Radioactive Wastes

Part 2: Multiple Representations

1. In the Radioactive Decay module, you represented a quantity or concentration of a radioactive material by a function of the form
   y = y₀b^t, with b < 1.
   Explain how to rewrite such a function in the form
   y = y₀e^-kt, with k > 0.
   In particular, explain how to get k from b and why k must be positive. [Hint: Write e^-kt as (e^-k)^t, and work backwards.] The coefficient k is often called the lambda value and designated by the Greek letter lambda. You may find it that way in your downloaded worksheet.
2. In Part 3 of the Radioactive Decay Module, you also represented a quantity or concentration of a radioactive material by an exponential function with base 2. Explain the connections between this representation and those with base b and base e.
3. Check your results in Steps 1 and 2 graphically: Given 500 milliCuries (mCi) of a substance with 9.5 day half-life (as in the Radioactive Decay module), write formulas in all three forms for the amount at time t. Graph all three formulas together, and verify that they represent the same function.
4. A Curie is the amount of a given nuclide that undegoes 3.7x10¹⁰ disintegrations per second (dps). What's a milliCurie? How many dps's correspond to 500 mCi?
5. What's a microCurie? In subsequent parts of this module, we will consider waste to have reached a "safe level" when it has decayed to no more than one microCurie (uCi).

---