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Learning Outcomes
Page 877
Chapter Summary
  • Spontaneous emission of particles or radiation from unstable nuclei is known as radioactivity. Unstable nuclei emit α particles, β particles, positrons, or γ rays.

  • Nuclear transmutation is the conversion of one nucleus to another. Nuclear reactions are balanced by summing the mass numbers and the atomic numbers.

  • Stable nuclei with low atomic numbers have neutron-to-proton ratios close to 1. Heavier stable nuclei have higher ratios. Nuclear stability is favored by certain numbers of nucleons including even numbers and “magic” numbers.

  • The difference between the actual mass of a nucleus and the mass calculated by summing the masses of the individual nucleons is the mass defect.

  • Nuclear binding energy, determined by using Einstein's equation E = mc2, is a measure of nuclear stability.

  • Uranium-238 is the parent of a natural radioactive decay series that can be used to determine the ages of rocks. Radiocarbon dating is done using carbon-14.

  • Transuranium elements are created by bombarding other elements with accelerated neutrons, protons, α particles, or other nuclei.

  • Nuclear fission is the splitting of a large nucleus into two smaller nuclei and one or more neutrons. When the free neutrons are captured efficiently by other nuclei, a nuclear chain reaction can occur in which the fission process is sustained. The minimum amount of fissionable material required to sustain the reaction is known as the critical mass.

  • Nuclear reactors use the heat from a controlled nuclear fission reaction to produce power. Fission is controlled, in part, by moderators—materials that limit the speed of liberated neutrons but that do not themselves undergo fission when bombarded with neutrons. The three important types of reactors are light water reactors, heavy water reactors, and breeder reactors. Breeder reactors produce more fissionable material than they consume.

  • Nuclear fusion, the type of reaction that occurs in the sun, is the combination of two light nuclei to form one heavier nucleus. Fusion reactions are sometimes referred to as thermonuclear reactions because they take place only at very high temperatures.

  • Radioactive isotopes are easy to detect and thus make excellent tracers in chemical reactions and in medical procedures.

  • High-energy radiation damages living systems by causing ionization and the formation of radicals, or free radicals, which are chemical species with unpaired electrons.

Key Words

Breeder reactor, 870

Critical mass, 868

Mass defect, 855

Moderator, 869

Nuclear binding energy, 855

Nuclear chain reaction, 865

Nuclear fission, 865

Nuclear fusion, 871

Nuclear transmutation, 851

Positron, 852

Radical, 876

Radioactive decay series, 858

Radioactivity, 851

Thermonuclear reaction, 871

Tracers, 873

Transuranium elements, 863

Key Equation



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Questions and Problems
Review Questions



How do nuclear reactions differ from ordinary chemical reactions?



What are the steps in balancing nuclear equations?



What is the difference between –10e and –10β?



What is the difference between an electron and a positron?




Complete the following nuclear equations, and identify X in each case:













Complete the following nuclear equations, and identify X in each case:









Review Questions



State the general rules for predicting nuclear stability.



What is the belt of stability?



Why is it impossible for the isotope to exist?



Define nuclear binding energy, mass defect, and nucleon.



How does Einstein's equation, E = mc2, enable us to calculate nuclear binding energy?



Why is it preferable to use nuclear binding energy per nucleon for a comparison of the stabilities of different nuclei?




The radius of a uranium-235 nucleus is about 7.0 × 10–3 pm. Calculate the density of the nucleus in g/cm3. (Assume the atomic mass is 235 amu.)



For each pair of isotopes listed, predict which one is less stable:



For each pair of elements listed, predict which one has more stable isotopes: (a) Co or Ni, (b) F or Se, (c) Ag or Cd.



In each pair of isotopes shown, indicate which one you would expect to be radioactive: (a) 1020Ne or 1017Ne, (b) 2040Ca or 2045Ca, (c) 4295Mo or 4392Tc, (d) 19580Hg or 19680Hg, (e) 20983Bi or 24296Cm.



Given that

calculate the change in mass (in kg) per mole of H2 formed.



Estimates show that the total energy output of the sun is 5 × 1026 J/s. What is the corresponding mass loss in kg/s of the sun?



Calculate the nuclear binding energy (in joules) and the binding energy per nucleon of the following isotopes:



Calculate the nuclear binding energy (in joules) and the binding energy per nucleon of the following isotopes:

  • (a) 24He (4.002603 amu) and (b) 18474W (183.950928 amu).



