Calculate the nuclear binding energy per nucleon for

Define nuclear binding energy, mass defect, and nucleon

How does Einsteins equation, E 5 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 3 1023 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: (a) 6 3Li or 9 3Li, (b) 23 11Na or 25 11Na, (c) 48 20Ca or 48 21Sc.

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) 20 10Ne and 10 17Ne, (b) 40 20Ca and 45 20Ca, (c) 95 42Mo and 92 43Tc, (d) 195 80Hg and 196 80Hg, (e) 209 83Bi and 242 96Cm.

Given that H(g) 1 H(g) H2(g) H 5 2436.4 kJ/mol calculate the change in mass (in kg) per mole of H2 formed

Estimates show that the total energy output of the sun is 5 3 1026 J/s. What is the corresponding mass loss in kg/s of the sun?

Calculate the nuclear binding energy (in J) and the binding energy per nucleon of the following isotopes: (a) 7 3Li (7.01600 amu) and (b) 35 17Cl (34.95952 amu).

Calculate the nuclear binding energy (in J) and the binding energy per nucleon of the following isotopes: (a) 4 2He (4.0026 amu) and (b) 184 74W (183.9510 amu).

Discuss factors that lead to nuclear decay

Outline the principle for dating materials using radioactive isotopes.

Fill in the blanks in the following radioactive decay series: (a) 2228Th (b) 235U 227Ac (c) 233Pa

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 halflife of the reaction.

The radioactive decay of Tl-206 to Pb-206 has a half-life of 4.20 min. Starting with 5.00 3 1022 atoms of Tl-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 3 105 disintegrations per minute at 1:00 p.m. on December 3, 2003. At 2:15 p.m. on December 17, 2003, its activity was redetermined and found to be 2.6 3 104 disintegrations per minute. Calculate the half-life of 90Y.

Why do radioactive decay series obey first-order kinetics?

In the thorium decay series, thorium-232 loses a total of 6 particles and 4 particles in a 10-stage process. What is the final isotope produced?

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 yr. Calculate how long (in yr) it will take for 1.00 g of the isotope to be reduced to 0.200 g by decay.

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

Two radioactive isotopes X and Y have the same molar amount at t 5 0. A week later, there are four times as many X as there are Y. If the half-life of X is 2.0 d, calculate the half-life of Y in days.

Determine the symbol A ZX for the parent nucleus whose decay produces the same daughter as the 0 21 decay of 220 85At.

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: (a) X(p,) 12 6C, (b) 27 13Al(d,)X, (c) 55 25Mn(n,)X

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

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 198 80Hg was converted into gold by neutron bombardment. Write a balanced equation for this reaction.

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.

Define nuclear fusion, thermonuclear reaction, and plasma.

Why do heavy elements such as uranium undergo fission while 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: PbI2(s) Pb21(aq) 1 2I2(aq)

Consider the following redox reaction: IO2 4 (aq) 1 2I2(aq) 1 H2O(l2 I2(s) 1 IO2 3 (aq) 1 2OH2(aq) 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 2 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 26 59Fe (t1 2 5 46 days) to show that the iron in a certain food is converted into hemoglobin.

In the chapter, we saw that the unit curie corresponds to exactly 3.70 3 1010 nuclear disintegration per second for 1 g of radium. Derive this unit given that the half-life of 226 88Ra is 1.6 3 103 yr

Manganese-50 (red spheres) decays via 0 11 particle emission with a half-life of 0.282 s. (a) Write a balanced nuclear equation for the process. (b) From the diagram shown here, determine how many half-lives have elapsed. (The green spheres represent the decay product.)

How does a Geiger counter work?

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, 3 H, is radioactive and decays by electron emission. Its half-life is 12.5 yr. In ordinary water the ratio of 1 H to 3 H atoms is 1.0 3 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 237 93Np? (This isotope decays by -particle emission and has a half-life of 2.20 3 106 yr.) (b) Write a balanced nuclear equation for the decay of 237 93Np

The following equations are for nuclear reactions that are known to occur in the explosion of an atomic bomb. Identify X. (a) 235 92U 1 1 0n 140 56Ba 1 31 0n 1 X (b) 235 92U 1 1 0n 144 55Cs 1 90 37Rb 1 2X (c) 235 92U 1 1 0n 87 35Br 1 31 0n 1 X (d) 235 92U 1 1 0n 160 62Sm 1 72 30Zn 1 4X

Calculate the nuclear binding energies, in J/nucleon, for the following species: (a) 10B (10.0129 amu), (b) 11B (11.00931 amu), (c) 14N (14.00307 amu), (d) 56Fe (55.9349 amu).

