# An isotope of lead, 201Pb, has a half-life of 8.4 hours. How many hours ago was there 40% more of the substance?

##### 1 Answer

#### Explanation:

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:

where

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.