Lesson 2: A Scissor Cut: Snipping away at the Decay Process
Objective
To show how the decay process works. To identify the constant of atoms in the decay process. To graph exponential curves.
Materials
Pencil, paper, 1″ X 8″ paper strips, color crayons, scissors, graphing calculator or a computer with a graphing program.
Procedure
- 1. Take one strip of paper and fold it in half.
- 2. Unfold the strip. The left side represents the parent atoms and the right side
- represents the daughter atoms.
- 3. Color the daughter atoms (the right side) only.
- 4. Cut the fold so you have two separate pieces, a parent and a daughter.
- 5. Label the daughter ½ and set it aside. This is the first generation (Do not further cut
- the daughter strip)
- 6. Repeat steps 1-4 using the remaining parent atom. (Do not use a new strip.)
- 7. This time label the daughter strip ¼, and set it aside. This is the second generation.
- 8. Continue to repeat steps 1-4 using only the remaining parent atoms until you have six
- generations. (Six cuttings). Place all the daughter atoms in a row.
Complete the following exercises:
- 1. After the 3 rd cutting (half-life), how much of the parent strip is left? How much
- daughter atoms are now present?
- 2. After the 4 th cutting (half-life), what do you observe about the original length (total
- amount of parent atoms). How much of the parent atoms are left? What fraction of
- daughter atoms is now created?
- 3. If the progression continues, what can you predict about the subsequent white strips?
- Color strips?
- 4. Did you ever run out of the white (parent) strips? Explain your answer.
- 5. What type of functions should be used to show this relationship between parent and
- daughter atoms as the parent atoms decays and the daughter atoms grow? Graph the
- curves.
- 6. Draw a graph showing both functions as they occur. Use different colors to denote
- decay and growth. Color the asymptote green. What is the quantity of daughter
- atoms? after the 3 rd half-life? 4 th half-life? 5 th half-life? Show your work. Give the
- answer in fractional form. How much of the parent atoms remain after each
- problem above?
- 7. What is the sum-total of both parent and daughter in each case above?
- 8. This number is known by what mathematical term?
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