Skittles & Half-life                                                                                Barb Lamb

Adapted from Radioactive Skittles

 

 

 

My Aunt Helen will soon undergo some medical testing that will require her to swallow a radioactive isotope to be used as a tracer.  She is nervous about having a radioactive substance in her body even though the radiologist has told her not to worry.  This isotope has a half-life of 8 minutes.  What can I tell her about the concept of a “half-life” to help her understand what will be happening to this isotope?

 

Let’s look at…..

 

Radioactive Skittles

 

                                                                                                                               

                                                                                                                                                                                                                                                To help us with this idea.

 

 

                                                Radioactive Skittle                                                              Non-radioactive Skittle

 

 

You will need:                       2 bags of Skittles,  1 paper cup,  a paper towel,  a writing utensil, and your TI-83

 

 

Procedure:

 

1.                    Count out 100 Skittles from the 2 bags (you may eat any leftovers) and placed them all in the cup.  Record the number on the table below.  Place the paper towel on your desk (you will be pouring the Skittles onto the paper towel.)

 

2.                    Cover the cup with your hand as you shake your cup and pour the Skittles out onto the paper towel.  DO NOT turn over any of the Skittles!

 

3.                    Remove all of the non-radioactive Skittles (you may eat them, they’re safe!)  Count up the remaining radioactive ones and record this number on the table and replace these back into the cup.  This is decay period #1.

 

 

4.                    Repeat step #2 and 3 until you have enough data for all five decay periods.

 

5.                    Column 3 will be used for the class data.

 

 

Table #1

 

Decay Periods

No. of Radioactive Skittles

Total class data

              0

 

 

              1

 

 

              2

 

 

              3

 

 

              4

 

 

              5

 

 

 

 

 

 

 

 

 

 

 

 

Think and answer:

 

1.             What happened to the number of radioactive Skittles as you continued to pour them out, return them to the cup and pour them out again?   Can you see any pattern?    Can you describe the pattern?

 

 

 

 

 

  1. Suppose you had 100 mg of a radioactive substance “X”.  After 15 minutes, measurements indicated that only 50 mg of the substance were still radioactive;  the other 5 mg had decayed into some other elements.  Since half of the original substance remained, we say that the “half-life” of substance “X” is 15 minutes.  This is the time it takes for ½ of the original substance to decay into something else.  Which atoms actually decay is random.  This is the concept of a “half-life”.

 

 

 

 

 

 

  1. Fill out the following table to show that you understand the concept of half-life.

 

Table 2 – Decay of Substance “X”

 

No. of half-lives

Time elapsed

Amount still radioactive

            0

                0

500 mg

            1

            15 min.

250 mg

            2

            30 min.

 

            3

 

 

            4

            60 min.

 

            5

 

 

            6

 

 

 

 

  1. How are table #1 and table #2 similar?

 

 

 

 

 

 

 

 

 

  1. Try another half-life problem.  Iodine-131 is a radioactive substance that can be used to treat certain thyroid problems.  It has a half-life of 8 days.  Your friend with a thyroid condition is given 40 mg of I-131 to drink.  Assuming that all of the I-131 stays in her body, how much will remain after 4 half-lives?  (use a table if it helps)

 

 

 

 

 

 

 

 

  1. Graphs can be used to show the decay pattern of radioactive substance also.  Using your TI-83, press   STAT  and enter the class data from table #1 into  L1(decay periods) and  L2(no. of radioactive Skittles).   Turn the STAT PLOT on and sketch the graph below.

 

 

 

 

 

  1. Repeat the calculator directions from #6 with the data from table #2 and sketch that graph here.

 

 

 

 

 

  1. How do these two graphs compare?

 

 

 

 

 

  1. Consider the two graphs;  will the amount of radioactive material ever disappear?  Explain why or why not.

 

 

 

 

 

 

  1. Leave the data from step #7 in L1 and L2.  Press   STAT    >   CALC.    What type of regression should we do in order to write an equation for this data?     Listen and follow along in order to get the correct equation.

 

 

 

 

Teacher Notes

 

    1. Remind students to be careful pouring out their Skittles.  Paper plates can be used instead of paper towels.

 

 

    1. In table #2, time elapsed goes up by 15 minute intervals;  radioactive amounts are cut in half.

 

 

    1. #6, #7 should be similar in appearance to

 

 

 

 

 

 

 

 

    1. Final equation for #10 is  y = 500 (1/2)^x