List the particles or types of radiation that an unstable nucleus can produce.
Identify a subatomic particle in a nuclear equation.
Distinguish between chemical and nuclear reactions.
Demonstrate use of subatomic particles in balancing nuclear reactions.
List the rules for nuclear stability and use them to predict whether a particular nucleus is stable.
Define nuclear binding energy.
Calculate the nuclear binding energy of a nucleus.
Use the halflife of a radioactive decay in calculations.
Produce the balanced nuclear reaction for a nuclear transmutation.
Distinguish between fusion and fission.
Define critical mass and nuclear chain reaction.
Describe the basis of a nuclear reactor.
Provide examples of the uses of isotopes in science and medicine.
Explain why highenergy radiation is biologically harmful.
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 neutrontoproton 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 = mc^{2}, is a measure of nuclear stability.
Uranium238 is the parent of a natural radioactive decay series that can be used to determine the ages of rocks. Radiocarbon dating is done using carbon14.
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.
Highenergy radiation damages living systems by causing ionization and the formation of radicals, or free radicals, which are chemical species with unpaired electrons.

20.1 


20.1 
How do nuclear reactions differ from ordinary chemical reactions? 

20.2 
What are the steps in balancing nuclear equations? 

20.3 
What is the difference between _{–1}^{0}e and _{–1}^{0}β? 

20.4 
What is the difference between an electron and a positron? 

20.5 
Complete the following nuclear equations, and identify X in each case:



20.6 
Complete the following nuclear equations, and identify X in each case:


20.7 
State the general rules for predicting nuclear stability. 

20.8 
What is the belt of stability? 

20.9 
Why is it impossible for the isotope to exist? 

20.10 
Define nuclear binding energy, mass defect, and nucleon. 

20.11 
How does Einstein's equation, E = mc^{2}, enable us to calculate nuclear binding energy? 

20.12 
Why is it preferable to use nuclear binding energy per nucleon for a comparison of the stabilities of different nuclei? 

20.13 
The radius of a uranium235 nucleus is about 7.0 × 10^{–3} pm. Calculate the density of the nucleus in g/cm^{3}. (Assume the atomic mass is 235 amu.) 

20.14 
For each pair of isotopes listed, predict which one is less stable: 

20.15 
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. 

20.16 
In each pair of isotopes shown, indicate which one you would expect to be radioactive: (a) _{10}^{20}Ne or _{10}^{17}Ne, (b) _{20}^{40}Ca or _{20}^{45}Ca, (c) _{42}^{95}Mo or _{43}^{92}Tc, (d) ^{195}_{80}Hg or ^{196}_{80}Hg, (e) ^{209}_{83}Bi or ^{242}_{96}Cm. 

20.17 
Given that calculate the change in mass (in kg) per mole of H_{2} formed. 

20.18 
Estimates show that the total energy output of the sun is 5 × 10^{26} J/s. What is the corresponding mass loss in kg/s of the sun? 

20.19 
Calculate the nuclear binding energy (in joules) and the binding energy per nucleon of the following isotopes: 

20.20 
Calculate the nuclear binding energy (in joules) and the binding energy per nucleon of the following isotopes:


20.21 
Given that the nuclear binding energy of ^{48}Cr is 1.37340 × 10^{–12} J/nucleon, calculate the mass of a single ^{48}Cr atom. 

20.22 
Given that the nuclear binding energy of ^{192}Ir is 1.27198 × 10^{–12} J/nucleon, calculate the mass of a single ^{192}Ir atom. 

20.23 
Discuss factors that lead to nuclear decay. 

20.24 
Outline the principle for dating materials using radioactive isotopes. 

20.25 
Fill in the blanks in the following radioactive decay series:



20.26 
A radioactive substance undergoes decay as follows:
Calculate the firstorder decay constant and the halflife of the reaction. 


20.27 
The radioactive decay of T1206 to Pb206 has a halflife of 4.20 min. Starting with 5.00 × 10^{22} atoms of T1206, calculate the number of such atoms left after 42.0 min. 


