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August 7th, 2008, 02:45 PM   #1
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Half-life problem. Please help :)


Could you please help me with this problem?

"What is the half-life of a radioactive substance that has a decay rate of 25% per decade?

Hint: Remember that the Rule of 70 does not give a good approximation to half-life when the rate is larger than 15%. We must use the actual formula here."

Thanks a bunch..
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August 7th, 2008, 03:06 PM   #2
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Re: Half-life problem. Please help :)


The total amount of radioactive material remaining in a decay is always given by where K is the starting amount and is some positive constant related to the rate of decay.

If we measure t in years, then since after 10 years there will be 75% of the starting amount, we have the relationship


To work out the halflife, we need to find the value of t - call this - that corresponds to the time where the amount remaining is half the initial amount. This can be represented by the formula



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August 8th, 2008, 09:53 AM   #3
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If the half-life is t years, (3/4)^(t/10) = 1/2, so t = 10ln(1/2)/ln(3/4) = 24.1 to 3 significant figures.
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