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The half life for the radioactive decay of U-238 is 4.5 billion years and is ind

ID: 944326 • Letter: T

Question

The half life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. If a sample of U-238 initially contained 1.9 x 10 ^18 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today ? The half life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. If a sample of U-238 initially contained 1.9 x 10 ^18 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today ?

Explanation / Answer

For the first order kinetics

ln(Ao/At) = kt

Half life = ln2/k

k = ln2/4.5billion years^(-1)

substituting the values we get

ln(Ao/At) = ln2/4.5billion * 13.8 billion

ln(Ao/At) = 3.06667ln2

ln(Ao/At) = ln(8.378)

At = Ao/8.378 = 1.9 * 10^(18)/8.378 = 2.26 * 10^(17) atoms