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

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

Why is strontium-90 a particularly dangerous isotope for humans?

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

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?

Astatine, the last member of Group 7A, can be prepared by bombarding bismuth-209 with particles. (a) Write an equation for the reaction. (b) Represent the equation in the abbreviated form, as discussed in Section 19.4

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 rays. Because nitrogen content is usually high in explosives, detection of a high dosage of 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.

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).

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

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?

The usefulness of radiocarbon dating is limited to objects no older than 50,000 yr. 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 3 109 yr. (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

Both barium (Ba) and radium (Ra) are members of Group 2A and are expected to exhibit similar chemical properties. However, Ra is not found in barium ores. Instead, it is found in uranium ores. Explain

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 decay of 90Sr (89.907738 amu): 90 38Sr 90 39Y 1 0 21 t 1 2 5 28.1 yr The 90Y (89.907152 amu) further decays as follows: 90 39Y 90 40Zr 1 0 21 t 1 2 5 64 h 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 above two decays. (The mass of the electron is 5.4857 3 1024 amu.) (b) Starting with one mole of 90Sr, calculate the number of moles of 90Sr that will decay in a year. (c) Calculate the amount of heat released (in kilojoules) corresponding to the number of moles of 90Sr decayed to 90Zr in (b).

Calculate the energy released (in joules) from the following fusion reaction: 2 1H 1 3 1H 4 2He 1 1 0n The atomic masses are 2 1H 5 2.0140 amu, 3 1H 5 3.01603 amu, 4 2He 5 4.00260 amu, 1 0n 5 1.008665 amu.

As a result of being exposed to the radiation released during the Chernobyl nuclear accident, the dose of iodine-131 in a persons body is 7.4 mCi (1 mCi 5 1 3 1023 Ci). Use the relationship rate 5 lN to calculate the number of atoms of iodine-131 to which this radioactivity corresponds. (The half-life of 131I is 8.1 d.)

Referring to the Chemistry in Action essay on p. 890, why is it highly unlikely that irradiated food would become radioactive?

From the definition of curie, calculate Avogadros number, given that the molar mass of 226Ra is 226.03 g/mol and that it decays with a half-life of 1.6 3 103 yr.

As of 2011, elements 113 through 118 have all been synthesized. Element 113 (Uut) was formed by the alpha decay of element 115 (Uup); element 114 (Uuq) was created by bombarding 244Pu with 48Ca; element 115 (Uup) was created by bombarding 243Am with 48Ca; element 116 (Uuh) was created by bombarding 248Cm with 48Ca; element 117 (Uus) was created by bombarding 249Bk with 48Ca; element 118 (Uuo) was created by bombarding 249Cf with 48Ca. Write an equation for each synthesis. Predict the chemical properties of these elements. (Before transuranium elements are given proper names, they are temporarily assigned three-letter symbols all starting with U.)

Sources of energy on Earth include fossil fuels, geothermal, gravitational, hydroelectric, nuclear fission, nuclear fusion, solar, wind. Which of these have a nuclear origin, either directly or indirectly?

A person received an anonymous gift of a decorative box, 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 air-tight 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 need to consult a handbook of chemistry.)

(a) Calculate the energy released when an U-238 isotope decays to Th-234. The atomic masses are given by: U-238: 238.0508 amu; Th-234: 234.0436 amu; He-4: 4.0026 amu. (b) The energy released in (a) is transformed into the kinetic energy of the recoiling Th-234 nucleus and the particle. Which of the two will move away faster? Explain.

Cobalt-60 is an isotope used in diagnostic medicine and cancer treatment. It decays with ray emission. Calculate the wavelength of the radiation in nanometers if the energy of the ray is 2.4 3 10213 J/photon

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

The constituents of wine contain, among others, carbon, hydrogen, and oxygen atoms. A bottle of wine was sealed about 6 yr 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: 5730 yr; 15O: 124 s; 3 H: 12.5 yr. Assume that the activities of the isotopes were known at the time the bottle was sealed

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 damage. Explain what caused the accident. (Hint: Copper is an effective metal for reflecting neutrons.)

A radioactive isotope of copper decays as follows: 64Cu 64Zn 1 0 21 t 1 2 5 12.8 h 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 halflife of 1.3 3 109 yr decays at the rate of 2.9 3 104 dpm. Calculate the molar mass of the isotope.

