diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index d69ceca3..c046d44f 100755 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -6,7 +6,7 @@ { "id": "26fa757f3b505503", "type": "tabs", - "dimension": 46.035242290748904, + "dimension": 43.245227606461086, "children": [ { "id": "7220717c2848cdda", @@ -25,7 +25,7 @@ { "id": "f2710f80feb0fcd8", "type": "tabs", - "dimension": 53.964757709251096, + "dimension": 56.75477239353891, "children": [ { "id": "f2f0bf554b1c0989", diff --git a/300s School/302. NUCE 2100 - Fundamentals of Nuclear Engineering/2024-09-03 Homework 1.md b/300s School/302. NUCE 2100 - Fundamentals of Nuclear Engineering/2024-09-03 Homework 1.md index 6d0e8b0a..f6a4bb28 100644 --- a/300s School/302. NUCE 2100 - Fundamentals of Nuclear Engineering/2024-09-03 Homework 1.md +++ b/300s School/302. NUCE 2100 - Fundamentals of Nuclear Engineering/2024-09-03 Homework 1.md @@ -50,16 +50,21 @@ $\left(8.98755 \times 10^{13} \text{ J } \right) \times \frac{1 \text{ kg }}{3 \ *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:** - - - - - - -