Chapter 19

Boron Neutron-Capture Therapy In boron neutron-capture therapy (BNCT), a patient is given a compound containing \(^{10} \mathrm{B}\) that accumulates inside cancer tumors. Then the tumors are irradiated with neutrons, which are absorbed by \(^{10} \mathrm{B}\) nuclei. The product of neutron capture is an unstable form of \(^{11} \mathrm{B}\) that undergoes \(\alpha\) decay to \(^{7} \mathrm{Li}\). a. Write a balanced nuclear equation for the neutron absorption and \(\alpha\) decay process. b. Calculate the energy released by each nucleus of boron- 10 that captures a neutron and undergoes \(\alpha\) decay, given the following masses of the particles in the process: \(^{10} \mathrm{B}(10.0129 \mathrm{amu}),^{7} \mathrm{Li}(7.01600\) amu) \(^{4} \mathrm{He}(4.00260 \mathrm{amu}),\) and \(^{1} \mathrm{n}(1.00866 \mathrm{amu})\) c. Why is the formation of a nuclide that undergoes \(\alpha\) decay a particularly effective cancer therapy?

Balloon angioplasty is a common procedure for unclogging arteries in patients suffering from arteriosclerosis. Iridium-192 therapy is being tested as a treatment to prevent reclogging of the arteries. In the procedure, a thin ribbon containing pellets of \(^{192} \mathrm{Ir}\) is threaded into the artery. The half-life of \(^{192} \mathrm{Ir}\) is 74 days. How long will it take for \(99 \%\) of the radioactivity from \(1.00 \mathrm{mg}\) of \(^{192}\) Ir to disappear?

How is the rate of energy release controlled in a nuclear reactor?

How does a breeder reactor create fuel and energy at the same time?

Seaborgium (Sg, element 106 ) is prepared by the bombardment of curium-248 with neon-22, which produces two isotopes, \(^{265} \mathrm{Sg}\) and \(^{266} \mathrm{Sg}\). Write balanced nuclear reactions for the formation of both isotopes. Are these reactions better described as fusion or fission processes?

The fission of uranium produces dozens of isotopes. For each of the following fission reactions, determine the identity of the unknown nuclide: a. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{96} \mathrm{Zr}+?+2_{0}^{1} \mathrm{n}\) b. \(^235 \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{99} \mathrm{Nb}+?+4_{0}^{1} \mathrm{n}\) c. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{90} \mathrm{Rb}+?+3_{0}^{1} \mathrm{n}\)

For each of the following fission reactions, determine the identity of the unknown nuclide: a. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{137} \mathrm{I}+?+2_{0}^{1} \mathrm{n}\) b. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{137} \mathrm{Cs}+?+3_{0}^{1} \mathrm{n}\) c. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{141} \mathrm{Ce}+?+2_{0}^{1} \mathrm{n}\)

For each of the following fission reactions, determine th identity of the unknown nuclide: a. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{131} \mathrm{I}+?+2_{0}^{1} \mathrm{n}\) b. \(^{233} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{103} \mathrm{Ru}+?+3_{0}^{1} \mathrm{n}\) c. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{95} \mathrm{Zr}+?+3_{0}^{1} \mathrm{n}\)

For each of the following fission reactions, determine the identity of the unknown nuclide: a. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{147} \mathrm{Pm}+?+2_{0}^{1} \mathrm{n}\) b. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{94} \mathrm{Kr}+?+2_{0}^{1} \mathrm{n}\) c. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{95} \mathrm{Sr}+?+3_{0}^{1} \mathrm{n}\)

In what ways are the fusion reactions that formed \(\alpha\) particles during primordial nucleosynthesis different from those that fuel our Sun today?

How are the fusion reactions that are the basis for power production in the tokamak described in Section 19.9 different from those that power our Sun?

All of the following fusion reactions produce \(^{32}\) S. Calculate the energy released in each reaction from the masses of the isotopes: \(^{4} \mathrm{He}(4.00260 \mathrm{amu}),^{6} \mathrm{Li}(6.01512 \mathrm{amu}),^{12} \mathrm{C}\) \((12.00000 \mathrm{amu}),^{14} \mathrm{N}(14.00307 \mathrm{amu}),^{16} \mathrm{O}(15.99491 \mathrm{amu})\) \(^{24} \mathrm{Mg}\left(23.98504 \text { amu) },^{28} \mathrm{Si}(27.97693 \mathrm{amu}),^{32} \mathrm{S}\right.\) \((31.97207 \mathrm{amu})\) a. \(160+160 \rightarrow 32 \mathrm{S}\) b. \(^{28} \mathrm{Si}+^{4} \mathrm{He} \rightarrow^{32} \mathrm{S}\) c. \(^{14} \mathrm{N}+^{12} \mathrm{C}+^{6} \mathrm{L} \mathrm{i} \rightarrow^{32} \mathrm{S}\) d. \(^{24} \mathrm{Mg}+2^{4} \mathrm{He} \rightarrow^{32} \mathrm{S}\)

How much energy is released per nucleus of tritium produced during the following reactions? a. \(_{0}^{1} n+\frac{6}{3} L i \rightarrow \frac{4}{2} H e+\frac{3}{1} H\) b. \(_{0}^{1} n+_{3}^{7} L_{1} \rightarrow_{2}^{4} \mathrm{He}+_{1}^{3} \mathrm{H}+_{0}^{1} \mathrm{n}\)

It has been proposed that electrical power production in the future might be based on the fusion of deuterium to helium-4. a. Write a radiochemical equation describing the reaction (assume that \(^{4} \mathrm{He}\) is the only product). b. Calculate how much energy is released during the formation of 1 mole of \(^{4} \mathrm{He}\).

