3.E: Atoms and Nuclear Chemistry (Exercises)

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    The structure of the Atom

    PROBLEM 3-1 What are the charges and the relative masses of the three subatomic particles?

    PROBLEM 3-2 Describe the structure of an atom in terms of its protons, neutrons, and electrons.

    The Elements and The Periodic Table

    PROBLEM 3-3 What is an element? Why are chemical symbols so useful? What is the source of the letter(s) for a chemical symbol?

    PROBLEM 3-4 Write the chemical symbol for each element, try without consulting Table \(\PageIndex{3}\).

    1. Manganese, b. Magnesium, c. Neon, d. Nitrogen, e. Silver, f. Calcium, g. Gold, h. bromine, i. carbon

    PROBLEM 3-5 What element is represented by each chemical symbol?

    1. Na, b. Hg, c. Pb, d. Sn, e. U, f. O, g. F, h. P, i. K, j. I

    Atomic Number and Mass Number

    PROBLEM 3-6 What is the number of protons in the nucleus of each element? Use Table \(\PageIndex{1}\).

    a. sodium. p+=____________ b. oxygen. p+=____________ c. chlorine. p+=____________
    d. aluminum. p+=____________ e. iron. p+=____________ f. carbon. p+=____________

    PROBLEM 3-7 How many electrons are present in the atoms of each element?

    a. magnesium e-=____________ b. potassium e-=____________ c. iodine e-=____________
    d. sulfur e-=____________ e. hydrogen e-=____________ f. phosphorous. e-=____________

    Isotopes and Atomic Weight

    PROBLEM 3-8 How do isotopes of an element differ from each other?

    PROBLEM 3-9 Which of the following are isotopes of the same element? Explain.

    Isotopes.png

    PROBLEM 3-10 How many protons and neutrons are in each isotope?

    1. \(\mathrm{^{197}_{79}Au}\)
    2. \(\mathrm{^{23}_{11}Na}\)
    3. \(\mathrm{^{11}_5B}\)
    4. \(\mathrm{^{27}_{13}Al}\)
    5. 56Fe
    6. 224Rn
    7. \(\mathrm{^{2}_{1}H}\)
    8. \(\mathrm{^{112}_{48}Cd}\)
    9. 252Es
    10. 40K

    PROBLEM 3-11 Complete the following table.

    Number of Protons Number of Neutrons Element Name Isotope Symbol
          Isotope symbol 1.png

    95

    153

    		    
     

    21

    potassium

    		  

    PROBLEM 3-12 Define atomic mass. Why is it considered a weighted average?

    PROBLEM 3-13 In nature the element oxygen exists as three different isotopes, O-16, O-17, and O-18. Which isotope predominates? Explain.

    PROBLEM 3-14 Copper exists as a mixture of 2 isotopes. 63Cu and 65Cu. Which isotope predominates?

    Radiation

    PROBLEM 3-15 What are the major types of radioactivity? Write chemical equations demonstrating each type.

    PROBLEM 3-16 Which penetrates matter more deeply—alpha particles or beta particles? Suggest ways to protect yourself against both particles.

    PROBLEM 3-17 Which penetrates matter more deeply—alpha particles or gamma rays? Suggest ways to protect yourself against both emissions.

    PROBLEM 3-18 Give an example of a radioactive isotope.

    Nuclear Reactions and Nuclear Equations

    PROBLEM 3-19 Describe an alpha particle. What nucleus is it equivalent to?

    PROBLEM 3-20 Describe a beta particle. What subatomic particle is it equivalent to?

    PROBLEM 3-21 Explain what gamma rays are, and explain why it is inappropriate to refer to gamma rays as gamma “particles.”

    PROBLEM 3-22 Write the chemical equation for the alpha particle emission of:

    1. 244Pu. What is the daughter isotope? (Plutonium has an atomic number of 94)
    2. 212Fr. What is the daughter isotope? (Francium has an atomic number of 87)

    PROBLEM 3-23 Write the chemical equation for the beta particle emission of:

    1. 121Sn. What is the daughter isotope? (Tin has an atomic number of 50)
    2. 99Tc. What is the daughter isotope? (Technetium has an atomic number of 43)

    Units of Radioactivity

    PROBLEM 3-24 What units are used to quantify radioactivity?

    PROBLEM 3-25 Define: rad ​​​​​​ and rem.

    PROBLEM 3-26 How does a becquerel differ from a curie?

    PROBLEM 3-27 How is the curie defined?

    PROBLEM 3-28 A sample of radon gas has an activity of 140.0 mCi. If the half-life of radon is 1,500 y, how long before the activity of the sample is 8.75 mCi?

