ANSWERS TO LEARNING REVIEW

Transcription

1 9. A wooden post from an ancient village has 25% of the carbon-14 found in living trees. How old is the wooden post? The half-life of carbon-14 is 5730 years. 10. Why do you think that most nuclides used in medicine as radiotracers have short half-lives? 11. What safety features would prevent a nuclear explosion in case of a serious malfunction of a nuclear reactor? 12. Why do you think that the fusion process would supplant fission if the technology were available? 13. Whatdifferences exist between genetic and somatic damage caused by radioactivity? 14. Why is the ionizing ability of a radiation source important in determining the biological effects of radiation? ANSWERS TO LEARNING REVIEW 1. The sum of the atomic numbers (Z) and the sum of the mass numbers (A) must be the same on both sides of a nuclear equation b. c. d. A gamma ray has a mass number of zero and an atomic number of zero. A positron has a mass number of zero and an atomic number of 1+. An alpha particle has a mass number of four and an atomic number of 2+. A beta particle has a mass number of zero and an atomic number of 1-. When 2~~ Rn decays to produce an alpha particle and a gamma particle, the mass number of the new nuclide is decreased by four to 222. The atomic number decreases by two to eighty-four. The new nuclide would have a mass number of 222 and an atomic number of eighty-four. The element with atomic number of eighty-four is polonium, so the new nuclide is 2;; Po. + 0y+ 222Po 226Rn He 0 84 b. When~? Ga decays to produce a beta particle, the mass number of the new nuclide does not change. The atomic number increases by one to thirty-two. The new nuclide would have a mass number of seventy, and an atomic number of thirty-two. The element with an atomic number of thirty-two is germanium, so the new nuclide. 7 0 IS 32 e a e + 32 Oe Answers to Learning Review 425

2 c. When ~i: Nd decays to produce a beta particle, the mass number does not change. The atomic number increases by one to sixty-one. The new nuclide would have a mass number of 144 and an atomic number of sixty-one. The element with an atomic number of sixty-one is promethium, so the new nuclide is 1:1 4 Pm. 144 Nd p 60-1 e 61 m 4. This problem provides the nuclides before and after decay and asks for the identity of an unknown decay particle. Because the mass number does not change on either side, the mass number of the particle is zero. The atomic number decreases by one on the right side, so the atomic number of the unknown particle is 1- so that the sum of atomic numbers on each is the same. The unknown particle has a mass number of zero and an atomic number of -1. It is a ~-partic1e. This is an example of electron capture. 161Ho + 0e D Y b. This problem provides a nuclide on the left that decays to an unknown nuclide and a ~-partic1e. Because the mass number of the ~-particle is zero, the mass number of the unknown nuclide must be ten to balance the left side. The atomic number increases by one to become five to balance the four on the left side. The element with an atomic number of five is boron, so the nuclide is 1~ B. lob... lob+ 4 e 5-1 e c. This problem provides the identity of a particle that combines with an unknown nuclide to produce the nuclide i1 Sc. The ~-particle has a mass number of zero, so the mass number of the unknown nuclide must be forty-four. The f3-particle has an atomic number of 1-, so the atomic number of the unknown nuclide must be twenty-two so that the sum of the atomic numbers is the same on each side. The element with atomic number twenty-two is titanium, so the unknown nuclide is 44 TO T 44 S e c d. This problem provides a nuclide which reacts with an alpha particle to produce a proton and an unknown nuclide. The total mass number on the left side is 257. On the right, the proton has a mass number of one, so the unknown nuclide must have a mass number of 256 so that both sides are balanced. The total atomic number on the Radioactivity and Nuclear Energy

3 left side is 101. On the right, the proton has an atomic number of one, so that the atomic number of the unknown nuclide must be 100. The element with an atomic number of 100 is fermium, so the nuclide is iggfm. 253 Es + 4 He H Fm e. This problem provides a nuclide which decays to an unknown particle and to a nuclide of nickel. The mass number on both sides is fifty-nine, so the mass number of the unknown particle must be zero. The atomic number of the nuclide on the left is twenty-nine and the atomic number of the nuclide on the right is twenty-eight. The unknown particle has an atomic number of 1+. The particle with a mass number of zero and an atomic number of 1+ is a positron,?e. 59 Cu e + 59 Ni The problem provides a nuclide of uranium that is bombarded with a smaller carbon nucleus to produce an unknown nuclide and four neutrons. The total mass number on the left is 238 plus twelve, which is 250. Each neutron on the right has a mass number of one, so the total mass number of the neutrons is four. The mass number of the new nuclide is 246. The total atomic number on the left is ninety-two plus six, which is ninety-eight. Each of the four neutrons on the right has an atomic number of zero, so the atomic number of the new nuclide is ninety-eight. The element with an atomic number of ninety-eight is californium, Cf. The new nuclide is 29~6 Cf. 238 U + 12 C Cf on 6. The Geiger-MUller counter, or Geiger counter, has a probe which is placed close to the source of radioactivity. The probe contains atoms of argon gas which lose an electron when hit by a high-speed subatomic particle. The argon cation and accompanying electron produce a momentary pulse of electrical current which is detected by the Geiger counter. The amount ofradioactive material is directly related to the numberof pulses detected. Radioactivity can also be detected with a scintillation counter. High-speed decay particles collide with a substance inside the scintillation counter such as sodiumiodide. The sodium iodide emits a flash of light when struck. Each flash of light is counted and the number of flashes is directly related to the amount of radioactivity. Answers to Learning Review 427