In each of the diagrams shown here, identify the isotopes involved and the type of decay process. Use the A ZX symbol for each isotope. N Z 32 33 (a) 39 40 N Z 47 48 (b) 65 66 N Z 84 85 86 (c) 134 136 135

The diagram here shows part of the thorium decay series. Write a nuclear equation for each step of decay. Use the A ZX symbol for each isotope. 144 N Z 86 142 140 138 136 88 90 92

The half-life of 27Mg is 9.50 min. (a) Initially there were 4.20 3 1012 27Mg nuclei present. How many 27Mg nuclei are left 30.0 min later? (b) Calculate the 27Mg activities (in Ci) at t 5 0 and t 5 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?

The radioactive isotope 238Pu, used in pacemakers, decays by emitting an alpha particle with a half- life of 86 yr. (a) Write an equation for the decay process. (b) The energy of the emitted alpha particle is 9.0 3 10213 J, which is the energy per decay. Assuming that all the alpha particle energy is used to run the pacemaker, calculate the power output at t 5 0 and t 5 10 yr. Initially 1.0 mg of 238Pu was present in the pacemaker. (Hint: After 10 yr, the activity of the isotope decreases by 8.0 percent. Power is measured in watts or J/s.)

(a) Assuming nuclei are spherical in shape, show that its radius (r) is proportional to the cube root of mass number (A). (b) In general, the radius of a nucleus is given by r 5 r0A 1 3, where r0, the proportionality constant, is given by 1.2 3 10215 m. Calculate the volume of the 238U nucleus.

The quantity of a radioactive material is often measured by its activity (measured in curies or millicuries) rather than by its mass. In a brain scan procedure, a 70-kg patient is injected with 20.0 mCi of 99mTc, which decays by emitting -ray photons with a half-life of 6.0 h. Given that the RBE of these photons is 0.98 and only two-thirds of the photons are absorbed by the body, calculate the rem dose received by the patient. Assume all of the 99mTc nuclei decay while in the body. The energy of a gamma photon is 2.29 3 10214 J

Describe, with appropriate equations, nuclear processes that lead to the formation of the noble gases He, Ne, Ar, Kr, Xe, and Rn. (Hint: Helium is formed from radioactive decay, neon is formed from the positron emission of 22Na, the formation of Ar, Xe, and Rn are discussed in the chapter, and Kr is produced from the fission of 235U.)

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?

What is the source of heat for volcanic activities on Earth?

Alpha particles produced from radioactive decays eventually pick up electrons from the surroundings to form helium atoms. Calculate the volume (mL) of He collected at STP when 1.00 g of pure 226Ra is stored in a closed container for 100 yr. (Hint: Focusing only on half-lives that are short compared to 100 years and ignoring minor decay schemes in Table 19.3, first show that there are 5 particles generated per 226Ra decay to 206Pb.)

In 2006, an ex-KGB agent was murdered in London. Subsequent investigation showed that the cause of death was poisoning with the radioactive isotope 210Po, which was added to his drinks/food. (a) 210Po is prepared by bombarding 209Bi with neutrons. Write an equation for the reaction. (b) Who discovered the element polonium? (Hint: See Appendix 1.) (c) The halflife of 210Po is 138 d. It decays with the emission of an particle. Write an equation for the decay process. (d) Calculate the energy of an emitted particle. Assume both the parent and daughter nuclei to have zero kinetic energy. The atomic masses are: 210Po (209.98285 amu), 206Pb (205.97444 amu), 4 2 (4.00150 amu). (e) Ingestion of 1 g of 210Po could prove fatal. What is the total energy released by this quantity of 210Po?

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

The volume of an atoms nucleus is 1.33 3 10242 m3 . The nucleus contains 110 neutrons. Identify the atom and write the symbol of the atom as A ZX. (Hint: See Problem 19.97.)

In the chapter, we learned to calculate the nuclear binding energy, which pertains to the stability of a particular nucleus. It is also possible to estimate the binding energy of a single nucleon (neutron or proton) to the remainder of the nucleus. (a) From the following nuclear equation and nuclear masses, calculate the binding energy of a single neutron: 14 7N 13 7N 1 1 0n (Useful information: 14 7N: 14.003074 amu; 13 7N: 13.005738 amu; 1 0n: 1.00866 amu.) (b) By a similar procedure, we can calculate the binding energy of a single proton according to the equation 14 7N 13 6C 1 1 1p (Useful information: 13 6C: 13.003355 amu; 1 1p: 1.00794 amu.) Comment on your results.

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? Assume equal molar amounts and the same type of radiation and comparable energies per particle emitted.

