Some heavy nuclei, containing even more protons than the

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

Problem 1RQ Why does a chain reaction not occur in uranium mines?

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

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

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 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 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 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 4E Why will nuclear fission probably not be used directly for powering automobiles? How could it be used indirectly to power automobiles?

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

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

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.

Why doesn’t a chain reaction normally occur in uranium mines?

Why is a chain reaction more likely to occur in a big piece of uranium than in a small piece?

Which will leak more neutrons: two separate pieces of uranium or the same pieces stuck together?

What is meant by the idea of a critical mass?

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

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

What components are the safeguards to prevent a reactor from generating energy out of control?

What isotope is produced when U-238 absorbs a neutron?

What isotope is produced when U-239 emits a beta particle?

What do U-235 and Pu-239 have in common?

What isotope is produced when Np-239 emits a beta particle?

What is the effect of placing small amounts of fissionable isotopes with large amounts of U-238?

Name two isotopes that undergo nuclear fission.

What element reacts in a breeder reactor to breed nuclear fuel?

In what way is a nuclear reactor similar to a conventional fossil-fuel plant?

Cite three main advantages of fission power. Cite four main drawbacks.

What celebrated equation shows the equivalence of mass and energy?

Is work required to pull a nucleon out of an atomic nucleus? Does the nucleon, once outside, have more energy than it did when it was inside the nucleus? In what form is this energy?

Which ions of like charge and equal speed are least deflected in a mass spectrometer?

What is the basic difference between the graphs in Figure 34.15 and Figure 34.16?

In which element is the mass per nucleon greatest? Least?

What becomes of the “lost” mass per nucleon in fission and fusion reactions?

How does the mass per nucleon in uranium compare with the mass per nucleon in its fission fragments?

If the graph in Figure 34.16 is seen as an energy valley, what can be said about the energy of nuclear transformations that progress toward iron?

When a pair of hydrogen nuclei are fused to create helium, how does the mass of the resulting helium nucleus compare with the sum of the nuclear masses before fusion?

For helium to release energy, should it be fissioned or fused?

What isotopes of hydrogen fuse best at “moderate” temperatures?

Which isotope of hydrogen—deuterium or tritium—is abundant and which is scarce?

What kind of nuclear power is responsible for sunshine?

The kiloton, which is used to measure the energy released in an atomic explosion, is equal to \(4.2 \times 10^{12} \mathrm{~J}\) (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 \(1^{\circ} \mathrm{C}\) and that 4184 joules is equal to 1 kilocalorie, show that the energy released by a 20-kiloton bomb is enough to heat \(4.0 \times 10^{8}\) kilograms of water (nearly half a million tons) through \(50^{\circ} \mathrm{C}\).

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?

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 that results from this reaction receives about 80% of the energy, while the alpha particle gets only about 20%.

Assume that all of the following nuclei undergo fission into a pair of equal or nearly equal mass fragments. Using the periodic table and Figure 34.16 as your guide, rank from greatest to least the reduction in mass per nucleon for these nuclei after fission. (a) Uranium (b) Silver (c) Gold (d) Iron

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

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

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

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?

Why does a neutron make a better nuclear bullet than a proton?

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

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.

Which shape is likely to need more material for a critical mass: a cube or a sphere? Explain.

Does the average distance that a neutron travels through fissionable material before escaping increase or decrease when two pieces of fissionable material are assembled into one piece? Does this assembly increase or decrease the probability of an explosion?

U-235 releases an average of 2.5 neutrons per fission, while Pu-239 releases an average of 2.7 neutrons per fission. Which of these elements might you therefore expect to have the smaller critical mass?

Uranium and thorium occur abundantly in various ore deposits. However, plutonium could occur only in exceedingly tiny amounts in such deposits. What is your explanation?

Why, after a uranium fuel rod reaches the end of its fuel cycle (typically 3 years), does most of its energy come from the fissioning of plutonium?

If a nucleus of \({ }_{90}^{232} \mathrm{Th}\) absorbs a neutron and the resulting nucleus undergoes two successive beta decays (emitting electrons), what nucleus results?

The water that passes through the reactor core of a water-moderated fission reactor does not pass into the turbine. Instead, heat is transferred to a separate water cycle that is entirely outside the reactor. Why is this done?

Why is carbon better than lead as a moderator in nuclear reactors?