Given that the nuclear binding energy of 48Cr is 1.37340 × 10–12 J/nucleon, calculate the mass of a single 48Cr atom.



Given that the nuclear binding energy of 192Ir is 1.27198 × 10–12 J/nucleon, calculate the mass of a single 192Ir atom.

Review Questions



Discuss factors that lead to nuclear decay.



Outline the principle for dating materials using radioactive isotopes.

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Fill in the blanks in the following radioactive decay series:









A radioactive substance undergoes decay as follows:

Time (days) Mass (g)
0 500
1 389
2 303
3 236
4 184
5 143
6 112

Calculate the first-order decay constant and the half-life of the reaction.



The radioactive decay of T1-206 to Pb-206 has a half-life of 4.20 min. Starting with 5.00 × 1022 atoms of T1-206, calculate the number of such atoms left after 42.0 min.



A freshly isolated sample of 90Y was found to have an activity of 9.8 × 105 disintegrations per minute at 1:00 p.m. on December 3, 2010. At 2:15 p.m. on December 17, 2010, its activity was measured again and found to be 2.6 × 104 disintegrations per minute. Calculate the half-life of 90Y.



A wooden artifact has a 14C activity of 18.9 disintegrations per minute, compared to 27.5 disintegrations per minute for live wood. Given that the half-life of 14C is 5715 years, determine the age of the artifact.



In the thorium decay series, thorium-232 loses a total of six α particles and four β particles in a 10-stage process. What is the final isotope produced?



Consider the decay series A B C D where A, B, and C are radioactive isotopes with half-lives of 4.50 s, 15.0 days, and 1.00 s, respectively, and D is nonradioactive. Starting with 1.00 mole of A, and none of B, C, or D, calculate the number of moles of A, B, C, and D left after 30 days.



The activity of radioactive carbon-14 decay of a piece of charcoal found at a volcanic site is 11.2 disintegrations per second. If the activity of carbon-14 decay in an equal mass of living matter is 18.3 disintegrations per second, what is the age of the charcoal? (See Problem 20.29 for the half-life of carbon-14.)



The age of some animal bones was determined by carbon-14 dating to be 8.4 × 103 years old. Calculate the activity of the carbon-14 in the bones in disintegrations per minute per gram, given that the original activity was 15.3 disintegrations per minute per gram. (See Problem 20.29 for the half-life of carbon-14.)



Given that the half-life of 238U is 4.51 × 109 years, determine the age of a rock found to contain 1.09 mg 238U and 0.08 mg 206Pb.



Determine the ratio of 238U to 206Pb in a rock that is 1.7 × 108 years old. (See Problem 20.34 for the half-life of 238U.)

Review Questions



What is the difference between radioactive decay and nuclear transmutation?



How is nuclear transmutation achieved in practice?




Write balanced nuclear equations for the following reactions, and identify X:



Write the abbreviated forms for the following reactions:









Write balanced nuclear equations for the following reactions, and identify X:(a) 3480Se(d,p)X, (b) X(d,2p)39Li, (c) 105B(n,α)X.



Write the abbreviated forms for the following reactions:









Describe how you would prepare astatine-211, starting with bismuth-209.



A long-cherished dream of alchemists was to produce gold from cheaper and more abundant elements. This dream was finally realized when 19880Hg was converted into gold by neutron bombardment. Write a balanced equation for this reaction.

Visualizing Chemistry

Figure 20.7


VC 20.1

The fission of 235U can result in a variety of products, including those shown in Figure 20.7. Which of the following equations does not represent another possible fission process?








VC 20.2

How many neutrons are produced in the fission reaction shown?











VC 20.3

The fission of 235U shown in Figure 20.7 is represented by the equation

How does the combined mass of products compare to the combined mass of reactants for this process?



The combined mass of products is smaller than the combined mass of reactants.



The combined mass of products is larger than the combined mass of reactants.



The combined mass of products is equal to the combined mass of reactants.


VC 20.4

The fusion of 21H and 31H shown in Figure 20.7 is represented by the equation

How does the combined mass of products compare to the combined mass of reactants for this process?



The combined mass of products is smaller than the combined mass of reactants.



The combined mass of products is larger than the combined mass of reactants.



