Chapter 10–1 Chapter 10 Nuclear Chemistry Solutions to In-Chapter Problems 10.1 Refer to Example 10.1 to answer the question. • The atomic number (Z) = the number of protons. • The mass number (A) = the number of protons + the number of neutrons. • Isotopes are written with the mass number to the upper left of the element symbol and the atomic number to the lower left of the element symbol. Atomic Number Mass Number Number of Protons Number of Neutrons Isotope Symbol Cobalt-59 27 59 27 32 27 Co 59 Cobalt-60 27 60 27 33 27 Co 60 10.2 Fill in the table as in Example 10.1, using the rules in Answer 10.1. Atomic Number Mass Number Number of Protons Number of Neutrons Sr 38 85 a. 38 85 38 47 Ga 31 67 b. 31 67 31 36 Selenium-75 c. 34 75 34 41 10.3 An α particle has no electrons around the nucleus and a +2 charge, whereas a helium atom has two electrons around the nucleus and is neutral. 10.4 Use Table 10.1 to identify Q in each of the following symbols. Q 4 2 Q 0 –1 Q a. b. c. 0 +1 ! particle " particle positron 10.5 Write a balanced nuclear equation as in Example 10.2. [1] Write an incomplete equation with the original nucleus on the left and the particle emitted on the right. Radon-222 has an atomic number of 86. 222 He 2 4 + ? 86 Rn [2] Calculate the mass number and the atomic number of the newly formed nucleus on the right. • Radon-222 emits an α particle. • Mass number: Subtract the mass of an α particle (4) to obtain the mass of the new nucleus; 222 – 4 = 218. • Atomic number: Subtract the two protons of an α particle to obtain the atomic number of the new nucleus; 86 – 2 = 84. [3] Use the atomic number to identify the new nucleus and complete the equation. E\ 0F*UDZ+LOO (GXFDWLRQ 7KLV LV SURSULHWDU\ PDWHULDO VROHO\ IRU DXWKRUL]HG LQVWUXFWRU XVH 1RW DXWKRUL]HG IRU VDOH RU GLVWULEXWLRQ LQ DQ\ PDQQHU 7KLV GRFXPHQW PD\ QRW EH FRSLHG VFDQQHG GXSOLFDWHG IRUZDUGHG GLVWULEXWHG RU SRVWHG RQ D ZHEVLWH LQ ZKROH RU SDUW
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Chapter 10–1
Chapter 10 Nuclear Chemistry Solutions to In-Chapter Problems 10.1 Refer to Example 10.1 to answer the question.
• The atomic number (Z) = the number of protons. • The mass number (A) = the number of protons + the number of neutrons. • Isotopes are written with the mass number to the upper left of the element symbol and the
atomic number to the lower left of the element symbol.
Atomic Number Mass Number Number of
Protons Number of Neutrons
Isotope Symbol
Cobalt-59 27 59 27 32 27Co59
Cobalt-60 27 60 27 33 27Co
60
10.2 Fill in the table as in Example 10.1, using the rules in Answer 10.1.
Atomic Number Mass Number Number of Protons
Number of Neutrons
Sr3885a.
38 85 38 47
Ga3167b.
31 67 31 36 Selenium-75c. 34 75 34 41
10.3 An α particle has no electrons around the nucleus and a +2 charge, whereas a helium atom has
two electrons around the nucleus and is neutral. 10.4 Use Table 10.1 to identify Q in each of the following symbols.
Q42Q0
–1 Qa. b. c. 0+1
! particle " particle positron 10.5 Write a balanced nuclear equation as in Example 10.2.
[1] Write an incomplete equation with the original nucleus on the left and the particle emitted on the right. Radon-222 has an atomic number of 86.
222 He2
4 + ?86Rn [2] Calculate the mass number and the atomic number of the newly formed nucleus on the
right. • Radon-222 emits an α particle. • Mass number: Subtract the mass of an α particle (4) to obtain the mass of the new
nucleus; 222 – 4 = 218. • Atomic number: Subtract the two protons of an α particle to obtain the atomic number of
the new nucleus; 86 – 2 = 84.
[3] Use the atomic number to identify the new nucleus and complete the equation.
