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1.15: Nuclear Chemistry (Exercises)

  • Page ID
    15201
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    11.1 Radioactivity

    Concept Review Exercise

    1. What are the major types of radioactivity? Write chemical equations demonstrating each type.

    Answer

    1. 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)

    Exercises

    1. Define radioactivity.

    2. Give an example of a radioactive isotope.

    3. How many protons and neutrons are in each isotope?

      1. \(\mathrm{^{11}_5B}\)
      2. \(\mathrm{^{27}_{13}Al}\)
      3. 56Fe
      4. 224Rn
    4. How many protons and neutrons are in each isotope?

      1. \(\mathrm{^{2}_{1}H}\)
      2. \(\mathrm{^{112}_{48}Cd}\)
      3. 252Es
      4. 40K
    5. Describe an alpha particle. What nucleus is it equivalent to?

    6. Describe a beta particle. What subatomic particle is it equivalent to?

    7. Explain what gamma rays are.

    8. Explain why it is inappropriate to refer to gamma rays as gamma “particles.”

    9. Plutonium has an atomic number of 94. Write the chemical equation for the alpha particle emission of 244Pu. What is the daughter isotope?

    10. Francium has an atomic number of 87. Write the chemical equation for the alpha particle emission of 212Fr. What is the daughter isotope?

    11. Tin has an atomic number of 50. Write the chemical equation for the beta particle emission of 121Sn. What is the daughter isotope?

    12. Technetium has an atomic number of 43. Write the chemical equation for the beta particle emission of 99Tc. What is the daughter isotope?

    13. Energies of gamma rays are typically expressed in units of megaelectron volts (MeV), where 1 MeV = 1.602 × 10−13 J. Using data provided in the text, calculate the energy, in megaelectron volts, of the gamma ray emitted when radon-222 decays.

    14. The gamma ray emitted when oxygen-19 gives off a beta particle is 0.197 MeV. What is its energy in joules? (See Exercise 13 for the definition of a megaelectron volt.)

    15. Which penetrates matter more deeply—alpha particles or beta particles? Suggest ways to protect yourself against both particles.

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

    17. Define nuclear fission.

    18. What general characteristic is typically necessary for a nucleus to undergo spontaneous fission?

    Answers

    1. Radioactivity is the spontaneous emission of particles and radiation from atomic nuclei.

    2. C-14 or 14C is an example of radioactive isotope (answers may vary).
    1.  

      1. 5 protons; 6 neutrons
      2. 13 protons; 14 neutrons
      3. 26 protons; 30 neutrons
      4. 86 protons; 138 neutrons
    4.
    1. 1 proton; 1 neutron
    2. 48 protons; 64 neutrons
    3. 99 protons;153 neutrons
    4. 19 protons; 21 neutrons
    1. An alpha particle is a combination of two protons and two neutrons and is equivalent to a helium nucleus.

    6. A beta particle is an electron.
    1. Gamma rays are high-energy electromagnetic radiation given off in radioactive decay.

    8. Gamma rays have no mass. Hence not a particle.
    1. \(\mathrm{^{244}_{94}Pu\rightarrow \, _2^4He +\, ^{240}_{92}U}\); the daughter isotope is \(\mathrm{^{240}_{92}U}\), an atom of uranium.

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

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

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

    13. 0.512 MeV

    14. 3.16 x 10-14 J

    15. Beta particles; shielding of the appropriate thickness can protect against both alpha and beta particles.

    16. 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.

    17. Nuclear fission is when large nuclei break down into smaller nuclei.

    18. A nucleus must be very large. Examples are Th-232 and U-235.

    11.2 Half-Life

    Concept Review Exercises

    1. Define half-life.
    2. Describe a way to determine the amount of radioactive isotope remaining after a given number of half-lives.

    Answers

    1. Half-life is the amount of time needed for half of a radioactive material to decay.
    2. take half of the initial amount for each half-life of time elapsed

    Exercises

    1. Do all isotopes have a half-life? Explain.

    2. Which is more radioactive—an isotope with a long half-life or an isotope with a short half-life?

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

    4. 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?

    5. 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?

    6. 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?

    7. 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?

    8. 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?

    9. 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?

