SOLUTION: My daughter missed this class friday and has a final monday morning..can you please show how to get answer and correct answer? A 20g sample of a radioactive substance has a half l

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Question 177442: My daughter missed this class friday and has a final monday morning..can you please show how to get answer and correct answer? A 20g sample of a radioactive substance has a half life of 28 days.
a. how much of the sample is left after one year?
b. how many days will it take for the sample to reach 1 gram?
Thank you for your help!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
My daughter missed this class friday and has a final monday morning..can you please show how to get answer and correct answer? A 20g sample of a radioactive substance has a half life of 28 days.
a. how much of the sample is left after one year?
A(t) = Ao(1/2)^(t/n) where n is the half-life
A(365) = 20(1/2)^(365/28)
A(365) = 20(1/2)^(13.036)
A(365) = 20*0.0001191
A(365) = 0.00238 grams
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Let me know if you cannot follow the logic of this solution.
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b. how many days will it take for the sample to reach 1 gram?
1 = 20(1/2)^(t/28)
1/20 = (1/2)^(t/28)
Take the log of both sides to get:
(t/28)log(1/2) = log(1/20)
t/28 = log(1/20)/log(1/2)
t/28 = 4.3219..
t = 28*4.3219 = 121.013 days
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Cheers,
Stan H.