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source is at least 3 m away from the radiation detector. Switch on the detector and measure the background radiation level for 5 min or more. Record this measurement, including the units. If you are using an interface with a computer or graphing calculator, check with your teacher about recording your data electronically. 2 Centre the cobalt-60 radiation source over the zero mark on the metre-stick, and tape the source in place. If your radiation source is shielded so that it emits radiation only from one side, align the source to direct the radiation along the metre-stick (Figure 16.2). Required Skills Initiating and Planning Performing and Recording Analyzing and Interpreting Communication and Teamwork 3 Place the radiation detector on the metre-stick within a few centimetres of the radiation source. Measure the radiation level for at least 1 min. Record the radiation level and the distance between the source and the detector. 4 Increase the separation between the radiation source and the detector in steps of 5 cm. Measure the radiation level for at least 1 min at each distance. Record measurements for at least six distances. radiation source radiation detector metre-stick Figure 16.2 Analyzing and Interpreting 1. Which variable is the manipulated variable in this experiment? 2. Explain why you need to know the background radiation level in order to determine how the intensity of the radiation varies with distance. 3. Graph your data. What type of relationship do you think the graph shows? 4. Discuss with your lab partners how you could use a different graph to determine the exact relationship between the radiation intensity and the distance from the radiation source. Produce a graph using the method that you think will work best. Explain your choice. 5. List any assumptions you made when analyzing your data. Forming Conclusions 6. Do your data support the hypothesis? Explain. Think About It 1. What is radioactivity? 2. Where does the energy released in a nuclear reaction come from? 3. How can stars create elements? Discuss your answers in a small group and record them for later reference. As you complete each section of this chapter, review your answers to these questions. Note any changes in your ideas. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 789 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 790 16.1 The Nucleus Section 15.3 described how scattering experiments directed by Rutherford showed that more than 99.9% of the mass of an atom is
concentrated in a nucleus that is typically only a few femtometres (1015 m) in diameter. In 1918, Rutherford began a new series of experiments in which he bombarded nitrogen gas with alpha particles. He found that some of the nitrogen transmuted into oxygen and that the process also produced hydrogen nuclei. Rutherford concluded that the hydrogen nucleus was a fundamental particle that is a constituent of all nuclei. He called these particles protons, from protos, the Greek word for “first.” However, protons could not account for all of the mass of nuclei. For example, the charge-to-mass ratio for protons is twice that of helium nuclei. In 1920, Rutherford suggested that nuclei might also contain neutrons, neutral particles with about the same mass as a proton. Neutral particles are difficult to detect or measure because they do not interact with electric or magnetic fields. A variety of experiments over the next decade failed to find any neutrons. The breakthrough came in 1932 when James Chadwick showed that alpha rays striking a beryllium target produced radiation consisting of neutral particles. In a similar experiment with a boron target, he determined that the mass of a neutron is about 0.1% greater than the mass of a proton. femto: metric prefix meaning 1015 proton: a positively charged particle found in all nuclei neutron: a neutral particle found in nuclei info BIT Chadwick made two earlier attempts to discover the neutron, in 1923 and 1928. In 1935, he received the Nobel Prize in physics for his discovery. Nuclear Terms and Notation nucleon: a proton or neutron Protons and neutrons are called nucleons because they are both components of nuclei. Three numbers describe the composition of a nucleus: Atomic Number, Z: the number of protons in a nucleus Neutron Number, N: the number of neutrons in the nucleus Atomic Mass Number, A: the number of nucleons in the nucleus, Z N Scientists often indicate the composition of a nucleus with the notation A ZX, where X is the chemical symbol for the element. For example, a carbon nucleus with 6 protons and 6 neutrons has Z 6, N 6, and A 6 6 12. The notation for the carbon nucleus is 12 6C. Apply these terms and concepts in the next example. 790 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 791 Example 16