    Answers

    1. Only radioactive isotopes have half-lives.

    2. An isotope with a shorter half-life decay more rapidly is more radioactive.

    3. 1 half-life: 50%; 3 half-lives: 12.5%

    4. 9.0 min = 3 half-lives (make 3 arrows): 0.540 mg --> 0.270 mg --> 0.135 mg --> 0.0675 mg

    5. 0.0127 mg

    6. 51.0 d

    7. 100 000 y

    8. 25 y

    9. 12.3 s

    11.3 Units of Radioactivity

    Concept Review Exercise

    1. What units are used to quantify radioactivity?

    Answer

    1. the curie, the becquerel, the rad, the gray, the sievert, and the rem

    Exercises

    1. Define rad.

    2. Define rem.

    3. How does a becquerel differ from a curie?

    4. How is the curie defined?

    5. 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?

    6. 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?

    7. If a radioactive sample has an activity of 65 µCi, how many disintegrations per second are occurring?

    8. If a radioactive sample has an activity of 7.55 × 105 Bq, how many disintegrations per second are occurring?

    9. Describe how a radiation exposure in rems is determined.

    10. Which contributes more to the rems of exposure—alpha or beta particles? Why?

    11. Use Table 11.3.2 to determine which sources of radiation exposure are inescapable and which can be avoided. What percentage of radiation is unavoidable?

    12. What percentage of the approximate annual radiation exposure comes from radioactive atoms that are in the body naturally?

    13. Explain how a film badge works to detect radiation.

    14. Explain how a Geiger counter works to detect radiation.

    Answers

    1. Known as the radiation absorbed dose, a rad is the absorption of 0.01 J/g of tissue.

    2. Known as roentgen equivalent man, a rem 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.
    1. A becquerel is smaller and equals 1 decay per second. A curie is 3.7 × 1010 Bq.

    4. A curie is defined as 3.7 × 1010 decays per second.
    1. 6000 y

    6. 144 s
    1. 2.41 × 106 disintegrations per second

    8. 7.55 × 105 disintegrations per second
    1. The radiation exposure is determined by the number of rads times the quality factor of the radiation.

    10. Alpha contributes more than beta because of its bigger size and electrical charge.
     
    11. At least 16% (terrestrial and cosmic sources) of radioactivity is unavoidable; the rest depends on what else a person is exposed to.
     
    12. About 11% come from radioactive atoms that are in the body naturally.

    13. A film badge uses film, which is exposed as it is subjected to radiation.

    14. The Geiger counterconsists 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 and produce an electric pulse (clicking sound).

    11.4 Uses of Radioactive Isotopes

    Concept Review Exercise

    1. Describe some of the different ways that amounts of radioactivity are applied in society.

    Answer

    1. Radioactive isotopes are used in dating, as tracers, and in medicine as diagnostic and treatment tools.

    Exercises

    1. Define tracer is and give an example of how tracers work.

    2. Name two isotopes that have been used as tracers.

    3. Explain how radioactive dating works.

    4. Name an isotope that has been used in radioactive dating.

    5. 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?

    6. 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?

    7. What do you think are some of the positive aspects of irradiation of food?

    8. What do you think are some of the negative aspects of irradiation of food?

    9. Describe how iodine-131 is used to both diagnose and treat thyroid problems.

    10. List at least five organs that can be imaged using radioactive isotopes.

    11. Which radioactive emissions can be used therapeutically?

    12. Which isotope is used in therapeutics primarily for its gamma ray emissions?

    13. 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?

    14. 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?

    15. 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?

    Answers

    1. 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).

    2. Tritium (3H) and Carbon-14 (14C) (answers will vary)
    1. 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.

    4. Carbon-14 (14C) and Uranium-235 (235U) (answers will vary)
    1. about 11,400 y

    6. about 420,000 y
    1. increased shelf life (answers will vary)

    8. reduction in the food's vitamin content and cost
    1. 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.

    10. brain, bone, heart, thyroid, lung (answers will vary)

    11. gamma rays, beta particles, or alpha particles

    12. cobalt-60

    13. 125mCi x (5.0mL/45mCi)=14mL

    14. 36kg x (145μCi/kg) x (1mL/250μCi)=21mL

    15. 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

    11.5 Nuclear Energy

    Concept Review Exercises

    1. How is nuclear energy produced?

    2. What is the difference between fission and fusion?

    Answers

    1. Nuclear energy is produced by carefully controlling the speed of a fission reaction.

    2. In fission, large nuclei break down into small ones; in fusion, small nuclei combine to make larger ones. In both cases, a lot of energy is emitted.

    Exercises

    1. In the spontaneous fission of uranium-233, the following reaction occurs:

      233U + 1n → 142Ce + 82Se + 101n

      For every mole of 233U that decays, 0.1355 g of mass is lost. How much energy is given off per mole of 233U reacted?

