CONCEPT MAP: ACIDS AND BASES
11.11 Nuclear Fission and Nuclear Fusion
In the preceding section, we saw that particle bombardment of various elements causes artificial transmutation and results in the formation of new, usually heavier elements. Under very special conditions with a very few isotopes, however, different kinds of nuclear events occur. Certain very heavy nuclei can split apart, and certain very light nuclei can fuse together. The two resultant processes—nuclear fission for the fragmenting of heavy nuclei and nuclear fusion for the joining together of light nuclei—have changed the world since their discovery in the late 1930s and early 1940s.
The huge amounts of energy that accompany these nuclear processes are the result of mass-to-energy conversions and are predicted by Einstein’s equation
E = mc2
where E = energy, m = mass change associated with the nuclear reaction, and c = the speed of light 13.0 * 108 m/s2. Based on this relationship, a mass change as small as 1 μg results in a release of 2.15 * 104 kcal 19.00 * 104 kJ2 of energy!
Nuclear Fission
Uranium-235 is the only naturally occurring isotope that undergoes nuclear fission.
When this isotope is bombarded by a stream of relatively slow-moving neutrons, its nucleus splits to give isotopes of other elements. The split can take place in more than 400 ways, and more than 800 different fission products have been identified. One of the more frequently occurring pathways generates barium-142 and krypton-91, along with 2 additional neutrons plus the 1 neutron that initiated the fission:
1
0n + 23592U h 14256Ba + 9136Kr + 3 10n
As indicated by the balanced nuclear equation above, one neutron is used to ini- tiate fission of a 235U nucleus, but three neutrons are released. Thus, a nuclear chain reaction can be started: 1 neutron initiates one fission that releases 3 neutrons. Those 3 neutrons initiate three new fissions that release 9 neutrons. The 9 neutrons initiate nine fissions that release 27 neutrons, and so on at an ever-faster pace (Figure 11.7).
It is worth noting that the neutrons produced by fission reactions are highly ener- getic. They possess penetrating power greater than a and b particles, but less than g rays. In a nuclear fission reactor, the neutrons must first be slowed down to allow them to react. If the sample size is small, many of the neutrons escape before initiat- ing additional fission events, and the chain reaction stops. If a sufficient amount of
235U is present, however—an amount called the critical mass—then the chain re- action becomes self-sustaining. Under high-pressure conditions that confine the
235U to a small volume, the chain reaction occurs so rapidly that a nuclear explo- sion results. For 235U, the critical mass is about 56 kg, although the amount can be reduced to approximately 15 kg by placing a coating of 238U around the 235U to reflect back some of the escaping neutrons.
An enormous quantity of heat is released during nuclear fission—the fission of just 1.0 g of uranium-235 produces 3.4 * 108 kcal 11.4 * 109 kJ2 for instance. This heat can be used to convert water to steam, which can be harnessed to turn huge generators and produce electric power. Although the United States, France, and Japan are respon- sible for nearly 50% of all nuclear power generated worldwide, only about 19% of the
Nuclear fusion The joining together of light nuclei.
Nuclear fission The fragmenting of heavy nuclei.
Chain reaction A reaction that, once started, is self-sustaining.
Critical mass The minimum amount of radioactive material needed to sus- tain a nuclear chain reaction.
electricity consumed in the United States is nuclear-generated. In France, nearly 80%
of electricity is generated by nuclear power plants.
Two major objections that have caused much public debate about nuclear power plants are safety and waste disposal. Although a nuclear explosion is not possible under the conditions that typically exist in a power plant, there is a serious potential radia- tion hazard should an accident rupture the containment vessel holding the nuclear fuel and release radioactive substances to the environment. There have been several such instances in the last 35 years, most notably Three Mile Island in Pennsylvania (1979), Chernobyl in the Ukraine (1986), and the more recent Fukushima reactor damaged by the tsunami in Japan (2011). Perhaps even more important is the problem posed by disposal of radioactive wastes from nuclear plants. Many of these wastes have such long half-lives that hundreds or even thousands of years must elapse before they will be safe for humans to approach. How to dispose of such hazardous materials safely is an unsolved problem.