.1 How many neutrons are contained in a gold nucleus 197 79Au? Given Z 79 A 197 Required neutron number (N ) Analysis and Solution Since A Z N, N A Z 197 79 118 Paraphrase There are 118 neutrons in a nucleus of 197 79Au. Concept Check Practice Problems 1. How many neutrons are in a nucleus of 24 12Mg? 2. Find the atomic mass number for a uranium atom that contains 92 protons and 146 neutrons. Answers 1. 12 2. 238 How do the nuclei 12 6C, 13 6C, and 14 6C differ? How are they the same? Isotopes Many elements have two or more isotopes — forms that have the same number of protons (Z) but differing numbers of neutrons (N). For example, ordinary hydrogen (1 1H) are all isotopes of the element hydrogen. Specific isotopes can be indicated by the element name and the atomic mass number. For example, carbon-12 is another way of writing 12 1H), and tritium (3 1H), deuterium (2 6C. isotopes: atoms that have the same number of protons, but different numbers of neutrons All the isotopes of a particular element have the same number of protons and electrons. So, these isotopes have almost identical chemical properties. However, the physical properties can differ dramatically. In particular, one isotope of an element may be highly radioactive, while another is quite stable. Bombarding materials with electrons, neutrons, or other particles can create radioactive isotopes. Atomic Mass Units Atoms and nuclei are much, much smaller than everyday objects. So, even though a kilogram may be a convenient unit for expressing the mass of apples or oranges, it is not particularly useful for measuring the mass of a proton or a carbon nucleus. For calculations involving nuclei and subatomic particles, it is often convenient to use a mass unit that is much smaller than the kilogram. The atomic mass unit (u) is defined as exactly 1 12 of the mass of the carbon-12 atom: 1 u 1.660 539 1027 kg Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 791 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 792 Table 16.1 lists the masses of electrons and nucleons, in both kilograms and atomic mass units. Table 16.1 Some Properties of Sub
atomic Particles (to Six Decimal Places) Particle Electron Proton Neutron Charge (C) Mass (kg) Mass (u) 1.602 177 1019 1.602 177 1019 0 9.109 383 1031 1.672 622 1027 1.674 927 1027 5.485 799 104 1.007 276 1.008 665 Forces in the Nucleus Aside from hydrogen, all nuclei consist of two or more protons and a number of neutrons (Figure 16.3). Like charges repel each other, so what keeps these nuclei from flying apart? Example 16.2 Can gravitational force bind two protons in a nucleus together? Given Rounding the values listed in Table 16.1 gives proton mass m 1.67 1027 kg and proton charge q 1.60 1019 C. Required Determine if gravitational force can bind two protons in a nucleus together. Figure 16.3 Any nucleus heavier than hydrogen has protons and neutrons packed closely together. Practice Problems 1. Calculate the gravitational force that two protons exert on each other when they are 5 fm apart. 2. Calculate the electrostatic force that two protons exert on each other when they are 5 fm apart. Answers 1. 7 1036 N 2. 9 N Analysis and Solution Compare the gravitational and electrostatic forces between two protons in a nucleus. The magnitude of the gravitational force is F. g The magnitude of the electrostatic force is F e Fg Fe So, m2 Gm 1 2 r q2 kq 1 2 r Gm1m2 kq1q2. Gm1m2 r 2 kq1q2 r 2. This ratio shows that the relative strength of the two forces does not depend on the distance between the protons. In order for the gravitational attraction between the protons to overcome the electrostatic repulsion, the ratio have to be greater than 1. Fg Fe would Substituting the known values into the ratio of the forces gives Fg Fe (6.67 1011 Nm2/kg2)(1.67 1027 kg)2 (8.99 109 Nm2/C2)(1.60 1019 C)2 8.08 1037 Paraphrase The gravitational attraction is vastly weaker than the electrostatic repulsion, so gravity cannot be the force that holds a nucleus together. 792 Unit VIII Atomic Physics 16-PearsonPhys30
