Question 3.6: Assume that a Uranium-239 nucleus absorbs a passing low-spee......
Assume that a Uranium-239 nucleus absorbs a passing low-speed neutron. How much kinetic energy must the incoming neutron have to cause the nucleus to split apart? Approximately how fast must the neutron be traveling?
According to Table 3.6, the neutron must have a kinetic energy of 5.5 − 4.9 = 0.6 MeV. In a reactor, the velocity v of a neutron (in meters per second) is related to its kinetic energy E (in MeV) by the equation v = 1.383 × 10^7 E^{ 1/2}, which was first introduced to the reader in Chapter 2. Hence, if the neutron has a kinetic energy of 0.6 MeV, it must have a velocity greater than 1.07 × 10^7 m/s to cause a Uranium-239 nucleus to split apart. Another nucleus, such as the Uranium-234 nucleus, will have an entirely different set of properties than the Uranium-239 nucleus does.
| TABLE 3.6 | |||
| Critical Energies Required for the Nucleus of a Heavy Atom to Deform Enough to Split Apart | |||
| Fissioning Nucleus | Compound Nucleus |
Critical Energy, E_{CRIT} (in MeV) |
Binding Energy of the Least Tightly Bound Neutron** |
| Th-232 | No | 5.9 | ** |
| Th-233 | Yes | 6.5 | 5.1 |
| U-233 | No | 5.5 | ** |
| U-234 | Yes | 4.6 | 6.6 |
| U-235 | No | 5.75 | ** |
| U-236 | Yes | 5.3 | 6.4 |
| U-238 | No | 5.85 | ** |
| U-239 | Yes | 5.5 | 4.9 |
| Pu-239 | No | 5.5 | ** |
| Pu-240 | Yes | 4.0 | 6.4 |
Source: Lamarsh, J.R. Introduction to Nuclear Reactor Theory, second printing, Addison-Wesley Publishing Company, Inc., Reading, MA, 1972.
Note: The critical energies of fission and the binding energies are given in MeV.