Is the mass of an atomic nucleus greater or less than the sum of the masses of the separate nucleons composing it? Why don’t the nucleon masses add up to the total nuclear mass?

The energy release of nuclear fission is tied to the fact that the heaviest nuclei have about 0.1% more mass per nucleon than nuclei near the middle of the periodic table of the elements. What would be the effect on energy release if the 0.1% figure were instead 1%?

In what way are fission and fusion reactions similar? What are the main differences in these reactions?

How is chemical burning similar to nuclear fusion?

Mixing copper and zinc atoms produces the alloy brass. What would be produced with the fusion of copper and zinc nuclei?

Oxygen and hydrogen atoms combine to form water. If all three nuclei in a water molecule were fused, what element would be produced?

If a pair of carbon atoms were fused, and the product were to emit a beta particle, what element would be produced?

Which produces more energy: the fissioning of a single uranium nucleus or the fusing of a pair of deuterium nuclei? The fissioning of a gram of uranium or the fusing of a gram of deuterium? (Why do your answers differ?)

Why is there, unlike fission fuel, no limit to the amount of fusion fuel that can be safely stored in one locality?

If a fusion reaction produces no appreciable radioactive isotopes, why does a hydrogen bomb produce significant radioactive fallout?

List at least two major potential advantages of power production by fusion rather than by fission.

Ordinary hydrogen is sometimes called a perfect fuel because when it burns, harmless water is the product of the combustion. So why don’t we abandon fission and fusion energies, not to mention fossil-fuel energy, and just use hydrogen?

If a U-238 nucleus splits into two even pieces, and each piece emits an alpha particle, what elements are produced?

The energy of fission is mainly in the kinetic energy of its products. What becomes of this energy in a commercial power reactor?

Fermi’s original reactor was just “barely” critical because the natural uranium that he used contained less than 1% of the fissionable isotope U-235 (half-life 713 million years). What if, in 1942, Earth had been 9 billion years old instead of 4.5 billion years old? Would Fermi have been able to make a reactor go critical with natural uranium?

Why will nuclear fission probably not be used directly for powering automobiles? How could it be used indirectly to power automobiles?

To predict the approximate energy release of either a fission reaction or a fusion reaction, explain how a physicist makes use of the curve in Figure 34.16 or a table of nuclear masses and the equation \(E=m c^{2}\).

What nuclei will result if a U-235 nucleus, after absorbing a neutron and becoming U-236, splits into two identical fragments?

Heavy nuclei can be made to fuse—for instance, by firing one gold nucleus at another one. Does such a process yield energy or cost energy? Explain.

Light nuclei can be split. For example, a deuteron, which is a proton–neutron combination, can split into a separate proton and a separate neutron. Does such a process yield energy or cost energy? Explain.

Which process would release energy from gold: fission or fusion? Which would release energy from carbon? From iron?

If uranium were to split into three segments of equal size instead of two, would more energy or less energy be released? Defend your answer in terms of Figure 34.16.

Suppose the curve in Figure 34.16 for mass per nucleon versus atomic number had the shape of the curve in Figure 34.15. Then would nuclear fission reactions produce energy? Would nuclear fusion reactions produce energy? Defend your answers.

The “hydrogen magnets” in Figure 34.20 weigh more when apart than when combined. What would be the basic difference if the fictitious example instead consisted of “nuclear magnets” half as heavy as uranium?

In a nuclear fission reaction, which has more mass: the initial uranium or its products?

In a nuclear fusion reaction, which has more mass: the initial hydrogen isotopes or the fusion products?

Sustained nuclear fusion has yet to be achieved and remains a hope for abundant future energy. Yet the energy that has always sustained us has been the energy of nuclear fusion. Explain.

Explain how radioactive decay has always warmed Earth from the inside and how nuclear fusion has always warmed Earth from the outside.

The world has not been the same since the discovery of electromagnetic induction and its applications to electric motors and generators. Speculate and list some of the worldwide changes that are likely to follow the advent of successful fusion reactors.

Discuss, and make a comparison of, pollution by conventional fossil-fuel power plants and nuclear-fission power plants. Consider thermal pollution, chemical pollution, and radioactive pollution.

U-235 has a half-life of about 700 million years. What does this say about the likelihood of fission power on Earth 1 billion years from now?