    PROBLEM 3-29 A sample of curium has an activity of 1,600 Bq. If the half-life of curium is 24.0 s, how long before its activity is 25.0 Bq?

    PROBLEM 3-30 If a radioactive sample has an activity of 65 µCi, how many disintegrations per second are occurring?

    PROBLEM 3-31 If a radioactive sample has an activity of 7.55 × 105 Bq, how many disintegrations per second are occurring?

    PROBLEM 3-32 Describe how a radiation exposure in rems is determined.

    PROBLEM 3-33 Which contributes more to the rems of exposure—alpha or beta particles? Why?

    PROBLEM 3-34 What percentage of the approximate annual radiation exposure comes from radioactive atoms that are in the body naturally?

    PROBLEM 3-35 Explain how:

    1. a film badge works to detect radiation
    2. a Geiger counter works to detect radiation.

    Uses of Radioactive Isotopes

    PROBLEM 3-36 Describe some of the different ways that amounts of radioactivity are applied in society.

    PROBLEM 3-37 Define what a tracer is and give an example of how tracers work.

    PROBLEM 3-38 Name two isotopes that have been used as tracers.

    PROBLEM 3-39 Explain how radioactive dating works.

    PROBLEM 3-40 Name an isotope that has been used in radioactive dating.

    PROBLEM 3-41 The current disintegration rate for carbon-14 is 14.0 Bq. A sample of burnt wood discovered in an archaeological excavation is found to have a carbon-14 decay rate of 3.5 Bq. If the half-life of carbon-14 is 5,700 y, approximately how old is the wood sample?

    PROBLEM 3-42 A small asteroid crashes to Earth. After chemical analysis, it is found to contain 1 g of technetium-99 to every 3 g of ruthenium-99, its daughter isotope. If the half-life of technetium-99 is 210,000 y, approximately how old is the asteroid?

    PROBLEM 3-43 What do you think are some of the positive aspects of irradiation of food?

    PROBLEM 3-44 What do you think are some of the negative aspects of irradiation of food?

    PROBLEM 3-45 Describe how iodine-131 is used to both diagnose and treat thyroid problems.

    PROBLEM 3-46 List at least five organs that can be imaged using radioactive isotopes.

    PROBLEM 3-47 Which radioactive emissions can be used therapeutically?

    PROBLEM 3-48 Which isotope is used in therapeutics primarily for its gamma ray emissions?

    PROBLEM 3-49 What volume of a radioisotope should be given if a patient needs 125 mCi of a solution which contains 45 mCi in 5.0 mL?

    PROBLEM 3-50 Sodium-24 is used to treat leukemia. A 36-kg patient is prescribed 145 μCi/kg and it is supplied to the hospital in a vial containing 250 μCi/mL. What volume should be given to the patient?

    PROBLEM 3-51 Lead-212 is one of the radioisotopes used in the treatment of breast cancer. A patient needs a 15 μCi dose and it is supplied as a solution with a concentration of 2.5 μCi/mL. What volume does the patient need? Given the half-life of lead is 10.6 hours, what will be the radioactivity of the sample after approximately four days?

    Half-Life

    PROBLEM 3-52 Define half-life.

    PROBLEM 3-53 Describe a way to determine the amount of radioactive isotope remaining after a given number of half-lives.

    PROBLEM 3-54 Do all isotopes have a half-life? Explain.

    PROBLEM 3-55 Which is more radioactive—an isotope with a long half-life or an isotope with a short half-life?

    PROBLEM 3-56 What percent of a sample remains after one half-life? Three half-lives?

    PROBLEM 3-57 The half-life of polonium-218 is 3.0 min. How much of a 0.540 mg sample would remain after 9.0 minutes have passed?

    PROBLEM 3-58 The half-life of protactinium-234 is 6.69 hours. If a 0.812 mg sample of Pa-239 decays for 40.14 hours, what mass of the isotope remains?

    PROBLEM 3-59 How long does it take for 1.00 g of 103Pd to decay to 0.125 g if its half-life is 17.0 d?

    PROBLEM 3-60 How long does it take for 2.00 g of 94Nb to decay to 0.0625 g if its half-life is 20,000 y?

    PROBLEM 3-61 It took 75 y for 10.0 g of a radioactive isotope to decay to 1.25 g. What is the half-life of this isotope?

    PROBLEM 3-62 It took 49.2 s for 3.000 g of a radioactive isotope to decay to 0.1875 g. What is the half-life of this isotope?

