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. 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.