• From the periodic table, the element with an atomic number of 84 is polonium, Po. • Write the mass number and the atomic number with the element symbol to complete the
equation.
2He + 84Po222 4 21886Rn
10.6 Work backwards to write the equation that produces radon-222.
?
22688Ra
2He + 86Rn2224
2He + 86Rn2224Mass number = 222 + 4 = 226
Atomic number = 86 + 2 = 88 10.7 Write the balanced nuclear equation for each isotope as in Example 10.2 or Answer 10.5.
84Po218 42He + 82Pb214a.
b. 90Th2302He + 88Ra4 226
c. 99Es2522He + 97Bk4 248
10.8 Write a balanced nuclear equation for the β emission of iodine-131 as in Example 10.2.
[1] Write an incomplete equation with the original nucleus on the left and the particle emitted on the right. • Use the identity of the element to determine the atomic number; iodine has an atomic
number of 53.
I53131 +e–1
0 ?
[2] Calculate the mass number and the atomic number of the newly formed nucleus on the
right. • Mass number: Since a β particle has no mass, the masses of the new particle and the
original particle are the same, 131. • Atomic number: Since β emission converts a neutron into a proton, the new nucleus has
one more proton than the original nucleus; 53 = –1 + ?. Thus, the new nucleus has an atomic number of 54.
[3] Use the atomic number to identify the new nucleus and complete the equation.
• From the periodic table, the element with an atomic number of 54 is xenon, Xe. • Write the mass number and the atomic number with the element symbol to complete the
10.9 Write a balanced nuclear equation for the β emission of each isotope as in Example 10.2 and Answer 10.8.
F9
20 +e–10 Ne
1020a.
Sr3892 +e–1
0 Y3992b.
c. Cr2455 +e–1
0 Mn2555
10.10 Write a balanced nuclear equation for positron emission as in Example 10.3. a. [1] Write an incomplete equation with the original nucleus on the left and the particle
emitted on the right. • Use the identity of the element to determine the atomic number; arsenic has an atomic
number of 33.
As3374 + ?e+1
0
[2] Calculate the mass number and the atomic number of the newly formed nucleus on the
right. • Mass number: Since a β+ particle has no mass, the masses of the new particle and the
original particle are the same, 74. • Atomic number: Since β+ emission converts a proton into a neutron, the new nucleus has
one fewer proton than the original nucleus; 33 – 1 = 32. Thus, the new nucleus has an atomic number of 32.
[3] Use the atomic number to identify the new nucleus and complete the equation.
• From the periodic table, the element with an atomic number of 32 is germanium, Ge. • Write the mass number and the atomic number with the element symbol to complete the
equation.
As3374 +e+1
0 Ge3274
b. Use the same steps as in part (a).
O815 +e+1
0 N715
10.11 When β and γ emission occur together, the atomic number increases by one (due to the β
particle), and a γ ray is released.
Ir77192 + e–1
0Pt78192 +
Both ! particles and " rays are emitted.
"
10.12 When γ emission occurs alone, there is no change in the atomic number or the mass number.
When β and γ emission occur together, the atomic number increases by one (due to the β particle), and a γ ray is released.
10.15 If an artifact has 1/8 of the amount of C-14 compared to living organisms, it has decayed by three half-lives (½ × ½ × ½).
1 half-life
5,730 yearsx =3 half-lives 17,200 years
10.16 Use the amount of radioactivity (mCi/mL) as a conversion factor to convert the dose of radioactivity from millicuries to a volume in milliliters.
x =110 mCi dose 1 mL25 mCi
Millicuries cancel.
4.4 mLAnswer
mCi–mL conversion factor
10.17 Use the conversion factor given to convert mrem to rem.
x =200 mrem 1 rem1000 mrem
0.2 rema. x =0.014 rem1 rem
1000 mrem 14 mremb.
larger dose 10.18 Calculate the number of half-lives that pass in nine days.
9 days 1 half-life3 days
x = 3 half-lives 12
=x 12
x 12
18
10.19
b. Sm62153 + e–1
0Eu63153
a. Sm62153
62 protons, 62 electrons153 – 62 = 91 neutrons
One ! particleis emitted.