Neutron
Neutrons
Neutrons Neutrons
91Kr
36
14256Ba
23592U
23592U
23592U
23592U
▲ Figure 11.7 A chain reaction.
Each fission event produces additional neutrons that induce more fissions. The rate of the process increases at each stage. Such chain reactions usually lead to the formation of many different fission products in addition to the two indicated.
S U M M A R Y Revisiting the Chapter Goals 351
PROBLEM 11.19
What other isotope besides tellurium-137 is produced by nuclear fission of uranium-235?
23592U + 10n h 13752Te + 2 10n + ?
Nuclear Fusion
Just as heavy nuclei such as 235U release energy when they undergo fission, very light nuclei such as the isotopes of hydrogen release enormous amounts of energy when they undergo fusion. In fact, it is just such a fusion reaction of hydrogen nuclei to produce helium that powers our sun and other stars. Among the processes thought to occur in the sun are those in the following sequence leading to helium-4:
1
1H + 21H h 32He
32He + 32He h 42He + 211H
3
2He + 11H h 42He + 01e
Under the conditions found in stars, where the temperature is on the order of 2 * 107 K and pressures approach 105 atmospheres, nuclei are stripped of all their electrons and have enough kinetic energy that nuclear fusion readily occurs. The energy of our sun, and all the stars, comes from thermonuclear fusion reactions in their core that fuse hydrogen and other light elements, transmuting them into heavier elements. On Earth, however, the necessary conditions for nuclear fusion are not eas- ily created. For more than 50 years scientists have been trying to create the necessary conditions for fusion in laboratory reactors, including the Tokamak Fusion Test Reac- tor (TFTR) at Princeton, New Jersey, and the Joint European Torus (JET) at Culham, England. Recent advances in reactor design have raised hopes that a commercial fusion reactor will be realized within the next 20 years.
If the dream becomes reality, controlled nuclear fusion can provide the ultimate cheap, clean power source. The fuel is deuterium 12H2, available in the oceans in limit- less amounts, and there are few radioactive by-products.
PROBLEM 11.20
One of the possible reactions for nuclear fusion involves the collision of 2 deuterium nuclei. Complete the reaction by identifying the missing particle:
2
1H + 21H h 10n + ?
SUMMARY: REVISITING THE CHAPTER GOALS
1. What is a nuclear reaction, and how are equations for nuclear reactions balanced? A nuclear reaction is one that changes an atomic nucleus, causing the change of one element into another. Loss of an a particle leads to a new atom whose atomic number is 2 less than that of the starting atom. Loss of a b particle leads to an atom whose atomic number is 1 greater than that of the starting atom:
a emission: 23892U h 23490Th + 42He b emission: 13153 h 13154Xe+ -10 e
A nuclear reaction is balanced when the sum of the nucleons (protons and neutrons) is the same on both sides of the reaction arrow and when the sum of the charges on the nuclei plus any ejected subatomic particles is the same (see Problems 22, 24, 26, 38, 40, 41, 44–53, 81, 82, 84, 85, 90–95).
2. What are the different kinds of radioactivity? Radioac- tivity is the spontaneous emission of radiation from the nucleus of an unstable atom. The three major kinds of radiation are called alpha 1a2, beta 1b2, and gamma 1g2. Alpha radiation consists of helium nuclei, small particles containing 2 protons and
UNDERSTANDING KEY CONCEPTS
2 neutrons 142He2; b radiation consists of electrons 1-10e2; and g radiation consists of high-energy light waves. Every element in the periodic table has at least one radioactive isotope, or radio- isotope (see Problems 22, 25, 27, 29, 30–32, 40, 41, 44–47, 49, 81, 82, 93).