    Additional Exercises

    PROBLEM 3-63 Radioactive strontium is dangerous because it can chemically replace calcium in the human body. The bones are particularly susceptible to radiation damage. Write the nuclear equation for the beta emission of strontium-90.

    PROBLEM 3-64 Write the nuclear equation for the beta emission of iodine-131, the isotope used to diagnose and treat thyroid problems.

    PROBLEM 3-65 A banana contains 600 mg of potassium, 0.0117% of which is radioactive potassium-40. If 1 g of potassium-40 has an activity of 2.626 × 105 Bq, what is the activity of a banana?

    PROBLEM 3-66 Smoke detectors typically contain about 0.25 mg of americium-241 as part of the smoke detection mechanism. If the activity of 1 g of americium-241 is 1.26 × 1011 Bq, what is the activity of americium-241 in the smoke detector?

    Answers to Selected Problems

    The Elements and The Periodic Table

    PROBLEM 3-4 a. Mn b. Mg c. Ne d. N e. Ag f. Ca. g. Au. h.Br i. C

    PROBLEM 3-5 a. sodium. b. mercury. c. lead. d. tin. e. uranium. f. oxygen. g. fluorine. h. phosphorous. i. potassium. j. iodine

    Atomic Number and Mass Number

    PROBLEM 3-6 a. Sodium has 11 protons in its nucleus. b. Oxygen has 8 protons in its nucleus. c. Chlorine has 17 protons in its nucleus

    PROBLEM 3-7 a. Mg has 12 electrons. b. K has 19 electrons. c. I has 53 electrons.

    Isotopes and Atomic Weight

    PROBLEM 3-10

    1. In \(\mathrm{^{197}_{79}Au}\) there are 79 protons, and 197 − 79 = 118 neutrons in each nucleus.
    2. In \(\mathrm{^{23}_{11}Na}\) there are 11 protons, and 23 − 11 = 12 neutrons in each nucleus.
    3. 5 protons; 6 neutrons
    4. 13 protons; 14 neutrons
    5. 26 protons; 30 neutrons
    6. 86 protons; 138 neutrons
    7. 1 proton; 1 neutron
    8. 48 protons; 64 neutrons
    9. 99 protons;153 neutrons
    10. 19 protons; 21 neutrons

    Radiation

    PROBLEM 3-15 The major types of radioactivity are alpha decay, beta decay, and gamma ray emission; alpha decay with gamma emission: \(\mathrm{_{86}^{222}Rn \rightarrow \, _{84}^{218}Po + \, ^4_2He + \gamma}\); beta decay: \(\ce{_6^{14}C \rightarrow _7^{14}N + ^0_{-1}e}\) (answers will vary)

    PROBLEM 3-16 Beta particles; shielding of the appropriate thickness can protect against both alpha and beta particles.

    PROBLEM 3-17 Gamma rays; can be shielded by thick, dense material such as lead (Pb). Alpha particles has low energy; can shielded by a piece of paper.

    PROBLEM 3-18 C-14 or 14C is an example of radioactive isotope (answers may vary).

    Nuclear Reactions and Nuclear Equations

    PROBLEM 3-19 An alpha particle is a combination of two protons and two neutrons and is equivalent to a helium nucleus.

    PROBLEM 3-20 A beta particle is an electron.

    PROBLEM 3-21 Gamma rays are high-energy electromagnetic radiation given off in radioactive decay. Gamma rays have no mass. Hence, not a particle.

    PROBLEM 3-22

    a. \(\mathrm{^{244}_{94}Pu\rightarrow \, _2^4He +\, ^{240}_{92}U}\); the daughter isotope is \(\mathrm{^{240}_{92}U}\), an atom of uranium.

    b. \(\mathrm{^{212}_{87}Fr\rightarrow \, _2^4He +\, ^{208}_{85}At}\); the daughter isotope is \(\mathrm{^{208}_{85}At}\), an atom of astatine.

    PROBLEM 3-23

    a. \(\mathrm{_{50}^{121}Sn \rightarrow \, _{-1}^0e + \, _{51}^{121}Sb}\); the daughter isotope is \(\mathrm{_{51}^{121}Sb}\), an atom of antimony.

    b. \(\mathrm{_{43}^{99}Tc \rightarrow \, _{-1}^0e + \, _{44}^{99}Mo}\); the daughter isotope is \(\mathrm{_{44}^{99}Mo}\), an atom of antimony.

    Units of Radioactivity

    PROBLEM 3-24 the curie, the becquerel, the rad, the gray, the sievert, and the rem

    PROBLEM 3-25 A rad, known as the radiation absorbed dose, is the absorption of 0.01 J/g of tissue. A rem, known as the roentgen equivalent man, is an absorption of one rad times a factor. The factor is variable depending on the type of emission and the type of irradiated tissue.

