Chapter 19

Do radiotracers generally have long or short half-lives? Explain.

There is a trend in the United States toward using coal-fired power plants to generate electricity rather than building new nuclear fission power plants. Is the use of coal-fired power plants without risk? Make a list of the risks to society from the use of each type of power plant.

Which type of radioactive decay has the net effect of changing a neutron into a proton? Which type of decay has the net effect of turning a proton into a neutron?

Consider the following graph of binding energy per nucleon as a function of mass number a. What does this graph tell us about the relative half-lives of the nuclides? Explain your answer. b. Which nuclide shown is the most thermodynamically stable? Which is the least thermodynamically stable? c. What does this graph tell us about which nuclides undergo fusion and which undergo fission to become more stable? Support your answer.

What are transuranium elements and how are they synthesized?

Scientists have estimated that the earth's crust was formed 4.3 billion years ago. The radioactive nuclide \(176 \mathrm{Lu},\) which decays to 176 \(\mathrm{Hf}\) , was used to estimate this age. The half-life of 176 \(\mathrm{Lu}\) is 37 billion years. How are ratios of \(^{176} \mathrm{Lu}\) to 176 \(\mathrm{Hf}\) utilized to date very old rocks?

Why are the observed energy changes for nuclear processes so much larger than the energy changes for chemical and physical processes?

Natural uranium is mostly nonfissionable \(^{238} \mathrm{U}\) it contains only about 0.7\(\%\) of fissionable \(^{235} \mathrm{U}\) . For uranium to be useful as a nuclear fuel, the relative amount of \(^{235} \mathrm{U}\) must be increased to about 3\(\% .\) This is accomplished through a gas diffusion process. In the diffusion process, natural uranium reacts with fluorine to form a mixture of \(^{238} \mathrm{UF}_{6}(g)\) and 235 \(\mathrm{UF}_{6}(g) .\) The fluoride mixture is then enriched through a multistage diffusion process to produce a 3\(\%^{235} \mathrm{U}\) nuclear fuel. The diffusion process utilizes Graham's law of effusion (see Chapter 5,Section 5.7). Explain how Graham's law of effusion allows natural uranium to be enriched by the gaseous diffusion process.

Much of the research on controlled fusion focuses on the problem of how to contain the reacting material. Magnetic fields appear to be the most promising mode of containment. Why is containment such a problem? Why must one resort to magnetic fields for containment?

Describe the relative penetrating powers of alpha, beta, and gamma radiation.

Explain the difference between somatic damage from radiation and genetic damage. Which type causes immediate damage to the exposed individual?

A recent study concluded that any amount of radiation exposure can cause biological damage. Explain the differences between the two models of radiation damage, the linear model and the threshold model.

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a.\(_{1}^{3} \mathrm{H}(\beta)\) b. \(_{3}^{8} \operatorname{Li}(\beta \text { followed by } \alpha)\) c. \(\quad_{4}^{7}\) Be (electron capture) d. \(_{5}^{8} \mathrm{B}(\text { positron })\)

In each of the following radioactive decay processes, supply the missing particle. a. \(^{60} \mathrm{Co} \rightarrow^{60} \mathrm{Ni}+?\) b. \(^{97} \mathrm{Tc}+? \rightarrow^{97} \mathrm{Mo}\) c. \(^{99} \mathrm{Tc} \rightarrow^{99} \mathrm{Ru}+?\) d. \(^{239} \mathrm{Pu} \rightarrow^{235} \mathrm{U}+?\)

Write balanced equations for each of the processes described below. a. Chromium-51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture. b. Iodine-131, used to treat hyperactive thyroid glands, decays by producing a \(\beta\) particle. c. Phosphorus- \(32,\) which accumulates in the liver, decays by \(\beta\) -particle production.

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. 68 Ga (electron capture) b. 62 Cu (positron) c. 212 \(\mathrm{Fr}(\alpha)\) d. 129 \(\mathrm{Sb}(\beta)\)

In each of the following radioactive decay processes, supply the missing particle. a. \(^{73} \mathrm{Ga} \rightarrow^{73} \mathrm{Ge}+?\) b. \(^{192} \mathrm{Pt} \rightarrow^{188} \mathrm{Os}+?\) c. \(^{205} \mathrm{Bi} \rightarrow^{205} \mathrm{Pb}+?\) d. \(^{241} \mathrm{Cm}+? \rightarrow^{241} \mathrm{Am}\)

Uranium-2355 undergoes a series of \(\alpha\) -particle and \(\beta\) -particle productions to end up as lead-207. How many \(\alpha\) particles and \(\beta\) particles are produced in the complete decay series?

