# Get a half-life. (Hands-on Activity and Math Skills).

A radioactive element is an element with an unstable nucleus that decays over time. And half-life is the time it takes for a radioactive substance to lose half its radioactivity. Uranium has a half-life of 4.5 billion years--meaning if you looked at a chunk of the element today, 4.5 billion years later, half of it would be gone. Here are two activities to help you better visualize the concept of radioactive decay and half-life.

Activity 1

You Need:

1,000 pennies * container large enough to hold the pennies * graph paper * pencil * ruler

To Do:

1. Find a large, flat surface, such as a large table or floor.

2. Randomly toss the pennies onto the surface.

3. Remove all pennies that land tail-side up--representing decayed atoms--and place them in a pile away from your work surface.

4. Collect all the remaining pennies and toss again. Remove the decayed atoms and place in a second pile.

5. Repeat the experiment until all the pennies have been removed; start a new pile after each toss.

6. Construct a data table. Count up each pile of pennies to record the number of decayed and undecayed atoms for each half-life.

7. Use your data to create a line graph. On the x-axis, plot the number of half-lives, and on the y-axis, undecayed atoms.

Conclusion:

The chance that any penny will come up tails is always 50 percent.

Approximately half the pennies remain after the first toss, about 1/4 after the second, and then 1/8, 1/16, etc. When a quantity decreases by a fixed fraction--here 1/2--it's known as exponential decay. The time it takes for 1/2 the pennies to be removed is called the half-life. This is analogous to the time it takes for a radioactive substance to lose half its radioactivity.

Activity 2

1. Gold-198 has a half-life of 2.69 days. If you start with 200 grams, how much remains after 10.76 days?

2. Iodine-131 has a half-life of 8.1 days. There are 5 grams left after 32.4 days. How many grams were there to begin with?

3. If a 100-gram sample of nitrogen-16 decays to 12.5 grams in 21.39 seconds, what is its half-life?