-Chap16 7/24/08 4:32 PM Page 793 strong nuclear force: the force that binds together the protons and neutrons in a nucleus PHYSICS INSIGHT Measurements of interactions between subatomic particles suggest that there is a fourth fundamental force, the weak nuclear force. This force acts on electrons. binding energy: the net energy required to liberate all of the protons and neutrons in a nucleus Since gravity is far too weak, there must be some other force that holds the particles in a nucleus together. Physicists call this force the strong nuclear force, and think that it is a fundamental force of nature, like gravity and the electrostatic force. The strong nuclear force has a very short range. Although it is more powerful than the electrostatic force within a nucleus, the strong nuclear force has a negligible effect on particles that are more than a few femtometres apart. The strong nuclear force acts on both neutrons and protons, but does not affect electrons. Chapter 17 describes fundamental forces in more detail. Binding Energy and Mass Defect Removing a nucleon from a stable nucleus requires energy because work has to be done on the nucleon in order to overcome the strong nuclear force. The binding energy, Eb, of a nucleus is the energy required to separate all of its protons and neutrons and move them infinitely far apart. In other words, the binding energy is the difference between the total energy of the separate nucleons and the energy of the nucleus with the nucleons bound together: Eb Enucleons Enucleus where Enucleons is the sum of the energies of the nucleons when they are free of the nucleus and Enucleus is the energy of the nucleus. Mass-energy Equivalence The equivalence of mass and energy is part of the theory of relativity that Albert Einstein developed in 1905. This theory correctly predicted that mass and energy are related by the equation E mc2 where E is energy, m is mass, and c is the speed of light. Earlier in this section, you learned that physicists commonly use the atomic mass unit, u, for calculations involving nuclei and subatomic particles. For nuclear calculations, it is useful to know the energy equivalent for 1 u: E 1 u c2 (1.660 539 1027 kg)(2.997 925 108 m/s)2 1.492 418 1010 J 1.492 418 1010 J 931.494 1 MeV 1 eV 1.602 177 1019 J
Thus, 1 u is equivalent to about 149.2 pJ or 931.5 MeV. The binding energy of most nuclei is equivalent to only a small fraction of an atomic mass unit. Nuclear reactions can involve conversions between mass and energy. The law of conservation of energy still applies if the conversions are taken into account. For any closed system, the total of the energy and the energy equivalent of the mass in the system is constant. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 793 16-PearsonPhys30-Chap16 7/28/08 10:14 AM Page 794 Example 16.3 Calculate the energy equivalent for 0.0034 u of mass, in joules and in electron volts. Analysis and Solution Simply multiply 0.0034 u by the appropriate equivalence factors: 0.0034 u 1.492 1010 J 1 u 5.1 1013 J 0.0034 u 931.5 MeV 1 u 3.2 MeV Paraphrase The energy equivalent for 0.0034 u is 5.1 1013 J or 3.2 MeV. Practice Problems 1. Find the energy equivalent, in electron volts, for 0.221 u. 2. Find the mass equivalent to 250 MeV. Answers 1. 206 MeV 2. 0.268 u Mass Defect Rearranging Einstein’s equation for mass-energy equivalence gives m E c2. Dividing the equation for binding energy by c2 leads to a formula for the mass defect, m, of a nucleus: Enucleons c2 Eb c2 m mnucleons Enucleus c2 mnucleus where mnucleons is the sum of the masses of the separate nucleons and mnucleus is the mass of the nucleus. Thus, the mass of a nucleus is equal to the total mass of its constituents, less the mass corresponding to the binding energy. Physicists have determined the masses of atoms and nucleons with great accuracy. Tables of atomic data generally list the masses of neutral atoms rather than the masses of nuclei alone without any electrons. The following formula uses atomic masses to calculate the mass defect for a nucleus: m Zm1 1H Nmneutron matom where m1 number, and N is the neutron number. 1H is the mass of a neutral hydrogen atom, Z is the atomic Since m1 1H includes the masses of both a proton and an electron