3. How are the rates of nuclear reactions expressed? The rate of a nuclear reaction is expressed in units of half-life 1t1>22, where one half-life is the amount of time necessary for one half of the radioactive sample to decay (see Problems 21, 23, 28, 29, 54–59, 77, 83, 85).
4. What is ionizing radiation? High-energy radiation of all types—a particles, b particles, g rays, and X rays—is called ion- izing radiation. When any of these kinds of radiation strikes an atom, it dislodges an orbital electron and gives a reactive ion that can be lethal to living cells. Gamma rays and X rays are the most penetrating and most harmful types of external radiation; a and b particles are the most dangerous types of internal radiation because of their high energy and the resulting damage to sur- rounding tissue (see Problems 33–37, 63, 65, 72, 76, 84, 86, 87).
5. How is radioactivity measured? Radiation intensity is expressed in different ways according to the property being measured. The curie (C i) measures the number of radioactive
disintegrations per second in a sample; the roentgen (R) measures the ionizing ability of radiation. The rad measures the amount of radiation energy absorbed per gram of tissue; and the rem measures the amount of tissue damage caused by radiation.
Radiation effects become noticeable with a human exposure of 25 rem and become lethal at an exposure above 600 rem (see Problems 60–69, 79, 80).
6. What is transmutation? Transmutation is the change of one element into another brought about by a nuclear reaction.
Most known radioisotopes do not occur naturally but are made by bombardment of an atom with a high-energy particle. In the ensuing collision between particle and atom, a nuclear change occurs and a new element is produced by artificial transmutation (see Problems 38, 39, 48, 50, 51, 53, 90, 94, 95).
7. What are nuclear fission and nuclear fusion? With a very few isotopes, including 23592U, the nucleus is split apart by neutron bombardment to give smaller fragments. A large amount of energy is released during this nuclear fission, lead- ing to use of the reaction for generating electric power. Nuclear fusion results when small nuclei such as those of tritium 131H2 and deuterium 121H2 combine to give a heavier nucleus (see Problems 42, 43, 48, 88, 91, 92).
KEY WORDS
Alpha (A) particle, p. 331 Artificial transmutation, p. 347 Beta (B) particle, p. 331
Chain reaction, p. 349 Cosmic rays, p. 341 Critical mass, p. 349 Decay series, p. 341
Electron capture (E.C.), p. 335
Gamma (G) radiation, p. 331 Half-life 1t1,22 p. 337
Ionizing radiation, p. 341 Nuclear decay, p. 332 Nuclear fission, p. 349 Nuclear fusion, p. 349 Nuclear reaction, p. 329 Nucleon, p. 329
11.21 Magnesium-28 decays by b emission to give aluminum-28.
If yellow spheres represent 2812Mg atoms and blue spheres represent
28
13Al atoms, how many half-lives have passed in the following sample?
11.22 Write a balanced nuclear equation to represent the decay reaction described in Problem 11.21.
11.23 Refer to Figure 11.4 and then make a drawing similar to those in Problem 11.21 representing the decay of a sample of 2812Mg after approximately four half-lives have passed.
11.24 Write the symbol of the isotope represented by the fol- lowing drawing. Blue spheres represent neutrons and red spheres represent protons.
11.25 Shown in the following graph is a portion of the decay series for plutonium-241 124194Pu2. The series has two kinds of arrows: shorter arrows pointing right and longer arrows pointing
Nuclide, p. 329 Positron, p. 335 Radioactivity, p. 330 Radioisotope, p. 331 Radionuclide, p. 331 Transmutation, p. 332 X rays, p. 341
Additional Problems 353 left. Which arrow corresponds to an a emission, and which to a
b emission? Explain.