Atomic number increases.
c. xinitial activity
12
150 mCi = 9.4 mCix 12
x 12
x 12
10.20 The emission of a positron decreases the atomic number by one, but the mass number stays the
10.21 Nuclear fission splits an atom into two lighter nuclei. Write the equation with the information given, and then balance the equation.
92U235 + 3 0n51Sb +133 1+ 0n
1
235 + 3 0n51Sb +13341Nb100 1+ 0n
1
?
The atomic number must be 41 = niobium:92 = 51 + X
The mass number of niobium must be 100:235 + 1 = 133 + X + 3, X = 100
92U 10.22 Balance each reaction.
+ +12 H1
1 H e+10a. 1
1 H b. 1
1 H + 12 H 2
3 He c. 1
1 H + 23 He 2
4 He + e+10
Solutions to End-of-Chapter Problems 10.23 Refer to Example 10.1 to answer the question.
• The atomic number (Z) = the number of protons. • The mass number (A) = the number of protons + the number of neutrons. • Isotopes are written with the mass number to the upper left of the element symbol and the
atomic number to the lower left of the element symbol.
a. Atomic Number
b. Number of Protons
c. Number of Neutrons d. Mass Number Isotope Symbol
Fluorine-18 9 9 9 18 F918
Fluorine-19 9 9 10 19 F9
19
10.24 Refer to Example 10.1 to answer the question.
• The atomic number (Z) = the number of protons. • The mass number (A) = the number of protons (Z) + the number of neutrons. • Isotopes are written with the mass number to the upper left of the element symbol and the
atomic number to the lower left of the element symbol.
a. Atomic number
b. Number of protons
c. Number of neutrons d. Mass number Isotope symbol
10.25 Fill in the table using Example 10.1 and the definitions in Answer 10.23.
Atomic Number Mass Number Number of
Protons Number of Neutrons
Isotope Symbol
a. Chromium-51 24 51 24 27 Cr2451
b. Palladium-103 46 103 46 57 Pd46
103
c. Potassium-42 19 42 19 23 K1942
d. Xenon-133 54 133 54 79 Xe54
133
10.26 Fill in the table using Example 10.1 and the definitions in Answer 10.23.
Atomic number Mass number Number of
protons Number of neutrons Isotope symbol
a. Sodium-24 11 24 11 13 Na1124
b. Strontrium-89 38 89 38 51 Sr38
89
c. Iron-59 26 59 26 33 Fe2659
d. Samarium-153 62 153 62 91 Sm62
153
10.27 Use the definitions in Section 10.1B and Table 10.1 to fill in the table.
Change in Mass Change in Charge a. α particle –4 –2 b. β particle 0 +1 c. γ ray 0 0 d. positron 0 –1
10.28 a. γ rays have the highest speed and α particles have the slowest speed. b. γ rays have the highest penetrating power and α particles have the lowest penetrating power.
c. Lab coats and gloves should be worn when working with substances that give off α particles. Heavy lab coats and gloves must be worn when working with substances that give off β particles. A lead shield is required to protect those working with substances that give off γ rays.
10.29 Use the definitions in Section 10.1B and Table 10.1 to fill in the table.
124 mg = 15.5 mg of phosphorus-32 124 – 15.5 = 109 mg of sulfur-32
c. 42 days = 3 half-lives
x 12
x 12
xinitial mass
12
124 mg = 7.75 mg of phosphorus-32 124 – 7.75 = 116 mg of sulfur-32
d. 56 days = 4 half-lives
x 12
x 12
x 12
10.47 If the half-life of an isotope is 24 hours, then two half-lives have passed in 48 hours. Therefore,
25% of the initial amount of isotope still remains.
xinitial mass
12
100% = 25%x 12
10.48 The half-life of carbon-14 can be used to date objects because the ratio of radioactive carbon-14
to stable carbon-12 is a constant value in living organisms. Once the organism dies, the radioactive carbon-14 decays and thus its concentration decreases. Scientists compare the ratio of C-14 to C-12 in an artifact to that in a living organism in order to determine the age of the artifact (i.e., the number of C-14 half-lives since death).
10.49 In artifacts over 50,000 years old, the percentage of carbon-14 is too small to accurately measure. 10.50 Radiocarbon dating can’t be used to estimate the age of rocks because the technique can only be
used for substances that are made of carbon. 10.51 Calculate the amount of radioactivity present after each amount of time has elapsed.
xinitial activity
12
20 mCi = 10 mCia.