The radioactive isotope \(^{242} \mathrm{Cm}\) decays by a series of \(\alpha\) -particle and \(\beta\) -particle productions, taking \(^{242} \mathrm{Cm}\) through many transformations to end up as \(^{206} \mathrm{P} \mathrm{b}\) . In the complete decay series, how many \(\alpha\) and \(\beta\) particles are produced?

The stable isotopes of boron are boron-10 and boron-11. Four radioactive isotopes with mass numbers 8, 9, 12, and 13 are also known. Predict possible modes of radioactive decay for the four radioactive isotopes of boron.

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine-17.

In 1994 it was proposed (and eventually accepted) that element 106 be named seaborgium, Sg, in honor of Glenn T. Seaborg, discoverer of the transuranium elements. a. \(^{263}\) Sg was produced by the bombardment of \(^{249} \mathrm{Cf}\) with a beam of \(^{18} \mathrm{O}\) nuclei. Complete and balance an equation for this reaction. b. \(^{263}\) g decays by \(\alpha\) emission. What is the other product resulting from the \(\alpha\) decay of \(^{263} \mathrm{Sg}\) ?

What is the rate of decay from 1.00 mol of radioactive nuclides having the following half-lives: \(12,000\) years? 12 hours? 12 seconds?

The rate constant for a certain radioactive nuclide is \(1.0 \times 10^{-3} \mathrm{h}^{-1} .\) What is the half-life of this nuclide?

Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of \(^{24} \mathrm{Am}\) is 433 years, and it decays by emitting \(\alpha\) particles. How many \(\alpha\) particles are emitted each second by a 5.00 -g sample of \(^{241} \mathrm{Am}\) ?

The number of radioactive nuclides in a sample decays from \(1.00 \times 10^{20}\) to \(2.50 \times 10^{19}\) in 10.0 minutes. What is the half-life of this radioactive species?

A chemist wishing to do an experiment requiring \(^{47} \mathrm{Ca}^{2+}\) (half- life \(=4.5\) days needs 5.0\(\mu \mathrm{g}\) of the nuclide. What mass of \(^{47} \mathrm{CaCO}_{3}\) must be ordered if it takes 48 \(\mathrm{h}\) for delivery from the supplier? Assume that the atomic mass of \(^{47} \mathrm{Ca}\) is 47.0 \(\mathrm{u} .\)

Radioactive copper-64 decays with a half-life of 12.8 days. a. What is the value of \(k\) in \(\mathrm{s}^{-1} ?\) b. A sample contains 28.0 \(\mathrm{mg}^{64} \mathrm{Cu}\) . How many decay events will be produced in the first second? Assume the atomic mass of \(^{64} \mathrm{Cu}\) is 64.0 \(\mathrm{u} .\) c. A chemist obtains a fresh sample of \(^{64} \mathrm{Cu}\) and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below 25\(\%\) of the initial measured value. How long does she have to do the experiment?

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July \(16,1945 .\) What percentage of the strontium- 90\(\left(t_{1 / 2}=28.9 \text { years) originally produced }\right.\) by that explosion still remains as of July \(16,2017 ?\)

Iodine- 131 is used in the diagnosis and treatment of thyroid disease and has a half-life of 8.0 days. If a patient with thyroid disease consumes a sample of \(\mathrm{Na}^{131} \mathrm{I}\) containing \(10 . \mu \mathrm{g}^{131 \mathrm{I}}\) how long will it take for the amount of \(^{131} \mathrm{I}\) to decrease to 1\(/ 100\) of the original amount?

Technetium- 99 has been used as a radiographic agent in bone scans \((43 \mathrm{Tc} \text { is absorbed by bones). If } 43 \mathrm{Tc} \text { has a half-life of }\) 6.0 hours, what fraction of an administered dose of \(100 . \mu \mathrm{g}\) 43 \(\mathrm{Tc}\) remains in a patient's body after 2.0 days?