20.28 
A freshly isolated sample of ^{90}Y was found to have an activity of 9.8 × 10^{5} 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 × 10^{4} disintegrations per minute. Calculate the halflife of ^{90}Y. 


20.29 
A wooden artifact has a ^{14}C activity of 18.9 disintegrations per minute, compared to 27.5 disintegrations per minute for live wood. Given that the halflife of ^{14}C is 5715 years, determine the age of the artifact. 


20.30 
In the thorium decay series, thorium232 loses a total of six α particles and four β particles in a 10stage process. What is the final isotope produced? 


20.31 
Consider the decay series A B C D where A, B, and C are radioactive isotopes with halflives 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. 


20.32 
The activity of radioactive carbon14 decay of a piece of charcoal found at a volcanic site is 11.2 disintegrations per second. If the activity of carbon14 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 halflife of carbon14.) 


20.33 
The age of some animal bones was determined by carbon14 dating to be 8.4 × 10^{3} years old. Calculate the activity of the carbon14 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 halflife of carbon14.) 


20.34 
Given that the halflife of ^{238}U is 4.51 × 10^{9} years, determine the age of a rock found to contain 1.09 mg ^{238}U and 0.08 mg ^{206}Pb. 


20.35 
Determine the ratio of ^{238}U to ^{206}Pb in a rock that is 1.7 × 10^{8} years old. (See Problem 20.34 for the halflife of ^{238}U.) 

20.36 
What is the difference between radioactive decay and nuclear transmutation? 

20.37 
How is nuclear transmutation achieved in practice? 

20.38 
Write balanced nuclear equations for the following reactions, and identify X: 


20.39 
Write the abbreviated forms for the following reactions:



20.40 
Write balanced nuclear equations for the following reactions, and identify X:(a) _{34}^{80}Se(d,p)X, (b) X(d,2p)_{3}^{9}Li, (c) ^{10}_{5}B(n,α)X. 


20.41 
Write the abbreviated forms for the following reactions:



20.42 
Describe how you would prepare astatine211, starting with bismuth209. 


20.43 
A longcherished dream of alchemists was to produce gold from cheaper and more abundant elements. This dream was finally realized when ^{198}_{80}Hg was converted into gold by neutron bombardment. Write a balanced equation for this reaction. 

VC 20.1 
The fission of ^{235}U 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 ^{235}U 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?



VC 20.4 
The fusion of ^{2}_{1}H and ^{3}_{1}H 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?


20.44 
Define nuclear fission, nuclear chain reaction, and critical mass. 

20.45 
Which isotopes can undergo nuclear fission? 

20.46 
Explain how an atomic bomb works. 

20.47 
Explain the functions of a moderator and a control rod in a nuclear reactor. 

20.48 
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? 

20.49 
No form of energy production is without risk. Make a list of the risks to society involved in fueling and operating a conventional coalfired electric power plant, and compare them with the risks of fueling and operating a nuclear fissionpowered electric plant. 

20.50 
Define nuclear fusion, thermonuclear reaction, and plasma. 

20.51 
Why do heavy elements such as uranium undergo fission whereas light elements such as hydrogen and lithium undergo fusion? 

20.52 
How does a hydrogen bomb work? 

20.53 
What are the advantages of a fusion reactor over a fission reactor? What are the practical difficulties in operating a largescale fusion reactor? 

20.54 
Describe how you would use a radioactive iodine isotope to demonstrate that the following process is in dynamic equilibrium: 

20.55 
Consider the following redox reaction: When KIO_{4} is added to a solution containing iodide ions labeled with radioactive iodine128, all the radioactivity appears in I_{2} and none in the IO_{3}^{–} ion. What can you deduce about the mechanism for the redox process? 