To start a deuterium-deuterium fusion reaction, it has been estimated that each nucleus needs an initial kinetic energy of about 4 3 10214 J. What would be the corresponding temperature for the process? Why is this temperature value an overestimate?

In a science fiction novel a nuclear engineer designed a car powered by deuterium-deuterium fusion. Over a certain period of time, the car consumed 0.2 g of deuterium fuel. How many gallons of gasoline would have to be burned to equal the energy generated by the deuterium fuel? (For useful information about gasoline energy content, see Problem 17.73.)

The leakage of radioactive materials to the environment when a nuclear reactor core malfunctions is often made worse by explosions at the nuclear plant caused by hydrogen gas, as was the case in Fukushima, Japan, in 2011. Explain what caused the hydrogen explosion. (Useful information: The nuclear fuel rods are held in zirconium alloy tubes.)

Problem 1E What is radioactivity? Who discovered it? How was it discovered?

What daughter nuclide forms when polonium-214 undergoes alpha decay?

Problem 2E Explain Marie Curie’s role in the discovery of radioactivity.

Which nuclear equation accurately represents the beta decay of Xe-133?

Define A , Z , and X in the following notation used to specify a nuclide:

Problem 3SAQ Which nuclide is most likely to undergo beta decay? a) Si-22 b) Rb-91 c) Ar-35 d) Co-52

Use the notation from Question 3 to write symbols for a proton, a neutron, and an electron.

Problem 5E What is an alpha particle? What happens to the mass number and atomic number of a nuclide that emits an alpha particle?

Problem 4SAQ Which form of radioactive decay would you be most likely to detect if it were happening in the room next to the one you are currently in? a) alpha b) beta c) gamma d) positron emission

Problem 6E What is a beta particle? What happens to the mass number and atomic number of a nuclide that emits a beta particle?

The chart below shows the mass of a decaying nuclide versus time. What is the half-life of the decay? a) 15 min b) 25 min c) 35 min d) 70 min

Problem 6SAQ Iron-59 is a beta emitter with a half-life of 44.5 days. If a sample initially contains 132 mg of iron-59, how much iron-59 is left in the sample after 265 days? a) 0.00 mg b) 2.13 mg c) 33.2 mg d) 66.0 mg

Problem 7E What is a gamma ray? What happens to the mass number and atomic number of a nuclide that emits a gamma ray?

An artifact has a carbon-14 decay rate of 8.55 disintegrations per minute per gram of carbon (8.55 dis/min g C). Living organisms have carbon-14 decay rate of 15.3 dis/min g C. How old is the artifact? (The half-life of carbon-14 is 5730 yr.) a) 4.81 x 103 yr b) 2.10 x 103 yr c) 3.20 x 103 yr d) 1.21 x 10-4 yr

Problem 8E What is a positron? What happens to the mass number and atomic number of a nuclide that emits a positron?

An igneous rock contains a Pb-206/U-238 mass ratio of 0.372. How old is the rock? (U-238 decays into Pb-206 with a half-life of 4.5 x 109 yr.) a) 4.50 x 109 yr b) 6.42 x 109 yr c) 2.05 x 109 yr d) 2.32 x 109 yr

Problem 9E Describe the process of electron capture. What happens to the mass number and atomic number of a nuclide that undergoes electron capture?

Calculate the nuclear binding energy per nucleon for cobalt-59, the only stable isotope of cobalt. The mass of cobalt-59 is 58.933198 amu. (The mass of is 1.00783 amu, and the mass of a neutron is 1.00866 amu.) a) 517.3 MeV b) 8.768 MeV c) 19.16 MeV d) 1.011 x 10-5 MeV

Problem 10E Rank alpha particles, beta particles, positrons, and gamma rays in terms of: (a) increasing ionizing power (b) increasing penetrating power.

Problem 10SAQ Which problem is not associated with nuclear power generation? a) danger of overheated nuclear core b) waste disposal c) global warming d) none of the above (All of the above are problems associated with nuclear power generation.)

Explain why the ratio of neutrons to protons (N/Z) is important in determining nuclear stability. How can you use the N/Z ratio of a nuclide to predict the kind of radioactive decay that it might undergo?

Problem 12E What are magic numbers? How are they important in determining the stability of a nuclide?

Describe the basic way that each device detects radioactivity: (a) film-badge dosimeter; (b) Geiger-Müller counter; and (c) scintillation counter.

Problem 14E Explain the concept of half-life with respect to radioactive nuclides. What rate law is characteristic of radioactivity?

