after 4,470,000,000 years?

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Answer 1 · 2018-03-21T18:02:43

A general equation for the amount of a radioactive substance as a function time is:

#A(t) = A(0)(1/2)^(t/t_(1/2))#

Where #A(0)# is the initial amount of the substance and #t_(1/2)# is the half-life of the substance.

We are given #A(0) = 60 " atoms"# and #t = 4.47xx10^9" yrs"#

Please observe that #t = 4.47xx10^9" yrs"# is approximately equal to the published half-life of Uranium 238, therefore, #t/t_(1/2)=1#

#A(4.47xx10^9" yrs") = (60" atoms")(1/2)^1#

#A(4.47xx10^9" yrs") = 30" atoms"#