20.56 
Explain how you might use a radioactive tracer to show that ions are not completely motionless in crystals. 

20.57 
Each molecule of hemoglobin, the oxygen carrier in blood, contains four Fe atoms. Explain how you would use the radioactive _{26}^{59}Fe ( = 46 days) to show that the iron in a certain food is converted into hemoglobin. 
20.58 
^{125}I is produced by a twostep process in which ^{124}Xe nuclei are bombarded with neutrons to produce ^{125}Xe—a process called neutron activation. ^{125}Xe then decays by electron capture to produce ^{125}I, which also decays by electron capture. Write nuclear equations for the two steps that produce ^{125}I from ^{124}Xe, and identify the product of the electron capture decay of ^{125}I. 

20.59 
The halflife of ^{125}I is 59.4 days. How long will it take for the activity of implanted ^{125}I seeds to fall to 5.00 percent of their original value? 

20.60 
List the factors that affect the intensity of radiation from a radioactive element. 

20.61 
What are rad and rem, and how are they related? 

20.62 
Explain, with examples, the difference between somatic and genetic radiation damage. 

20.63 
Compare the extent of radiation damage done by α, β, and γ sources. 

20.64 
How does a Geiger counter work? 


20.65 
Strontium90 is one of the products of the fission of uranium235. This strontium isotope is radioactive, with a halflife 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. 


20.66 
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? 


20.67 
Tritium (^{3}H) is radioactive and decays by electron emission. Its halflife is 12.5 years. In ordinary water the ratio of ^{1}H to ^{3}H atoms is 1.0 × 10^{17} to 1. (a) Write a balanced nuclear equation for tritium decay. (b) How many disintegrations will be observed per minute in a 1.00kg sample of water? 


20.68 
(a) What is the activity, in millicuries, of a 0.500g sample of (This isotope decays by αparticle emission and has a halflife of 2.20 × 10^{6} years.) (b) Write a balanced nuclear equation for the decay of . 


20.69 
The following equations are for nuclear reactions that are known to occur in the explosion of an atomic bomb. Identify X.



20.70 
Calculate the nuclear binding energies (in J/nucleon) for the following species: (a) ^{10}B (10.0129 amu), (b) ^{11}B (11.009305 amu), (c) ^{14}N (14.003074 amu), (d) ^{56}Fe (55.93494 amu). 


20.71 
Write complete nuclear equations for the following processes: (a) tritium (^{3}H) undergoes β decay, (b) ^{242}Pu undergoes αparticle emission, (c) ^{131}I undergoes β decay, (d) ^{251}Cf emits an α particle. 


20.72 
The nucleus of nitrogen18 lies above the stability belt. Write the equation for a nuclear reaction by which nitrogen18 can achieve stability. 


20.73 
Why is strontium90 a particularly dangerous isotope for humans? The halflife of strontium90 is 29.1 years. Calculate the radioactivity in millicuries of 15.6 mg of ^{90}Sr. 


20.74 
How are scientists able to tell the age of a fossil? 


20.75 
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? 


20.76 
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 lowenergy neutrons, converting some of the nitrogen14 nuclei to nitrogen15, 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 Xray detection method. 


20.77 
Astatine, the last member of Group 7A, can be prepared by bombarding bismuth209 with α particles. (a) Write an equation for the reaction. (b) Represent the equation in the abbreviated form as discussed in Section 20.4. 


20.78 
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). 


20.79 
The carbon14 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? 


20.80 
Tritium contains one proton and two neutrons. There is no significant protonproton repulsion present in the nucleus. Why, then, is tritium radioactive? 


20.81 
The usefulness of radiocarbon dating is limited to objects no older than 60,000 years. What percent of the carbon14, originally present in the sample, remains after this period of time? 


20.82 
The radioactive potassium40 isotope decays to argon40 with a halflife of 1.2 × 10^{9} years. (a) Write a balanced equation for the reaction. (b) A sample of moon rock is found to contain 18 percent potassium40 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.) 


20.83 
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 ^{90}Sr (89.907738 amu): The ^{90}Y (89.907152 amu) further decays as follows: Zirconium90 (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 ^{90}Sr, calculate the number of moles of ^{90}Sr that will decay in a year. (c) Calculate the amount of heat released (in kJ) corresponding to the number of moles of ^{90}Sr decayed to ^{90}Zr in part (b). 