Explain the main concepts behind the technique of radiocarbon dating. How can radiocarbon dating be corrected for changes in atmospheric concentrations of C-14? What range of ages can be reliably determined by C-14 dating?

Problem 16E How is the uranium to lead ratio in a rock used to estimate its age? How does this dating technique provide an estimate for Earth's age? How old is Earth according to this dating method?

Problem 17E Describe fission. Include the concepts of chain reaction and critical mass in your description. How and by whom was fission discovered? Explain how fission can be used to generate electricity.

Problem 18E What was the Manhattan Project? Briefly describe its development and culmination.

Problem 19E Describe the advantages and disadvantages of using fission to generate electricity.

Problem 20E The products of a nuclear reaction usually have a different mass than the reactants. Why?

Problem 21E Explain the concepts of mass defect and nuclear binding energy. At what mass number does the nuclear binding energy per nucleon peak? What is the significance of this?

Problem 22E What is fusion? Why can fusion and fission both produce energy? Explain.

Problem 23E What are some of the problems associated with using fusion to generate electricity?

Problem 24E Explain transmutation and provide one or two examples.

Problem 25E How does a linear accelerator work? For what purpose is it used?

Problem 26E Explain the basic principles of cyclotron function.

Problem 27E How does radiation affect Irving organisms?

Problem 28E Explain why different kinds of radiation affect biological tissues differently, even though the amount of radiation exposure may be the same.

Problem 29E Explain the significance of the biological effectiveness factor in measuring radiation exposure. What types of radiation would you expect to have the highest biological effectiveness factor?

Problem 30E Describe some of the medical uses, both in diagnosis and in treatment of disease, of radioactivity.

Problem 31E Write a nuclear equation for the indicated decay of each nuclide: a. U-234 (alpha) b. Th-230 (alpha) c. Pb-214 (beta) d. N-13 (positron emission) e. Cr-51 (electron capture)

Write a nuclear equation for the indicated decay of each nuclide: (a) Po-210 (alpha) (b) Ac-227 (beta) (c) Tl-207 (beta) (d) O-15 (positron emission) (e) Pd-103 (electron capture)

Write a partial decay series for Th-232 undergoing the sequential decays: , , , .

Write a partial decay series for Rn-220 undergoing the sequential decays: , , , .

Fill in the missing particles in each nuclear equation.

Fill in the missing particles in each nuclear equation.

Problem 37E Determine whether or not each nuclide is likely to be stable. State your reasons. a. Mg-26 b. Ne-25 c. Co-51 d. Te-124

Problem 38E Determine whether or not each nuclide is likely to be stable. State your reasons, a. Ti-48 b. Cr-63 c. Sn-102 d. Y-S8

Problem 40E Neon and magnesium each has three stable isotopes while sodium and aluminum each has only one. Explain why this might be so.

The first six elements of the first transition series have the following number of stable isotopes: Explain why Sc, V, and Mn each has only one stable isotope while the other elements have several.

Problem 41E Predict a likely mode of decay for each unstable nuclide. a. Mo-109 b. Ru-90 c. P-27 d. Rn-196

Problem 42E Predict a likely mode of decay for each unstable nuclide. a. Sb-132 b. Te-139 c. Fr-202 d. Ba-123

Problem 43E Which one of each pair of nuclides would you expect to have the longer half-life? a. Cs-113 or Cs-125 b. Fe-62 or Fe-70

Problem 44E Which one of each pair of nuclides would you expect to have the longer half-life? a. Cs-149 or Cs-139 b. Fe-45 or Fe-52

Problem 45E One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will take for the amount of U-235 to reach 10.0% of its initial amount?

A patient is given 0.050 mg of technetium-99m, a radioactive isotope with a half-life of about 6.0 hours. How long does it take for the radioactive isotope to decay to 1.0 x 10-3 mg ? (Assume no excretion of the nuclide from the body.)

Problem 47E A radioactive sample contains 1.55 g of an isotope with a half-life of 3.8 days. What mass of the isotope remains after 5.5 days? (Assume no excretion of the nuclide from the body.)

Problem 48E At 8:00 a.m., a patient receives a 58 mg dose of I-131 to obtain an image of her thyroid. If the nuclide has a half-life of 8 days, what mass of the nuclide remains in the patient at 5:00 p.m. the next day?

A sample of F-18 has an initial decay rate of 1.5 x 105/s. How long will it take for the decay rate to fall to 2.5 x 103/s? (F-18 has a half-life of 1.83 hours.)