    PROBLEM 3-26 A becquerel is smaller and equals 1 decay per second. A curie is 3.7 × 1010 Bq.

    PROBLEM 3-27 A curie is defined as 3.7 × 1010 decays per second.

    PROBLEM 3-28 6000 y

    PROBLEM 3-29 144 s

    PROBLEM 3-30 2.41 × 106 disintegrations per second

    PROBLEM 3-31 7.55 × 105 disintegrations per second

    PROBLEM 3-32 The radiation exposure is determined by the number of rads times the quality factor of the radiation.

    PROBLEM 3-33 Alpha contributes more than beta because of its bigger size and electrical charge.

    PROBLEM 3-34 About 11% come from radioactive atoms that are in the body naturally.

    PROBLEM 3-35 A film badge uses film, which is exposed as it is subjected to radiation. The Geiger counter consists of a tube with electrodes and is filled with an inert (argon) gas. Radiation entering the tube ionizes the gas, and the ions are attracted to the electrodes, producing an electric pulse (a clicking sound).

    Uses of Radioactive Isotopes

    PROBLEM 3-36 Radioactive isotopes are used in dating, as tracers, and in medicine as diagnostic and treatment tools.

    PROBLEM 3-37 A tracer follows the path of a chemical or a physical process. One of the uses of a tracer is following the path of water underground (answers will vary).

    PROBLEM 3-38 Tritium (3H) and Carbon-14 (14C) (answers will vary)

    PROBLEM 3-39 Radioactive dating works by comparing the amounts of parent and daughter isotopes and calculating back to how long ago all of the material was just the parent isotope.

    PROBLEM 3-40 Carbon-14 (14C) and Uranium-235 (235U) (answers will vary).

    PROBLEM 3-41 about 11,400 y

    PROBLEM 3-42 about 420,000 y

    PROBLEM 3-43 increased shelf life (answers will vary)

    PROBLEM 3-44 reduction in the food's vitamin content and cost

    PROBLEM 3-45 Iodine-131 is preferentially absorbed by the thyroid gland and can be used to measure the gland’s activity or destroy bad cells in the gland.

    PROBLEM 3-46 brain, bone, heart, thyroid, lung (answers will vary)

    PROBLEM 3-47 gamma rays, beta particles, or alpha particles

    PROBLEM 3-48 cobalt-60

    PROBLEM 3-49 125mCi x (5.0mL/45mCi)=14mL

    PROBLEM 3-50 36kg x (145μCi/kg) x (1mL/250μCi)=21mL

    PROBLEM 3-51 Volume given: 15μCi x (1mL/2.5μCi) = 6.0mL

    Elapsed time in hours: 4 days x (24 hr/day) = 96 hr

    Number of half-lives: 96 hrs/10.6 hours = 9

    Radioactivity remaining after 9 half-lives: 0.029 μCi

    Half-Life

    PROBLEM 3-52 Half-life is the amount of time needed for half of a radioactive material to decay.

    PROBLEM 3-53 Take half of the initial amount for each half-life of time elapsed

    PROBLEM 3-54 Only radioactive isotopes have half-lives.

    PROBLEM 3-55 An isotope with a shorter half-life decay more rapidly is more radioactive.

    PROBLEM 3-56 1 half-life: 50%; 3 half-lives: 12.5%

    PROBLEM 3-57 9.0 min = 3 half-lives (make 3 arrows): 0.540 mg --> 0.270 mg --> 0.135 mg --> 0.0675 mg

    PROBLEM 3-58 0.0127 mg

    PROBLEM 3-59 51.0 d

    PROBLEM 3-60 100 000 y

    PROBLEM 3-61 25 y

    PROBLEM 3-62 12.3 s

    Additional Exercises

    PROBLEM 3-63 \(\mathrm{^{90}_{38}Sr\rightarrow \, _{-1}^{0}e + \, _{39}^{90}Y}\)

    PROBLEM 3-64 \(\mathrm{^{131}_{53}I\rightarrow \, _{-1}^{0}e + \, _{54}^{131}Xe}\)

    PROBLEM 3-65 about 18 Bq

    PROBLEM 3-66 3.15 x 107 Bq

    This page titled 3.E: Atoms and Nuclear Chemistry (Exercises) was last modified on Thu, 31 Jul 2025 00:06:33 GMT and is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Sol Parajon Puenzo (Cañada College) via source content that was edited to the style and standards of the LibreTexts platform.