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.obsidian/workspace.json vendored
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300s School/302. NUCE 2100 - Fundamentals of Nuclear Engineering/2024-09-03 Homework 1.md
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*a. To what nucleus does $^3\text{H}$ decay?*
[Helium-3](https://people.physics.anu.edu.au/~ecs103/chart/)
*b. What is the mass in grams of 1 mCi of tritium?*
$1 \text{ mCi } \times \left( 3.7\times 10^{10} \frac{\text{decay}}{\text{s}}\right)$
First, we need to find the decay constant of tritium:
$\lambda = \frac{0.693 \text{ decay}}{12.26 \text{ years}} = 1.79241 \times 10^{-9} \frac{\text{decay}}{\text{s}}$
And we also know that one millicurie is:
$1 \text{ mCi} = 3.7 \times 10^{10} \frac{\text{decay}}{\text{s}}$
Therefore we find multiple of the decay constant we need:
$$\text{Ratio} = \frac{1 \text{ mCi}}{\lambda} = \frac{3.7 \times 10^{10} \frac{\text{decay}}{\text{s}}}{1.79241 \times 10^{-9} \frac{\text{decay}}{\text{s}}} = 2.06426 \times 10^{19}$$
Then we know we need this many atoms to decay (on average) at the mean activity. We now can convert to grams:
$$\left(2.06426 \times 10^{19}\right) \times \frac{1 \text{ mol }^3H}{0.6022045 \times 10^{24} \text{atoms}} \times \frac{3.01605 \text{ g}}{1 \text{ mol } ^3H} = 1.03385 \times 10^{-4} \text{ g}$$
**8. Approximately what mass of $^{90}\text{Sr}$ (T-1/2 = 28.8 years) has the same activity as 1g of $^{60}\text{Co}$ (T-1/2 = 5.26 years)?**
First let's find the number of cobalt atoms:
$$1 \text{g} \times \frac{1 \text{ mol } ^{60}\text{Co}}{59.934 \text{ g}} = 1.66850 \times 10^{-2} \text{ mol } ^{60}\text{Co}$$
Now we can find how much more strontium we need:
$$\frac{28.8 \text{ years}}{5.26 \text{ years}} = 5.47528$$
Finally we multiply this number by the moles of cobalt, and convert back to mass for strontium-90:
$$5.47528 \times \frac{1.66850 \times 10^{-2} \text{ mol } ^{60}\text{Co}}{}$$
**9. Using the chart of the nuclides, complete the following reactions. If a daughter nucleus is radioactive, indicate the complete decay chain:**