As nuclear power is once again considered as an alternative energy source, it is important to know the decay rate of all of the radioactive materials involved. In a typical Uranium-235 fission event, a U-235 nucleus absorbs a thermal neutron, producing a compound nucleus U-236 in a highly excited state. It is this nucleus, not the U-235 nucleus, that actually undergoes fission, splitting into two fragments. These fragments, between them, emit two neutrons, leaving Xe-140 and Sr-94 as fission fragments. The fragments Xe-140 and Sr-94 are both highly unstable and undergo beta decay (with the emission of an electron) until each reaches a stable end product. Find the differential equations that describe this situation. What is the half-life of this material? What are the long term environmental implications of creating all this radioactive waste?
- Derivatives of exponential function (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 131)