The amount of a sample remaining after t days is given by the equation mc005-1.jpg, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
Answers
Given : The amount of a sample remaining after t days is given by the equation P(t) = A(.5)^t/h . A sample contains 18% of its original amount of Radon-222
To find : Which is the best estimate for the age of the sample
Solution:
P(t) = A(.5)^t/h
A is the initial amount of the sample
h is the half-life in days
half-life of Radon-222 is about 3.8 days
=> h = 3.8
A sample contains 18% of its original amount of Radon-222
=> P(t) = (18/100)A = 0.18A
0.18A = A(.5)^(t/3.8)
=> (.5)^(t/3.8) = 0.18
=> (t/3.8) log(0.5) = log(0.18)
=> (t/3.8) (-0.301) = (-0.7447)
=> t = 9.4
9.4 Days is best estimate for the age of the Sample
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