148
90
Atomic number (Z)
Number of neutrons
92 94 96
146 144 142
140
11.26 Identify and write the symbol for each of the five nuclides in the decay series shown in Problem 11.25.
11.27 Identify the isotopes involved, and tell the type of decay process occurring in the following nuclear reaction:
81
80
79 67
Atomic Number
68 69
Neutrons
11.28 What is the half-life of the radionuclide that shows the following decay curve?
100
0
Time (years)
Sample remaining (%)
5 10 15 20 25
80 60 40 20 0
11.29 What is wrong with the following decay curve? Explain.
100
0
Days
Sample remaining (%)
10 20 30 40 50 60 70
80 60 40 20 0
ADDITIONAL PROBLEMS
RADIOACTIVITY
11.30 What does it mean to say that a substance is radioactive?
11.31 Describe how a radiation, b radiation, g radiation, posi- tron emission, and electron capture differ.
11.32 List three of the five ways in which a nuclear reaction dif- fers from a chemical reaction.
11.33 What happens when ionizing radiation strikes an atom in a chemical compound?
11.34 How does ionizing radiation lead to cell damage?
11.35 What are the main sources of background radiation?
11.36 How can a nucleus emit an electron during b decay when there are no electrons present in the nucleus to begin with?
11.37 What is the difference between an a particle and a helium atom?
NUCLEAR DECAY AND TRANSMUTATION
11.38 What does it mean to say that a nuclear equation is balanced?
11.39 What are transuranium elements, and how are they made?
11.40 What happens to the mass number and atomic number of an atom that emits an a particle? A b particle?
11.41 What happens to the mass number and atomic number of an atom that emits a g ray? A positron?
11.42 How does nuclear fission differ from normal radioactive decay?
11.43 What characteristic of uranium-235 fission causes a chain reaction?
11.44 What products result from radioactive decay of the fol- lowing b emitters?
(a) 3516S (b) 2410Ne (c) 9038Sr
11.45 What radioactive nuclides will produce the following products following a decay?
(a) 18676Os (b) 20485At (c) 24194Pu
11.46 Identify the starting radioisotopes needed to balance each of these nuclear reactions:
(a) ? + 42He h 11349In (b) ? + 42He h 137N + 10n
11.47 Identify the radioisotope product needed to balance each of these nuclear reactions:
(a) 2611Na h? + -01e (b) 21283Bi h ? + 42He 11.48 Balance the following equations for the nuclear
fission of 23592U:
(a) 23592U + 10n h 16062Sm + 7230Zn + ? 10n (b) 23592U + 10n h 8735Br + ? + 3 10n
11.49 Complete the following nuclear equations and identify each as a decay, b decay, positron emission, or electron capture:
(a) 12650Sn h ? + 12651Sb (b) 21088Ra h ? + 20686Rn (c) 7636Kr + ? h 7635Br
11.50 For centuries, alchemists dreamed of turning base metals into gold. The dream finally became reality when it was shown that mercury-198 can be converted into gold-198 when bombarded by neutrons. What small particle is pro- duced in addition to gold-198? Write a balanced nuclear equation for the reaction.
11.51 Cobalt-60 1half@life = 5.3 years2 is used to irradiate food, to treat cancer, and to disinfect surgical equipment. It is produced by irradiation of cobalt-59 in a nuclear reactor.
It decays to nickel-60. Write nuclear equations for the for- mation and decay reactions of cobalt-60.
11.52 Bismuth-212 attaches readily to monoclonal antibodies and is used in the treatment of various cancers. This bis- miuth-212 is formed after the parent isotope undergoes a decay series consisting of four a decays and one b decay.
(the decays could be in any order). What is the parent iso- tope for this decay series?
11.53 Meitnerium-266 1266109Mt2 was prepared in 1982 by bom- bardment of bismuth-209 atoms with iron-58. What other product must also have been formed? Write a balanced nuclear equation for the transformation.
HALF-LIFE
11.54 What does it mean when we say that strontium-90, a waste product of nuclear power plants, has a half-life of 28.8 years?
11.55 How many half lives must pass for the mass of a radioactive sample to decrease to 35% of the original mass? To 10%?
11.56 Selenium-75, a b emitter with a half-life of 120 days, is used medically for pancreas scans.
(a) Approximately how long would it take for a 0.050 g sample of selenium-75 to decrease to 0.010 g?