20.84 
Which of the following poses a greater health hazard: a radioactive isotope with a short halflife or a radioactive isotope with a long halflife? Explain. [Assume the same type of radiation (α or β) and comparable energetics per particle emitted.] 


20.85 
From the definition of curie, calculate Avogadro's number, given that the molar mass of ^{226}Ra is 226.03 g/mol and that it decays with a halflife of 1.6 × 10^{3} years. 


20.86 
As a result of being exposed to the radiation released during the Chernobyl nuclear accident, the dose of iodine131 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 iodine131 to which this radioactivity corresponds. (The halflife of ^{131}I is 8.1 days.) 


20.87 
(a) Calculate the energy released when a U238 isotope decays to Th234. The atomic masses are as follows: U238: 238.05078 amu; Th234: 234.03596 amu; and He4: 4.002603 amu. (b) The energy released in part (a) is transformed into the kinetic energy of the recoiling Th234 nucleus and the α particle. Which of the two will move away faster? Explain. 


20.88 
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? 


20.89 
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.) 


20.90 
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? 


20.91 
Cobalt60 is an isotope used in diagnostic medicine and cancer treatment. It decays with γray emission. Calculate the wavelength of the radiation in nanometers if the energy of the γ ray is 2.4 × 10^{–13} J/photon. 


20.92 
Americium241 is used in smoke detectors because it has a long halflife (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. 


20.93 
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 halflives of the isotopes are: ^{13}C: 5715 years; ^{15}O: 124 s; ^{3}H: 12.5 years. Assume that the activities of the isotopes were known at the time the bottle was sealed. 

20.94 
Name two advantages of a nuclearpowered submarine over a conventional submarine. 

20.95 
In 1997 a scientist at a nuclear research center in Russia placed a thin shell of copper on a sphere of highly enriched uranium235. 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.) 

20.96 
A radioactive isotope of copper decays as follows: Starting with 84.0 g of ^{64}Cu, calculate the quantity of ^{64}Zn produced after 18.4 h. 

20.97 
A 0.0100g sample of a radioactive isotope with a halflife of 1.3 × 10^{9} years decays at the rate of 2.9 × 10^{4} disintegrations per minute. Calculate the molar mass of the isotope. 

20.98 
The halflife of ^{27}Mg is 9.50 min. (a) Initially there were 4.20 × 10^{12} ^{27}Mg nuclei present. How many ^{27}Mg nuclei are left 30.0 min later? (b) Calculate the ^{27}Mg activities (in Ci) at t = 0 and t = 30.0 min. (c) What is the probability that any one ^{27}Mg nucleus decays during a 1s interval? What assumption is made in this calculation? 

20.99 
(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 = r_{0}A^{1/3}, where r_{0}, the proportionality constant, is given by 1.2 × 10^{–15} m. Calculate the volume of the ^{238}U nucleus. 

20.100 
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? 

20.101 
Isotope X decays to isotope Y with a halflife of 45 days. Which diagram most closely represents the sample of X after 105 days? 

20.102 
In 2006, an exKGB agent was murdered in London. The investigation following the agent's death revealed that he was poisoned with the radioactive isotope ^{210}Po, which had apparently been added to his food. (a) ^{210}Po is prepared by bombarding ^{209}Bi with neutrons. Write an equation for the reaction. (b) The halflife of ^{210}Po is 138 days. It decays by αparticle 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 ^{210}Po, ^{206}Pb, and ^{4}_{2}α are 209.98286, 205.97444, and 4.00150 amu, respectively. (d) Ingestion of 1 μg of ^{210}Po could prove fatal. What is the total energy released by this quantity of ^{210}Po over the course of 138 days? 

20.103 
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 ^{226}Ra is stored in a closed container for 125 years. (Assume that there are five α particles generated per ^{226}Ra as it decays to ^{206}Pb.) 

20.104 
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. 
20.105 
Iridium192 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 ^{191}X(n,γ)^{192}Ir. (b) The mass of an ^{125}I nucleus is 124.904624 amu. Calculate the nuclear binding energy and the nuclear binding energy per nucleon. 