, the 1H includes the mass of Z electrons, matching the mass of the term Zm1 electrons included in matom. The differences in the binding energy of the electrons are small enough to ignore in most nuclear calculations. mass defect: difference between the sum of the masses of the separate nucleons and the mass of the nucleus PHYSICS INSIGHT Nuclear calculations often involve very small differences in mass. Such calculations can require data with six or more significant digits. 794 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 795 Concept Check Show that m Zmproton Nmneutron mnucleus. Example 16.4 Find the mass defect, expressed in kilograms, and the binding energy for a carbon-12 nucleus. Given Z 6 A 12 m 12.000 000 u Required mass defect (m) binding energy (Eb) Analysis and Solution The formula N A Z gives the number of neutrons in the nucleus: N 12 6 6 Practice Problems 1. Sodium 23 11Na has an atomic mass of 22.989 769 u. Find the mass defect for this nucleus. 2. Find the binding energy for 23 11Na. Answers 1. 0.200 286 u 2. 186.6 MeV 6C nucleus consists of 6 neutrons and 6 protons. Thus, the 12 Now, use m Zm1 1H Use mass data from Tables 7.5 and 7.6 on page 881. Recall that 1 u 1.660 539 1027 kg (page 791). m ZmH matom to find the mass defect. Nmneutron Nmneutron matom 6(1.007 825 u) 6(1.008 665 u) 12.000 000 u 0.098 940 u 1.660 539 1027 kg 1 u 1.6429 1028 kg Use the mass-energy equivalence to calculate the binding energy from the mass defect. 1 u 1.492 1010 J 931.5 MeV 0.098 940 u 1.492 1010 J 1 u 931.5 MeV 1 u or 0.098 940 u Eb 1.476 1011 J 92.16 MeV Paraphrase The mass defect for 12 the carbon-12 nucleus is 1.476 1011 J or 92.16 MeV. 6C is 1.6429 1028 kg. The binding energy of
Binding Energy per Nucleon You can compare the stability of different nuclei by dividing the binding energy of each nucleus by the number of nucleons it contains. The, the more stable the nucleus greater the binding energy per nucleon is. Figure 16.4 is a graph of binding energy per nucleon versus atomic mass number for stable nuclei. This graph peaks at about 8.79 MeV per 58Fe, and nucleon. The three most stable isotopes are nickel 28 iron 26 62Ni, iron 26 Eb A 56Fe. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 795 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 796 Figure 16.4 Binding energy per nucleon for stable isotopes ) 10 8 6 4 2 0 16 8 O 56 26 Fe 120 50 Sn 238 92 U 4 2 He 3 2 2 1 He H 50 100 150 200 250 Atomic Mass Number, A The graph also gives a hint about the process that causes the stars to shine. The binding energy per nucleon is much less for hydrogen than for helium. If hydrogen atoms combine to form helium, the nucleons move to a lower energy level and give off the difference in energy. In section 16.4, you will learn more about such nuclear reactions. 16.1 Check and Reflect 16.1 Check and Reflect Knowledge 10. Show that MeV/c2 has the dimensions 1. How many protons and neutrons do each of the following nuclei contain? (a) 90 13C (c) 56 (b) 6 26Fe 38Sr (d) 1 1H 2. Convert 1.6 1010 J to electron volts. 3. Calculate the energy equivalent of 0.25 u. 4. How much mass is converted into energy by a nuclear reaction that produces 5.00 GJ of energy? 5. Define the term isotope. 6. Explain why the mass of a stable nucleus is a bit less than Zmproton Nmneutron. Applications 7. Determine the binding energy for 10 22Ne. The atomic mass of 10 22Ne is 21.991 385 u. 8. The 19 40K isotope of potassium has an atomic mass of 39.963 998 u. (a) Determine the mass defect for 19 (b) Calculate the binding energy per 40K. nucleon for this isotope. of mass. Extensions 11. (a) Contrast the
strength and range of the electromagnetic force and the strong nuclear force. (b) Explain how the nature of these forces limits the maximum possible size for nuclei. 12. Suppose that the electrostatic force were much stronger. Describe how this change would affect the stability of nuclei. 1.20 fm and A is 13. Experiments have shown that most nuclei are approximately spherical with a radius 1 of r r0A, where r0 3 the atomic mass number. Use this formula to determine the radius of the nucleus of a 90Sr atom. Then estimate the distance 38 between adjacent nucleons in this nucleus. What can you conclude about the size of protons and neutrons? 