SOLUTION: A sample of a radioactive substance decayed to 91% of its original amount after a year. (Round your answers to two decimal places.) (a) What is the half-life of the substance? (

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Question 433433: A sample of a radioactive substance decayed to 91% of its original amount after a year. (Round your answers to two decimal places.)
(a) What is the half-life of the substance?
(b) How long would it take the sample to decay to 30% of its original amount?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A sample of a radioactive substance decayed to 91% of its original amount after a year.
(Round your answers to two decimal places.)
:
The decay formula: A = Ao*2^(-t/h)
Where
A = resulting amt after t time
Ao = initial amt
h = half-life the of substance
t = time (yrs)
:
(a) What is the half-life of the substance?
Let initial amt = 1
1*2(-1/h) = .91
Using nat logs
ln(2^(-1/h)) = ln(.91)
-1%2Fh*ln(2) = ln(.91)
-1%2Fh= ln%28.91%29%2Fln%282%29
-1%2Fh = -.13606
h = -1/.13606
h = 7.35 yrs is the half-life
:
(b) How long would it take the sample to decay to 30% of its original amount?
1*2^(-t/7.35) = .3
Doing it the same way with nat logs
-t%2F7.35 = ln%28.3%29%2Fln%282%29
-t%2F7.35 = -1.737
t = -7.35 * -1.737
t = +12.77 yrs for 30% to remain