Nuclear reactors generate power by harnessing the energy from nuclear fission. I
ID: 1615031 • Letter: N
Question
Nuclear reactors generate power by harnessing the energy from nuclear fission. In a fission reaction, uranium-235 absorbs a neutron, bringing it into a highly unstable state as uranium-236. This state almost immediately breaks apart into two smaller fragments, releasing energy. One typical reaction is 235_92 U + 1 0 n rightarrow Xe^140_54 + Sr^94_38 + 2 n^1_0, where n^1_0 on indicates a neutron. In this problem assume that all fission reactions are of this kind. In fact, many different fission reactions go on inside a reactor, but all have similar reaction energies, so it is reasonable to calculate with just one. The products of this reaction are unstable and decay shortly after fission, releasing more energy. In this problem, you will ignore the extra energy contributed by these secondary decays. You will need the following mass data: mass of U^235_92 = 235.04393 u, mass of Xe^140_54 = 139.92144 u, mass of Sr^94_38 = 93.91523 u, and mass of n^1_0 =1 008665 u What is the reaction energy Q of this reaction? Use c^2 = 931.5 Me V/u. Express your answer in millions of electron volts to three significant figures. MeV Using fission, what mass m of uranium-235 would be necessary to supply all of the energy that the United States uses in a year, roughly 1.0 times 10^19 J? Express your answer in kilograms to two significant figures.Explanation / Answer
a) Q = -(139.92144+93.91523+2*1.008665) + (235.04393 + 1.008665) {from the reaction}
= 0.1986 u [u=931.5]
= 185 MeV
b) number of reactions
= 1.0E19/(185.0E6*1.6E-19)
= 3.38E29
for one
235.04 u = 3.9E-25 kg
then
=3.38E29*3.9E-25
= 131820 kg
= 1.3E5 kg
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