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Half-life
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True or false? Knowing the half-life of a radioactive isotope helps us estimate how high its activity is after a certain period of time.
This piece of metal emits radiation. It is radioactive. This means some of its atoms break down – they decay. As this happens, there will be fewer and fewer radioactive particles. How will this affect the radioactivity of the metal?
Leon can illustrate it with an experiment. First, he bakes 64 cookies and leaves them in the kitchen. He wants to see how long it will take for his cookies to get eaten. Leon can’t predict exactly when each cookie will be eaten, but he can observe how fast the cookies disappear. Leon decides to write down how many cookies are left each day.
Soon, he’s able to present his findings using a graph. On a vertical axis he marks the number of cookies, from 0 to 64. On the horizontal axis, he marks the number of days that have passed. Initially, when the freshly-baked cookies smelled wonderful, they disappeared quickly. After one day, half of them had already been eaten.
Only 32 cookies were left. It took another day for the amount left to drop to 16. The fewer cookies were left, the fewer got eaten. After 3 days, there were 8 cookies left. After 4 days — 4 cookies left.
After 5 days — 2 cookies… On the 6th day, there was only one stale cookie left… The graph shows us how the number of cookies has changed over time. We notice the number of cookies decreased by half every day. So, what do Leon’s cookies have to do with radioactivity? In Leon’s experiment, as time went by, there were fewer and fewer cookies left to be eaten. The same happens with radioactive material.
Over time, there are fewer and fewer unstable nuclei that can decay. If you plot decay on a graph, with the number of radioactive nuclei on the vertical axis, and time on the horizontal axis, the graph will look very similar to the one Leon made. The time it takes for the number of nuclei to decrease by half, is always the same for a given radioactive isotope. This period of time is known as half-life. Using a device such as a Geiger counter, you can measure the rate at which radioactive nuclei decay over time.
This is called the activity. And look! When the number of radioactive nuclei has decreased by half, there are only half as many nuclei left, that can decay. This means that the activity is halved as well, after the same amount of time. So, half-life can be defined as two things: the time needed for the number of radioactive nuclei to halve; And as the time needed for the activity of a radioactive material, to decrease by half!
Knowing the half-life of different isotopes, helps us estimate how much of the material is still radioactive. Also, how high its activity is, after a certain period of time. Let’s look at an example! This radioactive material’s initial activity is equal to 240 decays per second. We know that its half-life is 10 days.
Can you calculate how high its activity is going to be after 20 days? Well, after 10 days, the initial activity halves, so it is equal to 240 divided by 2… which is 120 decays per second! After 20 days, the activity halves again, so 120 divided by 2… The activity after 20 days is equal to 60 decays per second! Now, can you tell how many days it will take for the activity of this material to reach 15 decays per second? How many half-lives is that?