Solution: Outline the principle for dating materials using

How do nuclear reactions differ from ordinary chemical reactions?

What are the steps in balancing nuclear equations?

What is the difference between 21 0 e and 21 0 ?

What is the difference between an electron and a positron?

Which of the following nuclear decays produces a daughter nucleus with a higher atomic number? , 0 11, 0 21, .

The table here is a summary of different modes of nuclear decay. Fill in the changes in atomic number (Z), number of neutrons (N), and mass number (A) in each case. Use 1 sign for increase, 2 sign for decrease, and 0 for no change.

Complete the following nuclear equations and identify X in each case: (a) 26 12Mg 1 1 1p 4 2 1 X (b) 59 27Co 1 2 1H 60 27Co 1 X (c) 235 92 U 1 1 0n 94 36Kr 1 139 56Ba 1 3X (d) 53 24Cr 1 4 2 1 0n 1 X (e) 20 8O 20 9F 1 X

Complete the following nuclear equations and identify X in each case: (a) 135 53I 135 54Xe 1 X (b) 40 19K 0 21 1 X (c) 59 27Co 1 1 0n 56 25Mn 1 X (d) 235 92U 1 1 0n 99 40Zr 1 135 52Te 1 2X

State the general rules for predicting nuclear stability.

What is the belt of stability?

Why is it impossible for the isotope 2 2He to exist?

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) 232Th 228Th (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.)