The combined mass of products is equal to the combined mass of reactants.

Review Questions



Define nuclear fission, nuclear chain reaction, and critical mass.



Which isotopes can undergo nuclear fission?



Explain how an atomic bomb works.



Explain the functions of a moderator and a control rod in a nuclear reactor.



Discuss the differences between a light water and a heavy water nuclear fission reactor. What are the advantages of a breeder reactor over a conventional nuclear fission reactor?



No form of energy production is without risk. Make a list of the risks to society involved in fueling and operating a conventional coal-fired electric power plant, and compare them with the risks of fueling and operating a nuclear fission-powered electric plant.

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Review Questions



Define nuclear fusion, thermonuclear reaction, and plasma.



Why do heavy elements such as uranium undergo fission whereas light elements such as hydrogen and lithium undergo fusion?



How does a hydrogen bomb work?



What are the advantages of a fusion reactor over a fission reactor? What are the practical difficulties in operating a large-scale fusion reactor?




Describe how you would use a radioactive iodine isotope to demonstrate that the following process is in dynamic equilibrium:



Consider the following redox reaction:

When KIO4 is added to a solution containing iodide ions labeled with radioactive iodine-128, all the radioactivity appears in I2 and none in the IO3 ion. What can you deduce about the mechanism for the redox process?



Explain how you might use a radioactive tracer to show that ions are not completely motionless in crystals.



Each molecule of hemoglobin, the oxygen carrier in blood, contains four Fe atoms. Explain how you would use the radioactive 2659Fe ( = 46 days) to show that the iron in a certain food is converted into hemoglobin.


125I is produced by a two-step process in which 124Xe nuclei are bombarded with neutrons to produce 125Xe—a process called neutron activation. 125Xe then decays by electron capture to produce 125I, which also decays by electron capture. Write nuclear equations for the two steps that produce 125I from 124Xe, and identify the product of the electron capture decay of 125I.


The half-life of 125I is 59.4 days. How long will it take for the activity of implanted 125I seeds to fall to 5.00 percent of their original value?

Review Questions



List the factors that affect the intensity of radiation from a radioactive element.



What are rad and rem, and how are they related?



Explain, with examples, the difference between somatic and genetic radiation damage.



Compare the extent of radiation damage done by α, β, and γ sources.

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How does a Geiger counter work?



Strontium-90 is one of the products of the fission of uranium-235. This strontium isotope is radioactive, with a half-life of 28.1 years. Calculate how long (in years) it will take for 1.00 g of the isotope to be reduced to 0.200 g by decay.



Nuclei with an even number of protons and an even number of neutrons are more stable than those with an odd number of protons and/or an odd number of neutrons. What is the significance of the even numbers of protons and neutrons in this case?



Tritium (3H) is radioactive and decays by electron emission. Its half-life is 12.5 years. In ordinary water the ratio of 1H to 3H atoms is 1.0 × 1017 to 1. (a) Write a balanced nuclear equation for tritium decay. (b) How many disintegrations will be observed per minute in a 1.00-kg sample of water?



(a) What is the activity, in millicuries, of a 0.500-g sample of (This isotope decays by α-particle emission and has a half-life of 2.20 × 106 years.) (b) Write a balanced nuclear equation for the decay of .



The following equations are for nuclear reactions that are known to occur in the explosion of an atomic bomb. Identify X.











Calculate the nuclear binding energies (in J/nucleon) for the following species: (a) 10B (10.0129 amu), (b) 11B (11.009305 amu), (c) 14N (14.003074 amu), (d) 56Fe (55.93494 amu).



Write complete nuclear equations for the following processes: (a) tritium (3H) undergoes β decay, (b) 242Pu undergoes α-particle emission, (c) 131I undergoes β decay, (d) 251Cf emits an α particle.



The nucleus of nitrogen-18 lies above the stability belt. Write the equation for a nuclear reaction by which nitrogen-18 can achieve stability.



Why is strontium-90 a particularly dangerous isotope for humans? The half-life of strontium-90 is 29.1 years. Calculate the radioactivity in millicuries of 15.6 mg of 90Sr.



How are scientists able to tell the age of a fossil?



20.75 After the Chernobyl accident, people living close to the nuclear reactor site were urged to take large amounts of potassium iodide as a safety precaution. What is the chemical basis for this action?