4 7. The half-life of potassium-42 is 12.4 hours, which means that fifty percent of a sample of potassium-42 would decay in 12.4 hours. Plutonium-239 has a half-life of 24,400 years, which means it would take 24,400 years for fifty percent of a plutonium-239 sample to decay. The shorter the half-life, the quicker a nuclide decays, so the nuclide with the smallest half-life produces the most decay events over time. Of the three nuclides, potassium-42 would produce the most decay events in any fixed amount of time. 8. Because the half-life of iodine-131 is eight days, the number of iodine-131 atoms in any sample will decrease by fifty percent after eight days. So, after eight days there will be 5.0 x 10 2 /2 = 2.5 x iodine-131 atoms left. After another eight days (for a total of sixteen days) there would be 2.5 x 10 2 /2 = 1.3 x 1020 iodine-131 atoms left. After another eight days (for a total of twenty-four days) there would be 1.3 x /2 = 6.3 x iodine-131 atoms left. After three more eight-day periods (for a total of forty-eight days) there would be 7.8 x iodine-131 atoms left. 9. A piece of wood which contains 25% of the carbon-14 found in freshly cut wood has undergone two half-life decays. The first half-life would decrease the carbon-14 from 100% to 50%, and the second half-life would decrease the carbon-14 content from 50% to 25%. So, a piece of wood which has undergone two half-life decays would be 2 times 5730, or 11,460, years old. 10. Using any radiotracer inside the human body poses some risk of damage by the high-speed decay particles. Radiotracers with a short half-life will rapidly decay and produce many decay particles in a short period of time. Doctors can use small amounts of radiotracer and still detect their presence because the numbers of decay particles are high at first. Because the half-life is short, most of the radiotracer usually decays quickly. 11. Nuclear reactors have many safety features, including control rods which are made of substances which absorb neutrons. The control rods can be raised or lowered between the fuel rods to control how fast the nuclear reaction occurs. If a serious problem occurs with the reactor, the control rods automatically lower into the core so that the fission process slows down. The amount of fissionable fuel present in any nuclear reactor is below the critical mass, so that even in the worst possible case a nuclear explosion would not occur. 12. Fusion would quickly supplant fission because fuel for fusion is readily available in sea water. Fusion reactors would produce helium as an end product, and not the wide variety of radionuclides produced from fission. Safe disposal of the nuclear waste from fission is a concern which does not occur with fusion reactors. 13. Somatic damage is the damage done directly to the tissues of the organism. Somatic damage usually occurs soon after exposure to the radiation source. Genetic damage is the kind of damage done to the reproductive machinery of the human body. Genetic damage occurs at the time of exposure but may not show up until the birth of offspring Radioactivity and Nuclear Energy

5 14. When biomo1ecu1es are ionized by a radiation source, they no longer perform their functions in the body. PRACTICE EXAM 1. Which statementabout radioactivedecay is not true? Loss of a y-ray results in a decrease by one in the mass number. b. Loss of a J3-particle results in an increase by one in the atomic number. c. Loss of a positron results in no change in the mass number. d. Loss of an a-particle results in a loss of four in mass number. e. Loss ofa J3-particle results in no change in the mass number. 2. What is the correct balanced nuclear reaction for the emission of a J3-partic1e from a nuclide of silver, WAg? b. c. d. e. 113 Ag e Ag I09 Ag 2 e'+ 45 Rh IN Ag----- ~e + 11lpd 113 A g Cd -1 e Ag e Pd 3. Which is the correct balanced nuclear equation for the process below? 253 Es + 4He B k on b. 253Es + 4He Md on c. 253Es + 4He Md on d. 253Es + 4He Md on e. 253 Es + 4He Bk + In Es +2He-----? +~n 4. A nuclide of radium, Ra, has a half-life of 3.6 days. If a sample of radium-223 begins with 8.5 x atoms, how many atoms will be left after 18.0 days? 2.1 x b. 1.1 X10 20 c. 5.3 X10 19 d. 2.7 X10 19 e. 1.3 x Practice Exam 429