Question 7.6: Earlier in this chapter we learned that when a uranium or pl......
Earlier in this chapter we learned that when a uranium or plutonium nucleus absorbs a low-speed neutron, it does not necessarily split apart. What percentage of the time does this happen for U-233 and Pu-239? If 30 billion U-233 and Pu-239 atoms absorb a thermal neutron, how much thermal energy is
The probability of a uranium or plutonium nucleus absorbing a low-speed neutron and not splitting apart is given by σ_c/σ_a, where σ_a = σ_c + σ_f. From Table 7.4, we see that a U-233 nucleus does not fission about 8% of the time it absorbs a thermal neutron and a Pu-239 nucleus does not fission about 26% of the time. In this case, they simply emit a gamma ray to return to a stable state.
Thirty billion fissions are required to produce 1 J of thermal energy. If each of these isotopes absorbs 30 billion neutrons, the fission of U-233 will produce 0.92 × 1 = 0.92 J and the fission of Pu-239 will produce 0.74 × 1 = 0.74 J.
| TABLE 7.4 | |||||
| Probability of Fission and Capture due to the Absorption of a Thermal Neutron | |||||
| Nuclear Fuel | Capture Cross Section σ_c (barns) | Fission Cross Section σ_f (barns) | Absorption Cross Section σ_a (barns) (σ_a = σ_c + σ_f) | Probability of Fission
(σ_f/σ_a) (%) |
Probability of Radiative Capture(σ_c/σ_a) (%) |
| U-233 | 45.800 | 528.45 | 574.25 | 92 | 8 |
| U-235 | 96.685 | 585.086 | 681.77 | 86 | 14 |
| Pu-239 | 270.000 | 747.401 | 1017.41 | 74 | 26 |
| Pu-241 | 362.000 | 1012.0 | 1374.00 | 74 | 26 |
| Note: Cross sections taken from Appendix C. | |||||