To detect bombs that may be smuggled onto airplanes, the Federal Aviation Administration (FAA) will soon require all major airports in the United States to install thermal neutron analyzers. The thermal neutron analyzer will bombard baggage with low-energy neutrons, converting some of the nitrogen-14 nuclei to nitrogen-15, with simultaneous emission of γ rays. Because nitrogen content is usually high in explosives, detection of a high dosage of γ rays will suggest that a bomb may be present. (a) Write an equation for the nuclear process. (b) Compare this technique with the conventional X-ray detection method.



Astatine, the last member of Group 7A, can be prepared by bombarding bismuth-209 with α particles. (a) Write an equation for the reaction. (b) Represent the equation in the abbreviated form as discussed in Section 20.4.



Explain why achievement of nuclear fusion in the laboratory requires a temperature of about 100 million degrees Celsius, which is much higher than that in the interior of the sun (15 million degrees Celsius).



The carbon-14 decay rate of a sample obtained from a young tree is 0.260 disintegration per second per gram of the sample. Another wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.186 disintegration per second per gram of the sample. What is the age of the object?



Tritium contains one proton and two neutrons. There is no significant proton-proton repulsion present in the nucleus. Why, then, is tritium radioactive?



The usefulness of radiocarbon dating is limited to objects no older than 60,000 years. What percent of the carbon-14, originally present in the sample, remains after this period of time?



The radioactive potassium-40 isotope decays to argon-40 with a half-life of 1.2 × 109 years. (a) Write a balanced equation for the reaction. (b) A sample of moon rock is found to contain 18 percent potassium-40 and 82 percent argon by mass. Calculate the age of the rock in years. (Assume that all the argon in the sample is the result of potassium decay.)



Nuclear waste disposal is one of the major concerns of the nuclear industry. In choosing a safe and stable environment to store nuclear wastes, consideration must be given to the heat released during nuclear decay. As an example, consider the β decay of 90Sr (89.907738 amu):

The 90Y (89.907152 amu) further decays as follows:

Zirconium-90 (89.904703 amu) is a stable isotope. (a) Use the mass defect to calculate the energy released (in joules) in each of the preceding two decays. (The mass of the electron is 5.4857 × 10–4 amu.) (b) Starting with 1 mole of 90Sr, calculate the number of moles of 90Sr that will decay in a year. (c) Calculate the amount of heat released (in kJ) corresponding to the number of moles of 90Sr decayed to 90Zr in part (b).



Which of the following poses a greater health hazard: a radioactive isotope with a short half-life or a radioactive isotope with a long half-life? Explain. [Assume the same type of radiation (α or β) and comparable energetics per particle emitted.]



From the definition of curie, calculate Avogadro's number, given that the molar mass of 226Ra is 226.03 g/mol and that it decays with a half-life of 1.6 × 103 years.



As a result of being exposed to the radiation released during the Chernobyl nuclear accident, the dose of iodine-131 in a person's body is 7.4 mC (1 mC = 1 × 10–3 Ci). Use the relationship rate = λN to calculate the number of atoms of iodine-131 to which this radioactivity corresponds. (The half-life of 131I is 8.1 days.)



(a) Calculate the energy released when a U-238 isotope decays to Th-234. The atomic masses are as follows: U-238: 238.05078 amu; Th-234: 234.03596 amu; and He-4: 4.002603 amu. (b) The energy released in part (a) is transformed into the kinetic energy of the recoiling Th-234 nucleus and the α particle. Which of the two will move away faster? Explain.



A person received an anonymous gift of a decorative cube, which he placed on his desk. A few months later he became ill and died shortly afterward. After investigation, the cause of his death was linked to the box. The box was airtight and had no toxic chemicals on it. What might have killed the man?



Identify two of the most abundant radioactive elements that exist on Earth. Explain why they are still present. (You may wish to consult a website such as that of the University of Sheffield and WebElements Ltd, UK, webelements.com.)



Sources of energy on Earth include fossil fuels, geothermal power, gravity, hydroelectric power, nuclear fission, nuclear fusion, the sun, and wind. Which of these have a “nuclear origin,” either directly or indirectly?



Cobalt-60 is an isotope used in diagnostic medicine and cancer treatment. It decays with γ-ray emission. Calculate the wavelength of the radiation in nanometers if the energy of the γ ray is 2.4 × 10–13 J/photon.



