# S1, Ep 12: What does half-life mean again?

### Caroline Christian, Ph.D.

The **half-life of a radioactive isotope is the time it takes for 50% of the isotopes to decay (change) into other atoms.**  What is a isotope?  Check out [last weeks blog post for the answer to this question](/content/chemistry-blog/s1-ep11-how-nuclear-isotopes-are-used/index.html). This is important because half-life is one of the ways we decide how dangerous an isotope is.  For example, if you were going for a medical test where they were going to inject you with a radioactive dye, would you rather your dye have a half-life of a couple of hours, a couple of days, a couple of weeks, or a couple of years?  You would definitely want your dye to have a half-life of a couple of hours so by the time you got home, it would almost be out of your system!  The hardest thing for students to remember is what **half-life means**, **it is the time for 50% of the isotopes to decay**.  Here is a graph to help illustrate what I mean.  A graph showing the decay of isotopes - on the vertical axis is fraction  of the isotope remaining, and the horizontal axis is time.

If I were to give you a problem such as Phosphorus-32, which is used to treat leukemia, has a half-life of 14.3 days.  If we start with 5.00 grams of this radioisotope, how much will be left after 2 half-lives?

Solution: After 1 half-life there will be 50% of the sample remaining, or 2.50 grams, and after 2 half-lives, there will be 25% of the sample remaining or **1.25 grams.**

Next problem: How many days will it take for the mass of Phosphorus-32 to drop to 0.3125 grams if we start with 5.00 grams?  The half-life is still 14.3 days.

Solution: This question does look a little harder, what I would recommend is to make a table so you can keep track of it all.

To get the middle column, all I did is divide the amount by 2 each time; this is 50% of the amount that is decaying each half-life. To get the right column, all I did is add 14.3 each time - this is the half-life.  So the answer is **57.2 days**.

Last question: How many half-lives have passed after 42.9 days if you start with 5.00 grams of Phosphorus-32? The half-life is.. you guessed it, 14.3 days!

Solution: You already have this problem solved, if you view the table up above, you will see you have used **3 half-lives**.