Quantum Physics

30.1 Nuclear Fission 975Applying Physics 30.1Unstable ProductsIf a heavy nucleus were to fission into just two productnuclei, they would be very unstable. Why is this?Explanation According to Figure 29.3, the ratio of thenumber of neutrons to the number of protons increaseswith Z. As a result, when a heavy nucleus splits in afission reaction to two lighter nuclei, the lighter nucleitend to have too many neutrons. This leads to instability,as the nucleus returns to the curve in Figure 29.3 bydecay processes that reduce the number of neutrons.EXAMPLE 30.1 The Fission of UraniumGoal Balance a nuclear equation to determine details of the fission fragments.Problem When 235 U is struck by a neutron, there are various possible fission fragments. Determine the number ofneutrons produced when the fission fragments are 140 Xe and 94 Sr (isotopes of xenon and strontium).Strategy This is something like balancing chemical equations: the atomic numbers and mass numbers shouldbalance on either side of the equation.SolutionWrite the equation describing the process, with anunknown number x of neutrons:The atomic numbers balance already, as they should.Write an equation relating the mass numbers:10 n 23592 U : 14054Xe 9438 Sr x(1 0 n)1 235 140 94 x : x 2Remark In this case, the number of protons balanced automatically. If that were not the case, there might be otherpossible daughter particles, such as protons or helium nuclei (also called alpha particles).Exercise 30.1Find the number of neutrons released if the two major fragments are 132 Sn and 101 Mo.AnswerThree neutronsQuick Quiz 30.1In the first atomic bomb, the energy released was equivalent to about 30 kilotonsof TNT, where a ton of TNT releases an energy of about 4.0 10 9 J. Estimate theamount of mass converted into energy in this event. (a) 1 g (b) 1 mg (c) 1 g(d) 1 kg (e) 20 kilotonsEXAMPLE 30.2GoalA Fission-Powered WorldRelate raw material to energy output.Problem (a) Calculate the total energy released if 1.00 kg of 235 U undergoes fission, taking the disintegrationenergy per event to be Q 208 MeV (a more accurate value than the estimate given previously). (b) How manykilograms of 235 U would be needed to satisfy the world’s annual energy consumption (about 4 10 20 J)?Strategy In part (a), use the concept of a mole and Avogadro’s number to obtain the total number of nuclei.Multiplying by the energy per reaction then gives the total energy released. Part (b) requires some light algebra.Solution(a) Calculate the total energy released from 1.00 kg of 235 U.Find the total number of nuclei in 1.00 kg of uranium:N 6.02 10 23 nuclei/mol235 g/mol (1.00 103 g) 2.56 10 24 nuclei