Thirty years before the creation of antihydrogen, television producer Gene Roddenberry \((1921-1991)\) proposed to use this form of antimatter to fuel the powerful "warp" engines of the fictional starship Enterprise. a. Why would antihydrogen have been a particularly suitable fuel? b. Describe the challenges of storing such a fuel on a starship.

Tiny concentrations of radioactive tritium \(\left(_{1}^{3} \mathrm{H}\right)\) occur naturally in rain and groundwater. The half-life of \(_{1}^{3} \mathrm{H}\) is 12 years. Assuming that tiny concentrations of tritium can be determined accurately, could the isotope be used to determine whether a bottle of wine with the year 1969 on its label actually contained wine made from grapes that were grown in \(1969 ?\) Explain your answer.

How much energy is required to remove a neutron from the nucleus of an atom of carbon- 13 (mass \(=13.00335\) amu)? (Hint: The mass of an atom of carbon-12 is exactly \(12.00000 \text { amu. })\)

Smoke Detectors Americium-241 \((t_{1 / 2}=433\) yr) is used in smoke detectors. The \(\alpha\) particles from this isotope ionize nitrogen and oxygen in the air, creating an electric current. When smoke is present, the current decreases, setting off the alarm. a. Does a smoke detector bear a closer resemblance to a Geiger counter or to a scintillation counter? b. How long will it take for the radioactivity of a sample of \(^{241} \mathrm{Am}\) to drop to \(1 \%\) of its original radioactivity? c. Why are smoke detectors containing \(^{241} \mathrm{Am}\) safe to handle without protective equipment?

Colorectal Cancer Treatment Cancer therapy with radioactive rhenium-188 shows promise in patients with colorectal cancer. a. Write the symbol for rhenium- 188 and determine the number of neutrons, protons, and electrons. b. Are most rhenium isotopes likely to have fewer neutrons than rhenium-188? c. The half-life of rhenium-188 is 17 h. If it takes 30 min to bind the isotope to an antibody that delivers the rhenium to the tumor, what percentage of the rhenium remains after binding to the antibody? d. The effectiveness of rhenium-188 is thought to result from penetration of \(\beta\) particles as deep as \(8 \mathrm{mm}\) into the tumor. Why wouldn't an \(\alpha\) emitter be more effective? e. Using an appropriate reference text, such as the \(C R C\) Handbook of Chemistry and Physics, pick out the two most abundant isotopes of rhenium. List their natural abundances and explain why the one that is radioactive decays by the pathway that it does.

Synthesis of a New Element In 2006 an international team of scientists confirmed the synthesis of a total of three atoms of \(_{118}^{294} \mathrm{Og}\) in experiments run in 2002 and \(2005 .\) They had bombarded a \(^{249} \mathrm{Cf}\) target with \(^{48} \mathrm{Ca}\) nuclei. a. Write a balanced nuclear equation describing the synthesis of \(_{118}^{294} \mathrm{Og}\) b. The synthesized isotope of Og undergoes \(\alpha\) decay \(\left(t_{1 / 2}=0.9 \mathrm{ms}\right) .\) What nuclide is produced by the decay process? c. The nuclide produced in part (b) also undergoes \(\alpha\) decay \(\left(t_{1 / 2}=10 \mathrm{ms}\right) .\) What nuclide is produced by this decay process? d. The nuclide produced in part (c) also undergoes \(\alpha\) decay \(\left(t_{1 / 2}=0.16 \mathrm{s}\right) .\) What nuclide is produced by this decay process? e. If you had to select an element that occurs in nature and that has physical and chemical properties similar to Og, which element would it be?

The synthesis of new elements and specific isotopes of known elements in linear accelerators involves the fusion of smaller nuclei. a. An isotope of platinum can be prepared from nickel-64 and tin-124. Write a balanced equation for this nuclear reaction. (You may assume that no neutrons are ejected in the fusion reaction.) b. Substituting tin- 132 for tin- 124 increases the rate of the fusion reaction 10 times. Which isotope of \(\mathrm{Pt}\) is formed in this reaction?

The discovery of six skeletons in an Italian cave at the beginning of the 20 th century was considered a significant find in Stone Age archaeology. The age of these bones has been debated. The first attempt at radiocarbon dating indicated an age of 15,000 years. Redetermination of the age in 2004 indicated an older age for two bones, between 23,300 and 26,400 years. What is the ratio of \(^{14} \mathrm{C}\) in a sample 15,000 years old to one 25,000 years old?

Atmospheric testing of nuclear weapons in the 1950 s and '60s produced an increase in the concentration of carbon-14 in the atmosphere. Use one or more balanced nuclear equations to explain how this could have happened.

Dating Prehistoric Bones In 1997 anthropologists uncovered three partial skulls of prehistoric humans in the Ethiopian village of Herto. From the amount of \(^{40} \mathrm{Ar}\) in the volcanic ash in which the remains were buried, their age was estimated at between 154,000 and 160,000 years. a. \(^{40} \mathrm{Ar}\) is produced by the decay of \(^{40} \mathrm{K}\left(t_{1 / 2}=\right.\) \(\left.1.28 \times 10^{9} \mathrm{yr}\right) .\) Propose a decay mechanism for \(^{40} \mathrm{K}\) to \(^{40} \mathrm{Ar}\). b. Why did the researchers choose \(^{40}\) Ar rather than \(^{14} \mathrm{C}\) as