A sample of Tl-201 has an initial decay rate of 5.88 x 104/s. How long will it take for the decay rate to fall to 287/s? (Tl-201 has a half-life of 3.042 days.)

Problem 51E A wooden boat discovered just south of the Great Pyramid in Egypt has a carbon-14/carbon-12 ratio that is 72.5% of that found in living organisms. How old is the boat?

Problem 52E A layer of peat beneath the glacial sediments of the last ice age has a carbon-14/carbon-12 ratio that is 22.8% of that found in living organisms. How long ago was this ice age?

An ancient skull has a carbon-14 decay rate of 0.85 disintegrations per minute per gram of carbon ( 0.85 dis/min g C ). How old is the skull? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min g C and that carbon-14 has a halflife of 5730 yr.)

A mammoth skeleton has a carbon-14 decay rate of 0.48 disintegrations per minute per gram of carbon ( 0.48 dis/min g C ). When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min g C and that carbon-14 has a half-life of 5730 yr.)

Problem 55E A rock from Australia contains 0.438 g of Pb-206 to every 1.00 g of U-238. Assuming that the rock did not contain any Pb-206 at the time of its formation, how old is the rock?

Problem 56E A meteor has a Pb-206:U-238 mass ratio of 0.855:1.00. What is the age of the meteor? (Assume that the meteor did not contain any Pb-206 at the time of its formation.)

Problem 57E Write the nuclear reaction for the neutron-induced fission of U-235 to form Xe-144 and Sr-90. How many neutrons are produced in the reaction?

Problem 58E Write the nuclear reaction for the neutron-induced fission of U-235 to produce Te-137 and Zr-97. How many neutrons are produced in the reaction?

Problem 59E Write the nuclear equation for the fusion of two H-2 atoms to form He-3 and one neutron.

Problem 60E Write the nuclear equation for the fusion of H-3 with H-1 to form He-4.

Problem 61E A breeder nuclear reactor is a reactor in which non fissionable (nonfissile) U-238 is converted into fissionable (fissile) Pu-239. The process involves bombardment of U-238 by neutrons to form U-239, which then undergoes two sequential beta decays. Write nuclear equations for this process.

Problem 62E Write the series of nuclear equations to represent the bombardment of Al-27 with a neutron to form a product that subsequently undergoes an alpha decay followed by a beta decay.

Problem 63E Rutherfordium-257 was synthesized by bombarding Cf-249 with C-12. Write the nuclear equation for this reaction.

Problem 64E Element 107, now named bohrium, was synthesized by German researchers by colliding bismuth-209 with chromium-54 to form a bohrium isotope and one neutron. Write the nuclear equation to represent this reaction.

Problem 65E If 1.0 g of matter is converted to energy, how much energy is formed?

A typical home uses approximately \(1.0\times10^3\mathrm{\ kWh}\) of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?

Problem 67E Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. O-16 (atomic mass = 15.994915 amu) b. Ni-58 (atomic mass = 57.935346 amu) c. Xe-129 (atomic mass = 128.904780 amu)

Problem 68E Calculate the mass defect and nuclear binding energy per nucleon of each nuclide. a. Li-7 (atomic mass = 7.016003 amu) b. Ti-48 (atomic mass = 47.947947 amu) c. Ag-107 (atomic mass = 106.905092 amu)

Problem 69E Calculate the quantity of energy produced per gram of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to form Xe-144 ( atomic mass = 143.9385 amu ) and Sr-90 ( atomic mass = 89.907738 amu ) (discussed in Problem 57). REFERENCE: Write the nuclear reaction for the neutron-induced fission of U-235 to form Xe-144 and Sr-90. How many neutrons are produced in the reaction?

Problem 70E Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58). REFERENCE: Write the nuclear reaction for the neutron-induced fission of U-235 to produce Te-137 and Zr-97. How many neutrons are produced in the reaction?

Problem 71E Calculate the quantity of energy produced per gram of reactant for the fusion of two H-2 (atomic mass = 2.014102 amu) atoms to form He-3 (atomic mass = 3.016029 amu) and one neutron (discussed in Problem 59). REFERENCE: Write the nuclear equation for the fusion of two H-2 atoms to form He-3 and one neutron.

Problem 72E Calculate the quantity of energy produced per gram of reactant for the fusion of H-3 (atomic mass = 3.016049 amu) with H-1 (atomic mass = 1.007825 amu) to form He-4 (atomic mass = 4.002603 amu ) (discussed in Problem 60). REFERENCE: Write the nuclear equation for the fusion of H-3 with H-1 to form He-4.

