Question 5.10: Develop a table that shows the macroscopic fission cross sec......
Develop a table that shows the macroscopic fission cross section Σ_f of plutonium dioxide (PuO_2) as a function of its plutonium content c using the fact that at thermal energies, the fission cross section varies with plutonium content according to the equation Σ_{f PuO_2} = N_{Pu-239} ⋅ σ_f{ Pu-239} = 0.190 ⋅ c (cm^{−1}) when the plutonium content c is measured in percent.
The results are shown in Table 5.13. Clearly this is a very interesting result because it shows that the macroscopic fission for PuO_2 is about 46% higher than the same cross section for UO_2. In other words, in a thermal water reactor, we would only need about 1/1.46 ≈ 68% as much plutonium to generate the same amount of thermal energy. This is one of the reasons Pu-239 is so highly prized as a nuclear fuel.
| TABLE 5.13 | |||
| Macroscopic Fission Cross Section for Plutonium Dioxide (PuO_2) as a Function of the Plutonium Content c | |||
| Substance | Symbol | Plutonium Content (%) | Fission Cross Section Σ_f (cm^{−1}) |
| Plutonium dioxide | PuO_2 | 2.5 | 0.475 |
| Plutonium dioxide | PuO_2 | 5.0 | 0.950 |
| Plutonium dioxide | PuO_2 | 7.5 | 1.425 |
| Plutonium dioxide | PuO_2 | 10.0 | 1.900 |
| Plutonium dioxide | PuO_2 | 12.5 | 2.375 |
| Plutonium dioxide | PuO_2 | 15.0 | 2.850 |
| Plutonium dioxide | PuO_2 | 17.5 | 3.325 |
| Plutonium dioxide | PuO_2 | 20.0 | 3.800 |
| Plutonium dioxide | PuO_2 | 22.5 | 4.275 |
| Plutonium dioxide | PuO_2 | 25.0 | 4.750 |
| Assumes only thermal neutrons cause the plutonium to fission. | |||