Phosphorus-32 2 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus- 32 is left from an original sample of 175 \(\mathrm{mg}\) \(\mathrm{Na}_{3}^{32} \mathrm{PO}_{4}\) after 35.0 days? Assume the atomic mass of \(^{32} \mathrm{P}\) is 32.0 \(\mathrm{u} .\)

The bromine- 82 nucleus has a half-life of \(1.0 \times 10^{3}\) min. If you wanted 1.0 g \(^{82}\mathrm{Br}\) and the delivery time was 3.0 days, what mass of NaBr should you order (assuming all of the Br in the NaBr was \(^{82} \mathrm{Br}\) )?

A living plant contains approximately the same fraction of carbon-14 4 as in atmospheric carbon dioxide. Assuming that the observed rate of decay of carbon-14 4 from a living plant is 13.6 counts per minute per gram of carbon, how many counts per minute per gram of carbon will be measured from a \(15,000\) -year-old sample? Will radiocarbon dating work well for small samples of 10 \(\mathrm{mg}\) or less? (For \(^{14} \mathrm{C}, t_{1 / 2}=5730\) years.)

Assume a constant \(1^{14} \mathrm{C} /^{12} \mathrm{C}\) ratio of 13.6 counts per minute per gram of living matter. A sample of a petrified tree was found to give 1.2 counts per minute per gram. How old is the tree? (For \(^{14} \mathrm{C}, t_{1 / 2}=5730\) years.)

A rock contains 0.688 \(\mathrm{mg}^{206} \mathrm{Pb}\) for every 1.000 \(\mathrm{mg}^{238} \mathrm{U}\) present. Assuming that no lead was originally present, that all the \(^{206}\mathrm{P}\) formed over the years has remained in the rock, and that the number of nuclides in intermediate stages of decay between \(^{238} \mathrm{U}\) and \(^{206 \mathrm{P}} \mathrm{b}\) is negligible, calculate the age of the rock. (For \(38 \mathrm{U}, t_{1 / 2}=4.5 \times 10^{9}\) years.)

The mass ratios of 40 \(\mathrm{Ar}\) to 40 \(\mathrm{K}\) also can be used to date geologic materials. Potassium-40 decays by two processes: $$_{19}^{40} \mathrm{K}+_{-1}^{0} \mathrm{e} \longrightarrow_{\mathrm{i} 8}^{40} \mathrm{Ar}(10.7 \%)$$ $$_{19}^{40} \mathrm{K} \longrightarrow_{20}^{40} \mathrm{Ca}+_{-1}^{0} \mathrm{e}(89.3 \%)$$ $$t_{1 / 2}=1.27 \times 10^{9}$$ a. Why are \(^{40}\mathrm{Ar} /^{40} \mathrm{K}\) ratios used to date materials rather than \(^{40}\mathrm{Ca} / 40 \mathrm{K}\) ratios? b. What assumptions must be made using this technique? c. A sedimentary rock has an Ar \(^{40} \mathrm{K}\) ratio of \(0.95 .\) Calculate the age of the rock. d. How will the measured age of a rock compare to the actual age if some \(^{40}\) Ar escaped from the sample?

The earth receives \(1.8 \times 10^{14} \mathrm{kJ} / \mathrm{s}\) of solar energy. What mass of solar material is converted to energy over a \(24-\mathrm{h}\) period to provide the daily amount of solar energy to the earth? What mass of coal would have to be burned to provide the same amount of energy? (Coal releases 32 \(\mathrm{kJ}\) of energy per gram when burned.)

Many transuranium elements, such as plutonium-232 , have very short half- lives. (For \(^{232} \mathrm{Pu}\) , the half-life is 36 minutes.) However, some, like protactinium- 231 (half-life \(=3.34 \times 10^{4}\) years), have relatively long half-lives. Use the masses given in the following table to calculate the change in energy when 1 mole of \(^{232} \mathrm{Pu}\) nuclei and 1 mole of \(^{231} \mathrm{Pa}\) nuclei are each formed from their respective number of protons and neutrons. (Since the masses of \(^{232} \mathrm{Pu}\) and \(^{231} \mathrm{Pa}\) are atomic masses, they each include the mass of the electrons present. The mass of the nucleus will be the atomic mass minus the mass of the electrons.)

