Quantum Physics

974 Chapter 30 Nuclear Energy and Elementary ParticlesSequence of events ina nuclear fission process The fission of 235 U by slow (low-energy) neutrons can be represented by thesequence of events10 n 23592 U : 23692 U* : X Y neutrons [30.1]where 236 U * is an intermediate state that lasts only for about 10 12 s beforesplitting into nuclei X and Y, called fission fragments. There are many combinationsof X and Y that satisfy the requirements of conservation of energy andcharge. In the fission of uranium, about 90 different daughter nuclei can beformed. The process also results in the production of several (typically two orthree) neutrons per fission event. On the average, 2.47 neutrons are released perevent.A typical reaction of this type is10 n 23592 U : 141 9256 Ba 36 Kr 31 0 n[30.2]The fission fragments, barium and krypton, and the released neutrons have agreat deal of kinetic energy following the fission event.The breakup of the uranium nucleus can be compared to what happens to adrop of water when excess energy is added to it. All of the atoms in the drop haveenergy, but not enough to break up the drop. However, if enough energy is addedto set the drop vibrating, it will undergo elongation and compression until theamplitude of vibration becomes large enough to cause the drop to break apart. Inthe uranium nucleus, a similar process occurs (Fig. 30.1). The sequence of eventsis as follows:1. The 235 U nucleus captures a thermal (slow-moving) neutron.2. The capture results in the formation of 236 U * , and the excess energy of thisnucleus causes it to undergo violent oscillations.3. The 236 U * nucleus becomes highly elongated, and the force of repulsionbetween protons in the two halves of the dumbbell-shaped nucleus tends toincrease the distortion.4. The nucleus splits into two fragments, emitting several neutrons in the process.The energy released in a typical fission process Q can be estimated. From Figure29.4, we see that the binding energy per nucleon is about 7.2 MeV for heavy nuclei(those having a mass number of approximately 240) and about 8.2 MeV for nucleiof intermediate mass. This means that the nucleons in the fission fragments aremore tightly bound, and therefore have less mass, than the nucleons in the originalheavy nucleus. The decrease in mass per nucleon appears as released energywhen fission occurs. The amount of energy released is (8.2 7.2) MeV per nucleon.Assuming a total of 240 nucleons, we find that the energy released per fissionevent isQ 240 nucleons/(8.2 MeV/nucleon 7.2 MeV/nucleon) 240 MeVThis is a large amount of energy relative to the amount released in chemicalprocesses. For example, the energy released in the combustion of one molecule ofthe octane used in gasoline engines is about one hundred-millionth the energyreleased in a single fission event!Figure 30.1 A nuclear fissionevent as described by the liquid-dropmodel of the nucleus. (a) A slowneutron approaches a 235 U nucleus.(b) The neutron is absorbed by the235 U nucleus, changing it to 236 U*,which is a 236 U nucleus in an excitedstate. (c) The nucleus deforms andoscillates like a liquid drop. (d) Thenucleus undergoes fission, resultingin two lighter nuclei X and Y, alongwith several neutrons.236 U*235UX(a) (b) (c) (d)Y