Chapter 21

What is the effect of \(\beta\) decay on the ratio of neutrons to protons in a nucleus?

Explain how the product of \(\beta\) decay has a higher atomic number than the radio nuclide from which the product forms

How can the belt of stability be used to predict the probable decay mode of an unstable nuclide?

Compare and contrast positron-emission and electron-capture processes.

The ratio of neutrons to protons in stable nuclei increases with increasing atomic number. Use this trend to explain why multiple \(\alpha\) decay steps in the \(^{238} \mathrm{U}\) decay series are often followed by \(\beta\) decay.

Write a balanced nuclear equation for a. Beta emission by \(^{161} \mathrm{Tb}\) b. Alpha emission by \(^{255} \mathrm{Lr}\) c. Electron capture by \(^{67} \mathrm{Ga}\) d. Positron emission by \(^{72} \mathrm{As}\)

If the mass number of an isotope is more than twice the atomic number, is the neutron-to-proton ratio less than greater than, or equal to \(1 ?\)

Which isotope in each of the following pairs has more protons and which has more neutrons? (a) \(^{92}\) Mo or \(^{92} \mathrm{Zr}\) (b) \(^{28} \mathrm{Si}\) or \(^{28} \mathrm{Ar} ;\) (c) \(^{111}\) In or \(^{114} \mathrm{In}\).

Calculate the neutron-to-proton ratios for each of the following and predict the modes of decay for the following radioactive isotopes: \((\mathrm{a})^{47} \mathrm{Sc} ;(\mathrm{b})^{89} \mathrm{Zr} ;(\mathrm{c})^{230} \mathrm{Th}\).

Calculate the neutron-to-proton ratios for each of the following and predict the decay pathways of the following radioactive isotopes: \((\mathrm{a})^{238} \mathrm{U} ;(\mathrm{b})^{186} \mathrm{Re} ;(\mathrm{c})^{86} \mathrm{Y}\).

Arsenic-74 decays by \(\beta\) decay and by positron emission. Which nuclides are produced by each of these decay pathways?

Nine isotopes of sulfur have mass numbers ranging from 30 to \(38 .\) Five of the nine are radioactive: \(^{30} \mathrm{S},^{31} \mathrm{S},^{35} \mathrm{S},^{37} \mathrm{S}\) and \(^{38} \mathrm{S}\). Which of these isotopes do you expect to decay by \(\beta\) decay?

Explain why radiocarbon dating is not reliable for artifacts and fossils older than about 50,000 years.

Which of the following statements about \(^{14} \mathrm{C}\) dating are true? a. The amount of \(^{14} \mathrm{C}\) in all objects is the same. b. Carbon-14 is unstable and is readily lost from the atmosphere. c. The ratio of \(^{14} \mathrm{C}\) to \(^{12} \mathrm{C}\) in the atmosphere is a constant. d. Living tissue will absorb \(^{12} \mathrm{C}\) but not \(^{14} \mathrm{C}\).

Why is \(^{40} \mathrm{K}\) dating \(\left(t_{1 / 2}=1.28 \times 10^{9} \text { years }\right)\) useful only for rocks older than 300,000 years?

Where does the \(^{14} \mathrm{C}\) found in plants come from?

What percentage of a sample's original radioactivity remains after three half- lives?

What percentage of a sample's original radioactivity remains after six half- lives?

What is the half-life of \(a^{199}\) Au if \(16.5 \%\) of it decays in 168 hours?

Fukushima Disaster Explosions at a disabled nuclear Sower station in Fukushima, Japan, in 2011 may have released more cesium- 137 \(\left(t_{1 / 2}=30.2 \text { years }\right)\).Into the ocean than any other single event. How long will it take the radioactivity of this radionuclide to decay to \(5.0 \%\) of the level released in \(2011 ?\)

Spent fuel removed from nuclear power stations contains plutonium-\(239\left(t_{1 / 2}=2.41 \times 10^{4} years) \right.\) How long will it take a sample of this radionuclide to reach a level of radioactivity that is \(2.5 \%\) of the level it had when it was removed from a reactor?

Why do all nuclear reactions produce heat?

Which isotope of phosphorus do you predict will have the larger binding energy: \(^{31} \mathrm{P}\), which is stable and naturally occurring, or \(^{32} \mathrm{P}\), which is radioactive with a half-life of 14.3 days?

Substitution of carbon- 11 for some of the carbon- 12 atoms in glucose yields a useful compound for imaging brain function.a. Write a balanced nuclear equation for the decay of \(^{11} \mathrm{C}\) b. Calculate the binding energy for \(^{11} \mathrm{C}\). The exact mass of \(^{11} \mathrm{C}\) is \(1.82850 \times 10^{-26} \mathrm{kg}\)

Fluorine- 18 is often introduced into specific drug molecules for use as imaging agents. a. Write a balanced nuclear equation for the decay of \(^{18} \mathrm{F}\). b. Calculate the binding energy for \(^{18} \mathrm{F}\). The exact mass of \(^{18} \mathrm{F}\) is \(2.98915 \times 10^{-26} \mathrm{kg}\)

Bombardment of a \({ }^{239} \mathrm{Pu}\) target with \(\alpha\) particles produces \({ }^{242} \mathrm{Cm}\) and another particle. a. Use a balanced nuclear equation to determine the identity of the missing particle. b. The synthesis of which other nuclide described in this chapter involves the same subatomic particles?

