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kirstlen
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Homework Statement
The activity (decays per second) of a certain radionuclide is observed to decrease by 87.5% in 30 hours.
What is the half-life of the radionuclide?
Homework Equations
(1) A(t) = A[itex]_{0}[/itex]e[itex]^{-λt}[/itex]
(2) T(1/2) = 0.693/λ
The Attempt at a Solution
I'm just stuck on which approach to use, do I need to use the above equations or would I simply be able to cross-multiply and divide like this:
[itex]\frac{0.875}{30 hrs}[/itex] = [itex]\frac{0.50}{?}[/itex] in which I find the half life to be 17.14 hours.
With the other approach I used equation 1 and solved for λ using a hypothetical A[itex]_{0}[/itex] value of 100 so that A(t)=12.5 and found λ to be 0.0693 with t=30 hrs. Then I used the second equation to obtain T(1/2)=9.998 hours.
I'm just not sure which is the correct approach.