11.E: Nuclear Chemistry (Exercises)

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. Describe an alpha particle. What nucleus is it equivalent to?

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

6. Explain what gamma rays are.

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

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

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

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

11. Define nuclear fission.

Answers

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

2. Cobalt-60 or ⁶⁰Co

3.  

   1. 5 protons; 6 neutrons
   2. 13 protons; 14 neutrons
   3. 26 protons; 30 neutrons
   4. 86 protons; 138 neutrons

 

4. An alpha particle is a combination of two protons and two neutrons and is equivalent to a helium nucleus.

5. A beta particle is equivalent to an electron.

6. Gamma rays are high-energy electromagnetic radiation given off in radioactive decay.

 

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

 

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

 

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

10. Gamma radiation; shielding using lead apron/collar.

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

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. 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?

4. 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?

Answers

1. Only radioactive isotopes have half-lives.

2. Isotopes with short half-life produce more radioactive decay than those with long half-life.

3. 51.0 d

4.  25

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. How does a becquerel differ from a curie?

3. 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?

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

5. 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?

6. Explain how a film badge 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. A becquerel is smaller and equals 1 decay per second. A curie is 3.7 × 10¹⁰ Bq.

3. 6000 y

4. The radiation exposure is determined by the number of rads times the quality factor of the radiation.

5. At least 16% (terrestrial and cosmic sources) of radioactivity is unavoidable; the rest depends on what else a person is exposed to.

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

11.4 Uses of Radioactive Isotopes

Concept Review Exercise

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

2. How do the doses of radioisotopes used in diagnostic procedures and therapeutic treatment compare to one another?

Answer

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

2. Diagnostic amounts are much smaller than therapeutic amounts.

 

Exercises

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

2. Explain how radioactive dating works.

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

4. 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?

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

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

7. Which radioactive emissions can be used therapeutically?

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

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. 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.

3. Carbon-14

4. about 11,400 y

5. increased shelf life (answers will vary)

 

6. 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.

 

7. gamma rays, beta particles, or alpha particles

 

8. Cobalt-60

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. 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?

3. Briefly describe how a nuclear reactor generates electricity

4. What is a chain reaction?

Answers

1. 1.22 × 10¹³ J

2.  2.10 x 10¹² J

3.  A nuclear reactor generates heat, which is used to generate steam that turns a turbine to generate electricity.

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

11.6: Chapter Summary

Additional Exercises

1. 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.

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

3. 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?

Answers

 

 

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

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

3.  about 18 Bq