6 h = one half-life
xinitial activity
12
20 mCi = 5 mCib.
12 h = two half-lives
x 12
xinitial activity
12
20 mCi = 1 mCic.
24 h = four half-lives
x 12
x 12
x 12
10.52 Calculate the amount of radioactivity present after each amount of time has elapsed.
10.63 Nuclear fission is the splitting of nuclei and nuclear fusion is the joining of small nuclei to form larger ones.
10.64 The difference between the nuclear fission process that takes place in a nuclear reactor and the
nuclear fission that occurs in an atomic bomb is the amount of uranium-235 present. When the amount present is equal to the critical mass (the amount required for a chain reaction to take place) an atomic explosion occurs. When the amount present is less than the critical mass, as in a nuclear reactor, the energy is produced in a manner that can be controlled.
10.65 a. Nuclear fusion is a reaction that occurs in the sun.
b. Nuclear fission occurs when a neutron is used to bombard a nucleus. c. In both nuclear fission and nuclear fusion a large amount of energy is released. d. Nuclear fusion reactions require very high temperatures.
10.66 a. Nuclear fission splits a nucleus into lighter nuclei. b. Nuclear fusion joins two lighter nuclei into a heavier nucleus. c. Nuclear fission is used to generate energy in a nuclear power plant. d. Nuclear fission generates radioactive waste with a long half-life. 10.67 Nuclear fission splits an atom into two lighter nuclei. Balance each equation.
U92235 n0
1+ n01+ + 2Mo42
97a. ?
U92235 n0
1+ n01+ + 2Mo42
97Sn50137
92 – 42 = 50 = atomic number for Sn
[235 + 1] – [97 + 2(1)] = 137 = mass number
U92235 n0
1+ +b. Ba56140 n0
1+ 3
Kr3693U92
235 n01+ + Ba56
140 n01+ 3
?
92 – 56 = 36 = atomic number for Kr
[235 + 1] – [140 + 3(1)] = 93 = mass number
10.68 Nuclear fission splits an atom into two lighter nuclei. Balance each equation.
10.71 Write out the equation from the information given. Then balance the equation.
H12 + H1
2 H13 + H1
1
tritium 10.72 Write out the equation from the information given. Then balance the equation.
He23 + He2
3 He24 + H1
12
10.73 Two problems with generating electricity from nuclear power plants include the containment of
radiation leaks and the disposal of radioactive waste. 10.74 There are no nuclear power plants that use nuclear fusion to produce electricity because the
process requires very high temperatures (> 100,000,000 °C) and pressures (> 100,000 atm).
10.81 a. Iodine-131 is used for the treatment and diagnosis of thyroid diseases. b. Iridium-192 is used for the treatment of breast cancer. c. Thallium-201 is used for the diagnosis of heart disease.
10.82 a. Iodine-125 is used for the treatment of prostate cancers.
b. Technetium-99 is used to evaluate the functioning of the gall bladder and bile ducts, to determine sites of internal bleeding, or to find the location of metastatic cancers. c. Cobalt-60 is used in radiation treatment for cancer.
10.83 a. Iodine-125, with its longer half-life, is used for the treatment of prostate cancers with
implanted radioactive seeds. b. Iodine-131, with its shorter half-life, is used for the diagnostic and therapeutic treatment of
thyroid diseases and tumors. A patient is administered radioactive iodine-131, which is then incorporated into the thyroid hormone, thyroxine. Since its half-life is short, the radioactive iodine isotope decays so that little remains after a month or so.
10.84 Food is irradiated with γ rays in order to kill harmful bacteria, thus extending its shelf life. 10.85 Radiology technicians must be shielded to avoid exposure to excessive and dangerous doses of
radiation. 10.86 A lead apron is placed over a patient’s body when dental X-rays are taken in order to protect the
patient from exposure to the radiation. 10.87 High doses of stable iodine will prevent the absorption and uptake of the radioactive iodine-131.
10.88 Exposure to strontium-90 is especially hazardous to children, because they have fast-growing, dividing cells and their bodies readily take up calcium. Any substance with properties similar to calcium would also be readily absorbed.
10.89 Use conversion factors to solve the problem.