(b) Approximately how much selenium-75 would remain from a 0.050 g sample that has been stored for one year? (Hint: How many half-lives are in one year?) 11.57 Approximately how long would it take a sample of sele-
nium-75 to lose 75% of its radioactivity? To lose 99%?
(See Problem 11.56.)
11.58 The half-life of mercury-197 is 64.1 hours. If a patient undergoing a kidney scan is given 5.0 ng of mercury-197, how much will remain after 7 days? After 30 days?
11.59 Gold-198, a b emitter used to treat leukemia, has a half-life of 2.695 days. The standard dosage is about 1.0 mCi>kg body weight.
(a) What is the product of the b emission of gold-198?
(b) How long does it take a 30.0 mCi sample of gold-198 to decay so that only 3.75 mCi remains?
(c) How many millicuries are required in a single dosage administered to a 70.0 kg adult?
MEASURING RADIOACTIVITY 11.60 Describe how a Geiger counter works.
11.61 Describe how a film badge works.
11.62 Describe how a scintillation counter works.
11.63 Why are rems the preferred units for measuring the health effects of radiation?
11.64 Approximately what amount (in rems) of short-term expo- sure to radiation produces noticeable effects in humans?
11.65 Match each unit in the left column with the property being measured in the right column:
1.curie (a) Ionizing intensity of radiation 2.rem (b) Amount of tissue damage
3.rad (c) Number of disintegrations per second 4.roentgen (d) Amount of radiation per gram of tissue 11.66 Technetium-99m is used for radioisotope-guided surgical
biopsies of certain bone cancers. A patient must receive an injection of 28 mCi of technetium-99m 6–12 hours before surgery. If the activity of the solution is 15 mCi, what vol- ume should be injected?
11.67 Sodium-24 is used to study the circulatory system and to treat chronic leukemia. It is administered in the form of saline (NaCl) solution, with a therapeutic dosage of 180 mCi>kg body weight.
(a) What dosage (in mCi) would be administered to a 68 kg adult patient?
(b) How many milliliters of a 6.5 mCi>mL solution are needed to treat a 68 kg adult?
11.68 A selenium-75 source is producing 300 rem at a distance of 2.0 m?
(a) What is its intensity at 16 m?
(b) What is its intensity at 25 m?
11.69 If a radiation source has an intensity of 650 rem at 1.0 m, what distance is needed to decrease the intensity of exposure to below 25 rem, the level at which no effects are detectable?
CHEMISTRY IN ACTION
11.70 What are the three main classes of techniques used in nuclear medicine? Give an example of each. [Medical Uses of Radioactivity, p. 338]
11.71 A 2 mL solution containing 1.25 mCi>mL is injected into the bloodstream of a patient. After dilution, a 1.00 mL sample is withdrawn and found to have an activity of
Additional Problems 355
2.6 * 10-4mCi. Calculate total blood volume. [Medical Uses of Radioactivity, p. 338]
11.72 What is the purpose of food irradiation, and how does it work? [Irradiated Food, p. 345]
11.73 What kind of radiation is used to treat food? [Irradiated Food, p. 345]
11.74 What are the advantages of CT and PET relative to con- ventional X rays? [Body Imaging, p. 348]
11.75 What advantages does MRI have over CT and PET imag- ing? [Body Imaging, p. 348]
GENERAL QUESTIONS AND PROBLEMS
11.76 Film badge dosimeters typically include filters to target specific types of radiation. A film badge is constructed that includes a region containing a tin foil filter, a region containing a plastic film filter, and a region with no filter.
Which region monitors exposure to a-radiation? Which monitors exposure to b-radiation? Which monitors g-radiation? Explain.
11.77 Some dried beans with a 14C>12C ratio one-eighth of the cur- rent value are found in an old cave. How old are the beans?
11.78 Harmful chemical spills can often be cleaned up by treatment with another chemical. For example, a spill of H2SO4 might be neutralized by addition of NaHCO3. Why is it that the harmful radioactive wastes from nuclear power plants cannot be cleaned up as easily?
