Exponential Decay as a Recurring Theme in Physics
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Exponential Decay Using Twizzlers
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Objectives: The learner will
- Identify an exponential decay curve
- Find half-life and lifetime of an exponential decay
- Given data or a graph, generate the equation of the exponential decay curve
- Create a general model for all observed exponential decay phenomena
The following modules may be used at the instructor�s discretion. Module 1 is the introductory module.
Module 1: Introduction � Twizzler Half Life
Materials: 2 twizzlers per lab group, graph paper
Procedure:
- Have students prepare axes on the graph paper. The horizontal axis should be marked in half-lives (0-10) and the vertical axis labeled �Length of Twizzler.� (Note: the vertical axis should be long enough to accommodate the length of a single Twizzler.)
- Given 2 Twizzlers, the students place one of them on the vertical axis with one end touching the horizontal axis.
- The second Twizzler is cut in half. One of the halves is placed vertically on the graph over the 1-half-life mark.
- Cut the remaining piece in half. Put one of the halves vertically over the 2-half-life mark.
- Repeat until the Twizzlers are effectively uncuttable. (Is this a fundamental Twizzler Particle?)
- Mark the top of each Twizzler; connect the marks with a smooth curve. (Deduct at least 90% of credit for dot-to-dot graphing.)
Questions:
- How does the Twizzler length change as time (in half-lives) increases?
- How does the rate of decrease in Twizzler length change as time increases?
- What is the significance of a single half-life in terms of Twizzler length? 2 half-lives? 3 half-lives?
- Does the choice of starting point affect your answers to question 3?
- The curve you drew is an exponential decay curve. List the important characteristics of such a curve.
- If you had a 100-gram sample of a material the mass of which decayed in the manner of your Twizzlers, how much of it would you have after 1 half-life? 2 half lives? 3 half lives?
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