SOLUTION: Solve: The half-life of a substance is the time that it takes for half of the substance to remain after natural decay. If Uranium-238 has a half-life of 4.15 billion years, how lon

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Question 107547: Solve: The half-life of a substance is the time that it takes for half of the substance to remain after natural decay. If Uranium-238 has a half-life of 4.15 billion years, how long does it take for 90% of the substance to decay?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The half-life of a substance is the time that it takes for half of the substance to remain after natural decay. If Uranium-238 has a half-life of 4.15 billion years, how long does it take for 90% of the substance to decay?
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EQUATION:
A(t) = Ao(1/2)^[t/(4.15x10^9)]
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If 90% decays A(t) = 0.10Ao
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0.1Ao = Ao(1/2)^[t/(4.15x10^9)]
0.1 = (1/2)^[t/(4.15x10^9)]
Take the log of both sides to get:
[t/(4.15x10^9)]log(1/2) = log(0.10)
[t/(4.15x10^9)] = log(0.10)/log(0.5) = 3.3219
t = 13.786...x10^9 years (number of years till 90% has decayed)
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Cheers,
Stan H.
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