Problem 73E A 75 kg human is exposed to 32.8 rad of radiation. How much energy is absorbed by the person’s body? Compare this energy to the amount of energy absorbed by the person’s body if they jumped from a chair to the floor (assume that the chair is 0.50 m from the ground and that all of the energy from the fall is absorbed by the person).

Problem 75E PET studies require fluorine-18, which is produced in a cyclotron and decays with a half-life of 1.83 hours. Assuming that the F-18 can be transported at 60.0 miles/hour, how close must the hospital be to the cyclotron if 65% of the F-18 produced makes it to the hospital?

If a 55-gram laboratory mouse is exposed to 20.5 rad of radiation, how much energy is absorbed by the mouse’s body?

Problem 76E Suppose a patient is given 155 mg of I-131, a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person’s body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?

Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each. (Be-9 = 9.012182 amu, Bi-209 = 208.980384 amu, He-4 = 4.002603 amu, Li-6 = 6.015122 amu, Ni-64 = 63.927969 amu, Rg-272 = 272.1535 amu, Ta-179 = 178.94593 amu, and W-179 = 178.94707 amu).

Complete each nuclear equation and calculate the energy change (in J/mol of reactant) associated with each. (Al-27 = 26.981538 amu, Am-241 = 241.056822 amu, He-4 = 4.002603 amu, Np-237 = 237.048166 amu, P-30 = 29.981801 amu, S-32 = 31.972071 amu, and Si-29 = 28.976495 amu).

Problem 79E Write the nuclear equation for the most likely mode of decay for each unstable nuclide: a. Ru-114 b. Ra-216 c. Zn-58 d. Ne-31

Problem 80E Write the nuclear equation for the most likely mode of decay for each unstable nuclide: a. Kr-74 b. Th-221 c. Ar-44 d. Nb-85

Problem 81E Bismuth-210 is a beta emitter with a half-life of 5.0 days. If a sample contains 1.2 g of Bi-210 ( atomic mass = 209.984105 amu ), how many beta emissions occur in 13.5 days? If a person’s body intercepts 5.5% of those emissions, to what dose of radiation (in Ci) is the person exposed?

Problem 82E Polonium-218 is an alpha emitter with a half-life of 3.0 minutes. If a sample contains 55 mg of Po-218 (atomic mass = 218.008965 amu), how many alpha emissions occur in 25.0 minutes? If the polonium is ingested by a person, to what dose of radiation (in Ci) is the person exposed?

Radium-226 ( atomic mass = 226.025402 amu ) decays to radon-224 (a radioactive gas) with a half-life of 1.6 x 103 years. What volume of radon gas (at 25.0 oC and 1.0 atm) does 25.0 g of radium produce in 5.0 days? (Report your answer to two significant digits.)

In one of the neutron-induced fission reactions of U-235 ( atomic mass = 235.043922 amu ), the products are Ba-140 and Kr-93 (a radioactive gas). What volume of Kr-93 (at 25.0 oC and 1.0 atm) is produced when 1.00 g of U-235 undergoes this fission reaction?

Problem 85E When a positron and an electron annihilate one another, the resulting mass is completely converted to energy. Calculate the energy associated with this process in kJ/mol.

Problem 86E A typical nuclear reactor produces about 1.0 MW of power per day. What is the minimum rate of mass loss required to produce this much energy?

Find the binding energy in an atom of 3He, which has a mass of 3.016030 amu.

Problem 88E The overall hydrogen burning reaction in stars can be represented as the conversion of four protons to one ? particle. Use the data for the mass of H-1 and He-4 to calculate the energy released by this process.

The nuclide 247Es can be made by bombardment of 238U in a reaction that emits five neutrons. Identify the bombarding particle.

The nuclide 6Li reacts with 2H to form two identical particles. Identify the particles.

The half-life of 238U is 4.5 x 109 yr. A sample of rock of mass 1.6 g produces 29 dis/s. Assuming all the radioactivity is due to 238U, find the percent by mass of 238U in the rock.

The half-life of 232Th is 1.4 x 1010 yr. Find the number of disintegrations per hour emitted by 1.0 mol of 232Th in 1 minute.

A 1.50 L gas sample at 745 mm Hg and \(25.0\ ^{\circ}\mathrm{C}\) contains 3.55% radon-220 by volume. Radon-220 is an alpha-emitter with a half-life of 55.6 s. How many alpha particles are emitted by the gas sample in 5.00 minutes?