Complete the following nuclear equations describing the preparation of isotopes for nuclear medicine. a. \(^{197} \mathrm{Au}+? \rightarrow^{199} \mathrm{Hg}+\beta\) b. \(^{64} \mathrm{Ni}+^{1} \mathrm{H} \rightarrow^{64} \mathrm{Cu}+?\) c. \(^{63} \mathrm{Cu}+? \rightarrow^{66} \mathrm{Ga}+^{1} \mathrm{n}\) d. \(^{67} \mathrm{Zn}+^{1} \mathrm{n} \rightarrow^{67} \mathrm{Cu}+?\)

Complete the following nuclear equations. a. \(\quad \frac{13 i}{52} \mathrm{Te} \rightarrow \frac{131}{53} \mathrm{I}+?\) b. \(?+\frac{122}{54} X e+-_{-1}^{0} \beta\) c. \(?+_{2}^{4} \mathrm{He} \rightarrow_{7}^{13} \mathrm{N}+_{0}^{1} \mathrm{n}\) d. \(?+_{1}^{1} \mathrm{H} \rightarrow_{31}^{67} \mathrm{Ga}+2_{0}^{1} \mathrm{n}\)

Arrange the following particles in order of increasing mass: electron, \(\beta\) particle, positron, proton, neutron, \(\alpha\) particle, deuteron.

Scientists at the Fermi National Accelerator Laboratory in Illinois announced in the fall of 1996 that they had created "antihydrogen." How does antihydrogen differ from hydrogen?

Describe an anti-proton.

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

Why is energy released in a nuclear fusion process when the product is an element preceding iron in the periodic table?

Most of the ions that flow out from the sun in the solar wind are hydrogen ions. The ions of which element should be next most abundant?

Nucleosynthesis in Giant Stars \(A\) star needs a core temperature of about \(10^{7} \mathrm{K}\) for hydrogen fusion to occur. Core temperatures above \(10^{8} \mathrm{K}\) are needed for helium fusion. Why docs helium fusion require much higher temperatures?

Our sun contains carbon even though its core is not hot or dense enough to sustain carbon synthesis through the triple-alpha process. Where could the carbon have come from?

Early nucleosynthesis produced a universe that was more than \(99 \%\) hydrogen and helium with less than \(1 \%\) lithium. Why were the other elements not formed?

Calculate the energy released and the wavelength of the two photons emitted in the annihilation of an electron and a positron.

All of the following fusion reactions produce \(^{32}\) S. Calculate the energy released in each reaction from the masses of the isotopes: \(^{4} \mathrm{He}(4.00260 \mathrm{amu}),^{6} \mathrm{Li}(6.01512 \mathrm{amu}),^{12} \mathrm{C}\),\((12.000 \mathrm{amu}),^{14} \mathrm{N}(14.00307 \mathrm{amu}),^{16} \mathrm{O}(15.99491 \mathrm{amu})\),\(^{24} \mathrm{Mg}(23.98504 \mathrm{amu}),^{28} \mathrm{Si}(27.97693 \mathrm{amu}),^{32} \mathrm{S}\),\((31.97207 \mathrm{amu})\). a. \(16+^{16} \mathrm{O} \rightarrow^{32} \mathrm{S}\) b. \(^{23} \mathrm{Si}+^{4} \mathrm{He} \rightarrow^{32} \mathrm{S}\) \(c_{1}^{14} N+^{12} C+^{6} L i \rightarrow^{32} S\) d. \(^{24} \mathrm{Mg}+2^{4} \mathrm{He} \rightarrow^{32} \mathrm{S}\)

What nuclide is produced in the core of a giant star by each of the following fusion reactions? Assume there is only one product in each reaction. a. \(^{12} \mathrm{C}+^{4} \mathrm{He} \rightarrow\) b. \(^{20} \mathrm{Ne}+^{4} \mathrm{He} \rightarrow\) c. \(^{32} S+^{4}\) He \(\rightarrow\)

What nuclide is produced in the core of a giant star by each of the following fusion reactions? Assume there is only one product in each reaction. a. \(28 \mathrm{Si}+^{4} \mathrm{He} \rightarrow\) b. \(^{40} \mathrm{Ca}+^{4} \mathrm{He} \rightarrow\) c. \(^{24} \mathrm{Mg}+^{4} \mathrm{Hc} \rightarrow\)

What nuclide is produced in the core of a collapsing giant star by each of the following reactions? a. \({ }_{29}^{65} \mathrm{Cu}+3{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \boldsymbol{\beta}\) b. \({ }_{30}^{68} \mathrm{Zn}+2{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \beta\) c. \({ }_{38}^{88} \mathrm{Sr}+{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \beta\)

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 the identity of the unknown nuclide: a. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{131} \mathrm{I}+?+2_{0}^{1} \mathrm{n}\) b. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{103} \mathrm{Ru}+?+3_{0}^{1} \mathrm{n}\) 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. \(^{235} \mathrm{U}+_{0}^{1} \mathrm{n} \rightarrow^{95} \mathrm{Sr}+?+3_{0}^{1} \mathrm{n}\)

What is the difference between a level of radioactivity and a dose of radioactivity?