An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 40% more of the substance?
The half-life of a radioactive substance is the time in which half of any given sample of the substance undergoes radioactive decay. The mathematical basis of the phenomenon of radioactive decay is given by the half-life equation:
Now, the half-life
Using this in (1) to find
Now, in the question, we are given
The ratio of
Thus, equation (1) yields,
On taking the natural log on both sides, we get
The answer is a negative value of time because we were asked to calculate how many hours "ago" the substance was 40% more than it is now.