The most stable nucleus in terms of binding energy per nucleon is \(^{56}\mathrm{Fe}\) . If the atomic mass of \(^{56}\mathrm{Fe}\) is \(55.9349 \mathrm{u},\) calculate the binding energy per nucleon for \(^{56} \mathrm{Fe} .\)

Calculate the binding energy in J/nucleon for carbon-12 (atomic mass \(=12.0000\) u) and uranium-235 (atomic mass \(=\) 235.0439 u). The atomic mass of \(_{1}^{1} \mathrm{H}\) is 1.00782 \(\mathrm{u}\) and the mass of a neutron is 1.00866 u. The most stable nucleus known is \(^{56}\) Fe \((\text { see Exercise } 50)\) . Would the binding energy per nucleon for \(^{56} \mathrm{Fe}\) be larger or smaller than that of \(^{12} \mathrm{C}\) or \(^{235} \mathrm{U}\) ? Explain.

Calculate the binding energy for \(_{1}^{2} \mathrm{H}\) and \(_{1}^{3} \mathrm{H} .\) The atomic masses are \(_{1}^{2} \mathrm{H}, 2.01410 \mathrm{u} ;\) and \(^{3} \mathrm{H}, 3.01605 \mathrm{u} .\)

The binding energy per nucleon for magnesium- 27 is \(1.326 \times 10^{-12} \mathrm{J} /\) nucleon. Calculate the atomic mass of \(^{27} \mathrm{Mg}\) .

Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are \(_{1}^{1} \mathrm{H}, \quad 1.00782\) u; \(_{1}^{2} \mathrm{H}, \quad 2.01410 \quad \mathrm{u} ;\) and an electron, \(5.4858 \times 10^{-4}\) u. (Hint: Think carefully about how to account for the electron mass.) $$ _{1}^{1} \mathrm{H}+_{1}^{1} \mathrm{H} \longrightarrow_{1}^{2} \mathrm{H}+_{+1}^{0} \mathrm{e} $$

When using a Geiger-Müller counter to measure radioactivity, it is necessary to maintain the same geometrical orientation between the sample and the Geiger-Muller tube to compare different measurements. Why?

Consider the following reaction to produce methyl acetate: When this reaction is carried out with \(\mathrm{CH}_{3} \mathrm{OH}\) containing oxygen- \(18,\) the water produced does not contain oxygen-18. Explain.

A chemist studied the reaction mechanism for the reaction $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ by reacting \(\mathrm{N}^{16} \mathrm{O}\) with \(^{18} \mathrm{O}_{2}\) . If the reaction mechanism is $$ \begin{aligned} \mathrm{NO}+\mathrm{O}_{2} & \rightleftharpoons \mathrm{NO}_{3}(\text { fast equilibrium }) \\ \mathrm{NO}_{3}+\mathrm{NO} & \longrightarrow 2 \mathrm{NO}_{2}(\text { slow }) \end{aligned} $$ what distribution of \(^{18} \mathrm{O}\) would you expect in the NO \(_{2} ?\) Assume that \(\mathrm{N}\) is the central atom in \(\mathrm{NO}_{3},\) assume only \(\mathrm{N}^{16} \mathrm{O}^{16} \mathrm{O}_{2}\) forms, and assume stoichiometric amounts of reactants are combined.

Uranium-235 undergoes many different fission reactions. For one such reaction, when \(^{235} \mathrm{U}\) is struck with a neutron, \(^{144}\mathrm{Ce}\) and \(^{90}\mathrm{Sr}\) are produced along with some neutrons and electrons. How many neutrons and \(\beta\) -particles are produced in this fission reaction?

Breeder reactors are used to convert the nonfissionable nuclide 238 \(\mathrm{U}\) to a fissionable product. Neutron capture of the 238 \(\mathrm{U}\) is followed by two successive beta decays. What is the final fissionable product?

Which do you think would be the greater health hazard: the release of a radioactive nuclide of Sr or a radioactive nuclide of Xe into the environment? Assume the amount of radioactivity is the same in each case. Explain your answer on the basis of the chemical properties of Sr and Xe. Why are the chemical properties of a radioactive substance important in assessing its potential health hazards?