Solved: What is meant by the idea of a critical mass?

Problem 1E Do today’s nuclear power plants use fission, fusion, or both?

Problem 1P The kiloton, which is used to measure the energy released in an atomic explosion, is equal to 4.2 × 1012 J (approximately the energy released in the explosion of 1000 tons of TNT). Recalling that 1 kilocalorie of energy raises the temperature of 1 kg of water by 1°C and that 4184 joules is equal to 1 kilocalorie, show that 4.0 × 108 kilograms of water (nearly half a million tons) can be heated through 50°C by a 20-kiloton atomic bomb.

Problem 1R Assume that all of the following nuclei undergo fission into a pair of equal or nearly equal mass fragments. Using Figure 34.16 as your guide, rank from greatest to least the reduction in mass for these nuclei after fission. a. Uranium ________________ b. Silver ________________ c. Titanium ________________ d. Iron

Why does a chain reaction not occur in uranium mines?

Problem 2E Why doesn’t uranium ore spontaneously undergo a chain reaction?

Problem 2P The isotope of lithium used in a hydrogen bomb is Li-6, whose nucleus contains three protons and three neutrons. When a Li-6 nucleus absorbs a neutron, a nucleus of the heaviest hydrogen isotope, tritium, is produced. What is the other product of this reaction? Which of these two products fuels the explosive reaction?

Problem 2R Rank from greatest to least the reduction of mass per nucleon that accompanies the fusion of the following pairs of nuclei. a. Two hydrogen nuclei ________________ b. Two carbon nuclei ________________ c. Two aluminum nuclei ________________ d. Two iron nuclei

Problem 2RQ Why is a chain reaction more likely in a big piece of uranium than it is in a small piece?

Problem 3E Some heavy nuclei, containing even more protons than the uranium nucleus undergo “spontaneous fission,” splitting apart without absorbing a neutron. Why is spontaneous fission observed only in the heaviest nuclei?

Problem 3P An important fusion reaction in both hydrogen bombs and controlled-fusion reactors is the “DT reaction,” in which a deuteron and a triton (nuclei of heavy hydrogen isotopes) combine to form an alpha particle and a neutron with the release of much energy. Use momentum conservation to explain why the neutron resulting from this reaction receives about 80% of the energy, while the alpha particle gets only about 20%.

Problem 3RQ What is meant by the idea of a critical mass?

Problem 4RQ Which will leak more neutrons, two separate pieces of uranium or the same pieces stuck together?

Problem 5E Why does a neutron make a better nuclear bullet than a proton?

Problem 5RQ What were the two methods used to separate U-235 from U-238 in the Manhattan Project during World War II?

Why will the escape of neutrons be proportionally less in a large piece of fissionable material than in a smaller piece?

Problem 6RQ What are the three possible fates of neutrons in uranium metal?

Problem 7E A 56-kg sphere of U-235 constitutes a critical mass. If the sphere were flattened into a pancake shape, would it still be critical? Explain.

Problem 7RQ What are the three main components of a fission reactor?

Problem 8E Which shape is likely to need more material for a critical mass, a cube or a sphere? Explain.

Problem 8RQ What are the safeguards to prevent a reactor exploding like a fission bomb?