Americium-241 is used in smoke detectors because it has a long half-life (458 years) and its emitted α particles are energetic enough to ionize air molecules. Using the given schematic diagram of a smoke detector, explain how it works.



The constituents of wine contain, among others, carbon, hydrogen, and oxygen atoms. A bottle of wine was sealed about 6 years ago. To confirm its age, which of the isotopes would you choose in a radioactive dating study? The half-lives of the isotopes are: 13C: 5715 years; 15O: 124 s; 3H: 12.5 years. Assume that the activities of the isotopes were known at the time the bottle was sealed.

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Name two advantages of a nuclear-powered submarine over a conventional submarine.



In 1997 a scientist at a nuclear research center in Russia placed a thin shell of copper on a sphere of highly enriched uranium-235. Suddenly, there was a huge burst of radiation, which turned the air blue. Three days later, the scientist died of radiation exposure. Explain what caused the accident. (Hint: Copper is an effective metal for reflecting neutrons.)



A radioactive isotope of copper decays as follows:

Starting with 84.0 g of 64Cu, calculate the quantity of 64Zn produced after 18.4 h.



A 0.0100-g sample of a radioactive isotope with a half-life of 1.3 × 109 years decays at the rate of 2.9 × 104 disintegrations per minute. Calculate the molar mass of the isotope.



The half-life of 27Mg is 9.50 min. (a) Initially there were 4.20 × 1012 27Mg nuclei present. How many 27Mg nuclei are left 30.0 min later? (b) Calculate the 27Mg activities (in Ci) at t = 0 and t = 30.0 min. (c) What is the probability that any one 27Mg nucleus decays during a 1-s interval? What assumption is made in this calculation?



(a) Assuming nuclei are spherical in shape, show that the radius (r) of a nucleus is proportional to the cube root of mass number (A). (b) In general, the radius of a nucleus is given by r = r0A1/3, where r0, the proportionality constant, is given by 1.2 × 10–15 m. Calculate the volume of the 238U nucleus.



Modern designs of atomic bombs contain, in addition to uranium or plutonium, small amounts of tritium and deuterium to boost the power of explosion. What is the role of tritium and deuterium in these bombs?



Isotope X decays to isotope Y with a half-life of 45 days. Which diagram most closely represents the sample of X after 105 days?



In 2006, an ex-KGB agent was murdered in London. The investigation following the agent's death revealed that he was poisoned with the radioactive isotope 210Po, which had apparently been added to his food. (a) 210Po is prepared by bombarding 209Bi with neutrons. Write an equation for the reaction. (b) The half-life of 210Po is 138 days. It decays by α-particle emission. Write the equation for the decay process. (c) Calculate the energy of an emitted α particle. Assume both the parent and daughter nuclei have zero kinetic energy. The atomic masses of 210Po, 206Pb, and 42α are 209.98286, 205.97444, and 4.00150 amu, respectively. (d) Ingestion of 1 μg of 210Po could prove fatal. What is the total energy released by this quantity of 210Po over the course of 138 days?



Alpha particles produced by radioactive decay eventually pick up electrons from their surroundings to form helium atoms. Calculate the volume (in mL) of He collected at STP when 1.00 g of pure 226Ra is stored in a closed container for 125 years. (Assume that there are five α particles generated per 226Ra as it decays to 206Pb.)



An electron and a positron are accelerated to nearly the speed of light before colliding in a particle accelerator. The resulting collision produces an exotic particle having a mass many times that of a proton. Does this result violate the law of conservation of mass? Explain.


Iridium-192 can be used in brachytherapy. It is produced by a nuclear transmutation. (a) Identify the target nucleus X, and write the balanced nuclear equation for the reaction represented by 191X(n,γ)192Ir. (b) The mass of an 125I nucleus is 124.904624 amu. Calculate the nuclear binding energy and the nuclear binding energy per nucleon.

Page 883
Answers to In-Chapter Materials







2.6280 × 10–10 J; 1.2574 × 10–12 J/nucleon.



196.9665 amu.



9.3 × 103 yr. 20.3B 1.0 × 101 dps.



6.6 × 108 yr.



5.7 × 10–2 mg.













1.215 × 10–12 J/nucleon.



2.989 × 10–10 J.



1.645 × 10–35 kg.



beta emission, positron emission.



3.30 × 109 years.



0.935 dps.