11.79 Why is a scintillation counter or Geiger counter more useful for determining the existence and source of a new radiation leak than a film badge?
11.80 A Geiger counter records an activity of 28 counts per min- ute (cpm) when located at a distance of 10 m. What will be the activity (in cpm) at a distance of 5 m?
11.81 Most of the stable isotopes for elements lighter than Ca-40 have equal numbers of protons and neutrons in the nucleus. What would be the most probable decay mode for an isotope that had more protons than neutrons? More neutrons than protons?
11.82 Technetium-99m, used for brain scans and to monitor heart function, is formed by decay of molybdenum-99.
(a) By what type of decay does 99Mo produce 99mTc?
(b) Molybdenum-99 is formed by neutron bombardment of a natural isotope. If one neutron is absorbed and there are no other by-products of this process, from what isotope is 99Mo formed?
11.83 The half-life of technetium-99m (Problem 11.82) is 6.01 hours. If a sample with an initial activity of 15 mCi is injected into a patient, what is the activity in 24 hours, assuming that none of the sample is excreted?
11.84 Plutonium-238 is an a emitter used to power batteries for heart pacemakers.
(a) Write the balanced nuclear equation for this emission.
(b) Why is a pacemaker battery enclosed in a metal case before being inserted into the chest cavity?
11.85 Sodium-24, a beta-emitter used in diagnosing circulation problems, has a half-life of 15 hours.
(a) Write the balanced nuclear equation for this emission.
(b) What fraction of sodium-24 remains after 50 hours?
11.86 High levels of radioactive fallout after the 1986 accident at the Chernobyl nuclear power plant in what is now Ukraine resulted in numerous miscarriages in humans and many instances of farm animals born with severe defects. Why are embryos and fetuses particularly susceptible to the ef- fects of radiation?
11.87 One way to demonstrate the dose factor of ionizing radia- tion (penetrating distance * ionizing energy) is to think of radiation as cookies. Imagine that you have four cookies—
an a cookie, a b cookie, a g cookie, and a neutron cookie.
Which one would you eat, which would you hold in your hand, which would you put in your pocket, and which would you throw away?
11.88 What are the main advantages of nuclear fission rela- tive to nuclear fusion as an energy source? What are the drawbacks?
11.89 Although turning lead into gold in a nuclear reactor is tech- nologically feasible (Problem 11.50), it is not economical. It is far easier to convert gold into lead. The process involves a series of neutron bombardments, and can be summarized as
197
79Au + ? 10n h 20482Pb + ? -10e How many neutrons and b particles are involved?
11.90 Balance the following transmutation reactions:
(a) 25399Es + ? h 256101Md + 10n (b) 25098Cf + 115B h ? + 4 10n
11.91 The most abundant isotope of uranium, 238U, does not undergo fission. In a breeder reactor, however, a 238U atom captures a neutron and emits 2 beta particles to make a fis- sionable isotope of plutonium, which can then be used as fuel in a nuclear reactor. Write the balanced nuclear equation.
11.92 Boron is used in control rods for nuclear reactors because it can absorb neutrons to keep a chain reaction from becoming supercritical, and decays by emitting alpha particles. Balance the equation:
105B + 10n h ? + 42He
11.93 Thorium-232 decays by a 10-step series, ultimately yield- ing lead-208. How many a particles and how many b particles are emitted?
11.94 Californium-246 is formed by bombardment of uranium-238 atoms. If four neutrons are formed as by-products, what particle is used for the bombardment?
11.95 The most recently discovered element 117 (Ununseptium, Uus) was synthesized by nuclear transmutation reactions in which berkelium-249 was bombarded with calcium-48.
Two isotopes of Uus were identified:
48
20Ca + 24997Bk h 294117Uus + ? 10n
4820Ca + 24997Bk h 293117Uus + ? 10n How many neutrons are produced in each reaction?