    2. In the spontaneous fission of plutonium-241, the following reaction occurs:

      241Pu + 1n → 104Ru + 124Sn + 141n

      For every mole of 241Pu that decays, 0.1326 g of mass is lost. How much energy is given off per mole of 241Pu reacted?

    3. The two rarer isotopes of hydrogen—deuterium and tritium—can also be fused to make helium by the following reaction:

      2H + 3H → 4He + 1n

      In the course of this reaction, 0.01888 g of mass is lost. How much energy is emitted in the reaction of 1 mol of deuterium and tritium?

    4. A process called helium burning is thought to occur inside older stars, forming carbon:

      34He → 12C

      If the reaction proceeds with 0.00781 g of mass lost on a molar basis, how much energy is given off?

    5. Briefly describe how a nuclear reactor generates electricity.

    6. Briefly describe the difference between how a nuclear reactor works and how a nuclear bomb works.

    7. What is a chain reaction?

    8. Why must uranium be enriched to supply nuclear energy?

    Answers

    1. 1.22 × 1013 J

    2. 1.19 × 1013 J
    1. 1.70 × 1012 J

    4. 7.03 × 1011 J
    1. A nuclear reactor generates heat, which is used to generate steam that turns a turbine to generate electricity.

    6. Both nuclear reactor and nuclear bomb are powered by fission reaction however, in a nuclear reactor, the fission is monitored and controlled to occur continuously for a much longer time. In a nuclear bomb, the reaction is uncontrolled to explode in one event.

    7. A chain reaction is an ever-expanding series of processes that, if left unchecked, can cause a runaway reaction and possibly an explosion.

    8. Natural uranium ores contain only 0.7% U-235. Most nuclear reactors require enriched U-235 for their fuel.

    11.6: Chapter Summary

    Additional Exercises

    1. Given that many elements are metals, suggest why it would be unsafe to have radioactive materials in contact with acids.

    2. Many alpha-emitting radioactive substances are relatively safe to handle, but inhaling radioactive dust can be very dangerous. Why?

    3. Uranium can be separated from its daughter isotope thorium by dissolving a sample in acid and adding sodium iodide, which precipitates thorium(III) iodide:

      Th3+(aq) + 3I(aq) → ThI3(s)

      If 0.567 g of Th3+ were dissolved in solution, how many milliliters of 0.500 M NaI(aq) would have to be added to precipitate all the thorium?

    4. Thorium oxide can be dissolved in an acidic solution:

      ThO2(s) + 4H+ → Th4+(aq) + 2H2O(ℓ)

      How many milliliters of 1.55 M HCl(aq) are needed to dissolve 10.65 g of ThO2?

    5. 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.

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

    7. A common uranium compound is uranyl nitrate hexahydrate [UO2(NO3)2_6H2O]. What is the formula mass of this compound?

    8. Plutonium forms three oxides: PuO, PuO2, and Pu2O3. What are the formula masses of these three compounds?

    9. 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?

    10. 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?

    11. Uranium hexafluoride (UF6) reacts with water to make uranyl fluoride (UO2F2) and hydrogen fluoride (HF). Balance the following chemical equation:

      UF6 + H2O → UO2F2 + HF

    12. The cyclopentadienyl anion (C5H5) is an organic ion that can make ionic compounds with positive ions of radioactive elements, such as Np3+. Balance the following chemical equation:

      NpCl3 + Be(C5H5)2 → Np(C5H5)3 + BeCl2

    Answers

    1. Acids can dissolve metals, making aqueous solutions.

    2. Alpha rays are dangerous only when the alpha emitter is in direct contact with tissue cells inside the body.
    1. 14.7 mL

    4. 104 mL
    1. \(\mathrm{^{90}_{38}Sr\rightarrow \, _{-1}^{0}e + \, _{39}^{90}Y}\)
    6. \(\mathrm{^{131}_{53}I\rightarrow \, _{-1}^{0}e + \, _{54}^{131}Xe}\)
    1. 502 g/mol

    8. PuO = 260.06 g/mol; PuO2= 276.06 g/mol; Pu2O3= 536.12 g/mol

    9. about 18 Bq

    10. 3.15 x 107 Bq

    11. UF6 + 2H2O → UO2F2 + 4HF

    12. 2NpCl3 + 3Be(C5H5)2 → 2Np(C5H5)3 + 3BeCl2


    1.15: Nuclear Chemistry (Exercises) is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by LibreTexts.

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