Radioactive Wastes

Part 1. Background Information

If a radioactive material is stored for 10 half-lives, by what factor is the radiation reduced?

Answer:

Part 2. Multiple Representations

How do you transform (Subscript[y, o])(b^t) into (Subscript[y, o])(e^(- λ t))?  In particular, how do you find the lambda value λ from b?

Answer:

How do you transform either the base b or base e representation into a base 2 representation?

Answer:

Do your calculations below, and enter your formulas for representations with bases b, e, and 2.  Name these expressions yb, ye, and y2, respectively.

[Mathematica Tips: The natural logarithm function in Mathematica is Log, while the common (base 10) logarithm is Log[x,10].  Euler's number is predefined as E, so you can express the exponential function as E^(argument) or use Mathematica's built-in function Exp.]

yb[t_] :=  ?;
ye[t_] :=  ?;
y2[t_] :=  ?;
Plot[{yb[t], ye[t], y2[t]}, {t, 0, 20},  PlotRange -> {0, 500}, 
        AxesLabel -> {"t", "y"}];

Describe milliCurie (mCi) and microCurie (μCi) in disintegrations per second.  In particular, how many dps's correspond to 500 mCi?

Answer:

Part 3. Isotope Half-Lives

Phosphorus-32 (500 mCi)
	Reference date:
	Current date:
	Elapsed time:
	Current amount:
	λ value:
	Half-life:
	Time to reduce to 1 μCi:

Do your calculations and plot in the following cell.

Iodine-125 (500 mCi)
	Reference date:
	Current date:
	Elapsed time:
	Current amount:
	λ value:
	Half-life:
	Time to reduce to 1 μCi:

Do your calculations and plot in the cell below.

Iodine-131 (500 mCi)
	Half-life:
	λ value:
	Time to reduce to 1 μCi:

Do your calculations and plot in the cell below.

Part 4. Mixed Wastes

How long does it take to reduce 500 mCi of I-131 and 50 mCi of I-125 to 1 μCi?

Answer:

How much I-131 would have the same decay time as 50 mCi of I-125?  Is this likely to occur or not?

Answer:

Part 5. Summary