A 228 mL sample of an aqueous solution contains 2.35% MgCl2 by mass. Exactly one-half of the magnesium ions are Mg-28, a beta emitter with a half-life of 21 hours. What is the decay rate of Mg-28 in the solution after 4.00 days? (Assume a density of 1.02 g>mL for the solution.)

Problem 95E When a positron and an electron collide and annihilate each other, two photons of equal energy are produced. Find the wavelength of these photons.

The half-life of 235U , an alpha emitter, is 7.1 x 108 yr. Calculate the number of alpha particles emitted by 1.0 mg of this nuclide in 1.0 minute.

Given that the energy released in the fusion of two deuterons to a 3He and a neutron is 3.3 MeV, and in the fusion to tritium and a proton it is 4.0 MeV, calculate the energy change for the process 3He + 1n 3H + 1p . Suggest an explanation for why this process occurs at much lower temperatures than either of the first two.

The nuclide 18F decays by both electron capture and decay. Find the difference in the energy released by these two processes. The atomic masses are 18F = 18.000950 and 18O = 17.9991598 .

The space shuttle carries about 72,500 kg of solid aluminum fuel, which is oxidized with ammonium perchlorate according to the reaction shown here: The space shuttle also carries about 608,000 kg of oxygen (which reacts with hydrogen to form gaseous water). a. Assuming that aluminum and oxygen are the limiting reactants, determine the total energy produced by these fuels. ( for solid ammonium perchlorate is -295 kJ/mol. ) b. Suppose that a future space shuttle is powered by matter– antimatter annihilation. The matter could be normal hydrogen (containing a proton and an electron) and the antimatter could be antihydrogen (containing an antiproton and a positron). What mass of antimatter is required to produce the energy equivalent of the aluminum and oxygen fuel currently carried on the space shuttle?

Suppose that an 85.0-gram laboratory animal ingests 10.0 mg of a substance that contained 2.55% by mass Pu-239, an alpha emitter with a half-life of 24,110 years. a. What is the animal’s initial radiation exposure in curies? b. If all of the energy from the emitted alpha particles is absorbed by the animal’s tissues, and if the energy of each emission is \(7.77 \times 10^{-12} \ J\) , what is the dose in rads to the animal in the first 4.0 hours following the ingestion of the radioactive material? Assuming a biological effectiveness factor of 20, what is the 4.0-hour dose in rems?

Problem 101E In addition to the natural radioactive decay series that begins with U-238 and ends with Pb-206, there are natural radioactive decay series that begin with U-235 and Th-232. Both of these series end with nuclides of Pb. Predict the likely end product of each series and the number of ? decay steps that occur.

The hydride of an unstable nuclide of a Group IIA metal, MH2(s) , decays by a-emission. A 0.025 mol sample of the hydride is placed in an evacuated 2.0 L container at 298 K. After 82 minutes, the pressure in the container is 0.55 atm. Find the half-life of the nuclide.

The nuclide \({ }^{38} \mathrm{Cl}\) decays by beta emission with a half-life of 40.0 min. A sample of 0.40 mol of \(\mathrm{H}\ { }^{38} \mathrm{Cl}\) is placed in a 6.24 L container. After 80.0 min the pressure is 1650 mmHg. What is the temperature of the container?

When BF3 is bombarded with neutrons, the boron undergoes an decay, but the F is unaffected. A 0.20 mol sample of BF3 contained in a 3.0 L container at 298 K is bombarded with neutrons until half of the BF3 has reacted. What is the pressure in the container at 298 K?

Closely examine the diagram representing the beta decay of fluorine-21 and draw in the missing nucleus.

Problem 106E Approximately how many half-lives must pass for the amount of radioactivity in a substance to decrease to below 1% of its initial level?

Problem 107E A person is exposed for 3 days to identical amounts of two different nuclides that emit positrons of roughly equal energy. The halflife of nuclide A is 18.5 days and the half-life of nuclide B is 255 days. Which of the two nuclides poses the greater health risk?

Problem 108E Identical amounts of two different nuclides, an alpha emitter and a gamma emitter, with roughly equal half-lives are spilled in a building adjacent to your bedroom. Which of the two nuclides poses the greater health threat to you while you sleep in your bed? If you accidentally wander into the building and ingest equal amounts of the two nuclides, which one poses the greater health threat?

Drugstores in many areas now carry tablets, under such trade names as Iosat and NoRad, designed to be taken in the event of an accident at a nuclear power plant or a terrorist attack that releases radioactive material. These tablets contain potassium iodide (KI). Can you explain the nature of the protection that they provide? (Hint: see the label in the photo.)