Problema Solution
An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 30% more of the substance? (Give your answer correct to 1 decimal place.)
Answer provided by our tutors
The amount A of the material present at a time t is given by the model
A = A0*(1/2)^(t/h)
where A0 is the amount present initially, h is the half life of the material.
In our case we have h = 8.4 hr and we need to find t such that A = A0 + 0.30A0 = 1.30*A0
1.30*A0 = A0*(1/2)^(t/8.4)
(1/2)^(t/8.4) = 1.30
t/8.4 = (log 1.30)/(log 1/2)
t = 8.4*(log 1.30)/(log 1/2)
by solving we find
t = -3.2 hours
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3.2 hours ago there was 30% more of the substance.