Homework 6

Problem 1

Consider the following nuclear reaction

Using the table of nuclides, along with the mass of a neutron, compute the change in mass between reactants and products. Convert this mass to energy using $E=mc^2$. That is the fission energy in a single atom of U-235. The lecture notes states that 1 CMO requires about 2000 tons of U-235 fission. Verify this statement.

• 1 amu = 1.66054E-27 kg (the table of nuclides in the link above gives masses in amu).
• The speed of light is (google it)
• 1 CMO $\approx$ $1.6\times 10^{20}$ J (this number accounts for ~34% energy conversion efficiency)
• 1 kg = 2.20482 lbm
• 2000 lbm = 1 ton

Problem 2

On this slide of the lecture notes, the Isotope binding energy for O-16 is shown to be nearly 8 MeV. Compute this value as follows. From the table of nuclides, get the mass of O-16. Subtract this from the mass of 8 neutrons, 8 protons, and 8 electrons. Use conversions similar to those in Problem 1 to convert to energy in MeV. Note 1 MeV = 1.60218E-13 J. (An eV is an electron-volt, is the energy an electron gains in “falling” through a potential difference of one volt.) The chart lists the binding energy per nucleon, so divide your answer above by 16 to compare to the 8 MeV from the chart.

Problem 3

Describe the purpose and use of a moderator in nuclear reactors. What is the most common moderator?

Problem 4

What are the two most common types of nuclear reactors and their acronyms? What fuel do they use?

Problem 5

Using the results from problem 1 (about 2000 tons of U-235 needed per CMO of oil), and the current world electricity use 0.6 CMO per year, and the current reserves of U (natural, not U-235, so you need the fraction of U that is U-235, which is in the notes) of 5.3 million tons, how long will our uranium last if we fission all of the U-235?

Problem 6

Read (or browse) this article. The title is misleading, but the body is interesting. What’s a take-home message here?