Chapter 18

When nuclei undergo nuclear transformations, \(\gamma\) rays of characteristic frequencies are observed. How does this fact, along with other information in the chapter on nuclear stability, suggest that a quantum mechanical model may apply to the nucleus?

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?

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 \(^{235}\) U. For uranium to be useful as a nuclear fuel, the relative amount of \(^{235}\) 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 \(8,\) Section \(8-7\) ). 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?

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. \(\frac{3}{1} \mathrm{H}(\beta)\) b. \(\frac{8}{3} L i(\beta \text { followed by } \alpha)\) c. \(^{7}_{4}\) Be (electron capture)d. \(^{8}_{5} B\) (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. \(^{62} \mathrm{Cu}\) (positron) c. \(^{212} \operatorname{Fr}(\alpha)\) d. \(^{129} \operatorname{Sb}(\beta)\)

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. \(^{241} \mathrm{Cm}+? \rightarrow^{241} \mathrm{Am}\)

One type of commercial smoke detector contains a minute amount of radioactive americium-241 ( \(\left.^{(241} \mathrm{Am}\right),\) which decays by \(\alpha\) -particle production. The \(\alpha\) particles ionize molecules in the air, allowing it to conduct an electric current. When smoke particles enter, the conductivity of the air is changed and the alarm buzzes. a. Write the equation for the decay of \(^{241}_{95} \mathrm{Am}\) by \(\alpha\) -particle production. b. The complete decay of \(^{241} \mathrm{Am}\) involves successively \(\alpha, \alpha\) \(\boldsymbol{\beta}, \alpha, \alpha, \boldsymbol{\beta}, \alpha, \alpha, \alpha, \boldsymbol{\beta}, \alpha,\) and \(\boldsymbol{\beta}\) production. What is the final stable nucleus produced in this decay series? c. Identify the 11 intermediate nuclides.

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, \(\mathrm{Sg}\), in honor of Glenn T. Seaborg, discoverer of the transuranium elements.a. \(^{263} \mathrm{Sg}\) 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. \(^{263}\) Sg decays by \(\alpha\) emission. What is the other product resulting from the \(\alpha\) decay of \(^{263} \mathrm{Sg} ?\)

Many elements have been synthesized by bombarding relatively heavy atoms with high-energy particles in particle accelerators. Complete the following nuclear equations, which have been used to synthesize elements. a. \(\quad+\frac{4}{2} H e \rightarrow 243 B k+\frac{1}{0} n\) b. \(^{238} \mathrm{U}+^{12}_{6} \mathrm{C} \rightarrow$$\quad$$+6_{0}^{1} n\) c. \(^{249} \mathrm{Cf}+$$\quad$$\rightarrow \frac{260}{105} D b+4 \frac{1}{6} n\) d. \(^{249} \mathrm{Cf}+^{10}_{5} \mathrm{B} \rightarrow \frac{257}{153} \mathrm{Lr}+\)__________

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 \(^{241} \mathrm{Am}\) 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 \(^{241} \mathrm{Am} ?\)

Radioactive copper- 64 decays with a half-life of 12.8 days. a. What is the value of \(k\) in \(s^{-1} ?\) b. A sample contains \(28.0 \space\mathrm{mg}\space^{64} \mathrm{Cu}\). 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?

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 \(47.0 \mathrm{u}\)

The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to \(3.7 \times 10^{10}\) decay events per second (the number of decay events from 1 g radium in \(1 \mathrm{s}\) ). a. What mass of \(\mathrm{Na}_{2}^{38} \mathrm{SO}_{4}\) has an activity of \(10.0 \mathrm{mCi} ?\) Sulfur-38 has an atomic mass of 38.0 u and a half-life of \(2.87 \mathrm{h}\) b. How long does it take for \(99.99 \%\) of a sample of sulfur-38 to decay?

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July \(16,1945 .\) What percentage of the strontium- \(90(t_{1 / 2}=28.9\) years) originally produced . by that explosion still remains as of July \(16,2015 ?\)

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 \(\mathrm{Na}^{131}\) I containing \(10 . \mu \mathrm{g}^{131} \mathrm{I}\) how long will it take for the amount of \(^{131}\) I to decrease to \(1 / 100\) of the original amount?

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

Phosphorus- 32 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 \(1.0 \mathrm{g}^{82} \mathrm{Br}\) and the delivery time was 3.0 days, what mass of NaBr should you order (assuming all of the Br in the NaBr was \(\left.^{82} B r\right) ?\)

Fresh rainwater or surface water contains enough tritium ( \(^{3}_{1} \mathrm{H}\) ) to show 5.5 decay events per minute per \(100 .\) g water. Tritium has a half-life of 12.3 years. You are asked to check a vintage wine that is claimed to have been produced in \(1946 .\) How many decay events per minute should you expect to observe in \(100 .\) g of that wine?

