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Licorice Half-Life

This activity will demonstrate the concepts of radioactive decay. Radioactive decay is the process by which the nucleus of an atom sheds excess neutrons, protons, or electrons usually while emitting ionizing radiation in the form of alpha, beta, or gamma waves or particles. This activity will show how fast these atoms can decay along with teaching the mathematical concept of graphing and exponential decay

Materials:

You may find it helpful to repeat this activity using another material or another color of licorice type candy and a time interval of 20 seconds. Then, compare the resulting graphs.

INTRODUCTION

Radiation is everywhere. Our bodies and the world around us are radioactive and have been since the beginning of the planet. Radiation is natural and normal. Each day, there is nearly constant radiation hitting our bodies from the sun and outer space. Radioactivity is also in the ground, the air, the buildings we live in, the food we eat, the water we drink, and the products we use.

Radioactive decay is a stochastic (i.e. random) process meaning that if we only had one atom it would be impossible to predict when it would decay. However, as scientists we have measured more than one atom and have found the chance that a given atom will decay is constant over time. With a large sample of atoms we can calculate exactly when the radioactive decay will occur by measuring the half-life.

The half-life of any given element is the time that is required for one half of the sample to decay. If you have 10 grams (g) of a radioactive element to start with, after one half-life there will be 5 g of the radioactive element left. After another half-life, there will be 2.5 g of the original element left. After another half-life, 1.25 g will be left.

Some atoms have very short half-lives – like beryllium-14 which is half gone in only 5 seconds. Other atoms have a longer half-life, such as the radioactive decay of carbon-14 which is 5,730 years. Tellurium-128 has a half-life of 2.2 x 1,024 years!

In this activity, students will graph the exponential decay by constantly halving a piece of licorice at equal time intervals. This is symbolic of the decay of atoms by radiation, which is measured in half-life. From the potassium in bananas to the americium in nuclear waste, all unstable atoms have a half-life.

USE DIRECTIONS HANDOUT

(During the activity teachers should note for students that the decayed material is still present, just not radioactive. It did not disappear.)


STUDENT DIRECTIONS

Start with one piece of licorice* to place onto the graph paper. Stretch the full length of the licorice vertically over the time “zero” mark. Make a mark at the top of the licorice. This represents your 100% maximum radiation.

Your teacher will call out “GO” or “HALF-LIFE” at 10 second intervals up to 90 seconds. When your teacher says “GO” or “HALF-LIFE” you will have ten seconds to remove one-half of your licorice and set it aside. Place the remaining piece of licorice on the 10 seconds line and mark its current height. At 20 seconds, you should again remove half of the licorice and set it aside, then mark the height of the remaining portion on your graph at the 20 second line. Repeat this process until 90 seconds have gone by.

Plot the values in your data table on graph paper according to the teacher’s directions. The time should be plotted on the x-axis and the % percent of licorice remaining on the y-axis.

Now, connect all the height marks with a “best fit” line, completing a graph of the “Half-Life of Licorice.”

 *YOU SHOULD KNOW: The original strip of licorice represents radioactive material; the portion which is “set aside” during the activity represents the material that has “decayed” and is no longer radioactive.

 


  EVALUATION:

1. Did the licorice ever completely disappear or did it just get so small that you couldn’t divide it into halves?

2. If the entire earth were divided in half, and then in half again – over and over – like the piece of licorice, for as long as you could, what would be the smallest piece you would end up with?

3a. If you had started with twice as long a piece of licorice, would it have made any difference in the graph line you would have obtained?

3b.To try this, move back to a time (-10 seconds) and imagine how tall the licorice would have been.  What really changes when you use a longer piece of licorice?

4. Let’s go the other direction. Let us suppose the tiny bit of licorice at 90 seconds was your starting place. Then, suppose you would double it in size every 10 seconds as you moved left on your graph towards “0” seconds. At “0”, of course, you would have reached the size of one piece of licorice. However, what would be the size of the piece of licorice at MINUS (-) 40 seconds?

5. Using the same method as in questions 3 and 4, continue doubling your licorice until you would reach MINUS (-) 100 seconds. How large a piece would you have then?

6. Believe it or not, by the time you’ve reached MINUS (-) 1,000 seconds, the licorice would outweigh the earth! So, if you took, instead of the long piece of licorice your teacher gave you, a piece of licorice that was long enough to be rolled into a ball as big as the earth, at what point would you have “set aside” so much — and then eaten it — that you couldn’t nibble it in half anymore? Try putting your answer into minutes.

7. Does it really matter how large a sample you start with for this graph? WHY or WHY NOT?

8. Describe how the graph would be different if you took another piece of licorice exactly the same size as the first piece, but you divided it in half and marked it on the graph every 30 seconds instead of every 10 seconds?

 

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