What causes a radioactive particle to decay? We’ll never really know, but our best guess lies in probability. In this lesson, we are going to focus on the half-life, a way of measuring the probability that a particle will react.

## Introduction

Imagine you’re getting settled in to watch the new action film at your local theater. You have a big tub of popcorn on your lap, and you’re sitting back and watching as the previews begin. About 15 minutes later, the previews finish up and you notice half of your popcorn is gone! It must have been good. The movie starts and you slow down your eating a little, but 15 minutes after the movie has started, you have eaten half of what you had left and are down to a quarter of your popcorn.

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This continues for the rest of the movie until all of your popcorn is gone.

If we were to graph your popcorn eating during the movie, it may look something like this. You may notice a few things about this graph. First, your popcorn eating did not happen at a steady pace.

If that were the case, it would look more like a straight line. What it shows is that you ate faster at the beginning than at the end, because more popcorn is consumed in the first 15 minutes than in the second 15 minutes. The second thing you may notice is that every 15 minutes you eat half of what you had.

## Scaling Up

In nuclear reactions, most likely instead of starting out with 16 atoms or even 100 atoms, you would be measuring the amount you have in grams (or some other mass unit). The same rules still apply: If I start out with 20 grams of carbon-14 and wait about 5,730 years (the half-life of carbon-14), around 10 grams will remain and 10 grams will have been converted into nitrogen-14 (that’s the product of a carbon-14 atom that underwent beta decay).

This is how carbon dating works, and it’s used to determine how old an artifact is. Scientists measure how much carbon-14 is left in a sample, and they are able to estimate how many half-lives it went through. This will allow them to get an approximate idea of how old the material is.

## Lesson Summary

You are surrounded by radioactive isotopes. However, many don’t pose much of a threat because they have such long half-lives. The half-life of a radioactive isotope is the time it takes for half of the sample to react, or decay. This time can range anywhere from a portion of a second to thousands of years depending on the identity of the starting isotope.

## Learning Outcomes

After watching this lesson, you should be able to:

• Define half-life
• Describe how half-life graphs typically look
• Calculate the half-life decay of substances