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 \(^{206} \mathrm{Pb}\) 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 \(^{206} \mathrm{Pb}\) is negligible, calculate the age of the \(\text { rock. For }^{238} \mathbf{U}, t_{1 / 2}=4.5 \times 10^{9} \text { years. }\)

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: $$\begin{aligned} &_{19}^{40} \mathrm{K}+_{-1}^{0} \mathrm{e} \longrightarrow_{18}^{40} \mathrm{Ar}(10.7 \%) \quad t_{1 / 2}=1.27 \times 10^{9} \text { years }\\\ &_{19}^{40} \mathrm{K} \longrightarrow_{20}^{40} \mathrm{Ca}+_{-1}^{0} \mathrm{e}(89.3 \%) \end{aligned}$$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 \(^{40} \mathrm{Ar} /^{40} \mathrm{K}\) 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 -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.)

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 per nucleon for \(\frac{2}{1} \mathrm{H}\) and \(^{3}_{1}\) \(\mathrm{H}\). The atomic masses are \(\frac{2}{1} \mathrm{H}, 2.01410 \mathrm{u} ;\) and \(\frac{3}{1} \mathrm{H}, 3.01605 \mathrm{u}\)

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

The easiest fusion reaction to initiate is $$\frac{2}{1} \mathrm{H}+\frac{3}{1} \mathrm{H} \longrightarrow_{2}^{4} \mathrm{He}+\frac{1}{0} \mathrm{n}$$ Calculate the energy released per \(\frac{4}{2} \mathrm{He}\) nucleus produced and per mole of \(^{4}_{2}\) He produced. The atomic masses are \(\frac{2}{1} \mathrm{H}\) \(2.01410 \mathrm{u} ; \frac{3}{1} \mathrm{H}, 3.01605 \mathrm{u} ;\) and \(\frac{4}{2} \mathrm{He}, 4.00260 \mathrm{u} .\) The masses of the electron and neutron are \(5.4858 \times 10^{-4} \mathrm{u}\) and \(1.00866 \mathrm{u}\) respectively.

When using a Geiger-Müller counter to measure radioactivity, it is necessary to maintain the same geometrical orientation between the sample and the Geiger-Müller 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 \(\mathrm{NO}_{2} ? \)Assume that \(\mathrm{N}\) is the central atom in \(\mathrm{NO}_{3},\) assume only \(\mathrm{N}^{16} \mathrm{O}^{18} \mathrm{O}_{2}\) 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 \(^{90}\) 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 \(\frac{238}{92} \mathrm{U}\) to a fissionable product. Neutron capture of the \(\frac{238}{92} \mathrm{U}\) 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 \(\mathrm{Sr}\) and Xe. Why are the chemical properties of a radioactive substance important in assessing its potential health hazards?

Consider the following information: i. The layer of dead skin on our bodies is sufficient to protect us from most \(\alpha\) -particle radiation. ii. Plutonium is an \(\alpha\) -particle producer. iii. The chemistry of \(\mathrm{Pu}^{4+}\) is similar to that of \(\mathrm{Fe}^{3+}\). iv. Pu oxidizes readily to \(\mathrm{Pu}^{4+}\) Why is plutonium one of the most toxic substances known?

Predict whether each of the following nuclides is stable or unstable (radioactive). If the nuclide is unstable, predict the type of radioactivity you would expect it to exhibit. a. \(_{19}^{45} \mathrm{K}\) b. \(\frac{56}{26} \mathrm{Fe}\) c. \(\frac{20}{11} \mathrm{Na}\) d. \(^{194}_{81} \mathrm{TI}\)

Each of the following isotopes has been used medically for the purpose indicated. Suggest reasons why the particular element might have been chosen for this purpose. a. cobalt-57, for study of the body's use of vitamin \(\mathbf{B}_{12}\) b. calcium- \(47,\) for study of bone metabolism c. iron-59, for study of red blood cell function

At a flea market, you've found a very interesting painting done in the style of Rembrandt's "dark period" (1642-1672). You suspect that you really do not have a genuine Rembrandt, but you take it to the local university for testing. Living wood shows a carbon- 14 activity of 15.3 counts per minute per gram. Your painting showed a carbon- 14 activity of 15.1 counts per minute per gram. Could it be a genuine Rembrandt?

Define "third-life" in a similar way to "half-life," and determine the "third- life" for a nuclide that has a half-life of 31.4 years.

A proposed system for storing nuclear wastes involves storing the radioactive material in caves or deep mine shafts. One of the most toxic nuclides that must be disposed of is plutonium- 239 which is produced in breeder reactors and has a half-life of 24,100 years. A suitable storage place must be geologically stable long enough for the activity of plutonium-239 to decrease to \(0.1 \%\) of its original value. How long is this for plutonium-239?

A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases \(4 \times 10^{9} \mathrm{J}\) of energy when exploded. Using \(2 \times 10^{13} \mathrm{J} / \mathrm{mol}\) as the energy released by fission of \(^{235} \mathrm{U},\) approximately what mass of \(^{235} \mathrm{U}\) undergoes fission in this atomic bomb?

During the research that led to production of the two atomic bombs used against Japan in World War II. different mechanisms for obtaining a super- critical mass of fissionable material were investigated. In one type of bomb, a "gun" shot one piece of fissionable material into a cavity containing another piece of fissionable material. In the second type of bomb, the fissionable material was surrounded with a high explosive that, when detonated, compressed the fissionable material into a smaller volume. Discuss what is meant by critical mass, and explain why the ability to achieve a critical mass is essential to sustaining a nuclear reaction.