9. Use Figure 16.4 to estimate the binding e TEST energy for each of these nuclei: (a) 13 56Fe (c) 238 (b) 26 92U 6C To check your understanding of nuclei, follow the eTEST links at www.pearsoned.ca/school/physicssource. 796 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 797 16.2 Radioactive Decay The French physicist, Antoine Henri Becquerel (1852–1908), discovered radioactive decay in 1896 while conducting an experiment to see if a fluorescent compound of uranium would emit X rays when exposed to sunlight. During a period of cloudy weather, Becquerel put the uranium compound away in a drawer along with a photographic plate wrapped in black paper. When he developed the plate several days later, he was surprised to find that it was fogged even though the fluorescent compound had not been exposed to sunlight. Becquerel realized that the radiation that fogged the plate must be coming from the uranium in the compound. He also found that a magnetic field would deflect some of this radiation. The husband and wife team of Marie Curie (1867–1934) and Pierre Curie (1859–1906) began an extensive study of this radiation. They showed that thorium was also radioactive, and discovered two new elements, radium and polonium, that were both much more radioactive than uranium. Indeed, Marie coined the term radioactive. She also demonstrated that the intensity of radiation from uranium compounds was not affected by the other elements in the compound or by processes such as being heated, powdered, or dissolved. The intensity depended only on the quantity of uranium. Therefore, the radioactivity must result from
a process within the uranium nucleus. Rutherford and others identified three forms of nuclear radiation: Alpha (): the emission of a helium nucleus Beta (): the emission of a high-energy electron Gamma (): the emission of a high-energy photon Initially, this classification was based on how much material each type of radiation could penetrate. In radiation from naturally occurring isotopes, the alpha particles typically do not penetrate much more than a thin metal foil or sheet of paper, whereas beta particles can pass through up to 3 mm of aluminium, and gamma rays can penetrate several centimetres of lead. The three types of radiation result from different processes within nuclei. Concept Check Figure 16.5 shows the paths that,, and rays take when passing through a magnetic field. What can you conclude about the electrical properties of these rays? β γ radiation source α Figure 16.5 The paths of,, and rays in a magnetic field info BIT Marie Curie was the first person to win two Nobel Prizes. She died of leukemia, almost certainly the result of years of exposure to radiation in her laboratory. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 797 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 798 16-2 Design a Lab 16-2 Design a Lab Radiation Shielding The Question What common materials provide effective shielding against,, and radiation? Figure 16.6 Radiation meters Design and Conduct Your Investigation Check with your teacher about the radiation sources and radiation meters (Figure 16.6) available for this investigation. Then design your experiment. List the materials you will need and outline the procedure. Try this procedure and modify it if necessary. Keep careful records of your results. Then analyze your data, and explain your conclusions. Conservation Laws and Radioactive Decay In addition to conserving momentum and energy, all radioactive decay processes obey these additional conservation laws: • Charge: The net electrical charge cannot change in a decay process. Any change in the electrical charge of the nucleus must be exactly offset by an opposite change elsewhere in the system. For example, if the charge on a nucleus decreases by 2e, then a particle with a charge of 2e must be emitted. • Atomic Mass Number: The total of the atomic mass numbers for the final products must equal the atomic mass number of the original nucleus. In other words, the total number of nucleons remains constant. 798 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08
4:32 PM Page 799 Example 16.5 Determine which of these radioactive decay processes are possible. (a) 214Po → 82 84 208Pb 4 2 226Ra 4 2 28Ni 1 0n (b) 230Th → 88 90 27Co → 60 (c) 60 (1 0n represents a neutron) Analysis and Solution Compare the charge and atomic mass number of the original nucleus to those of the decay products. (a) Charge: 84 82 2 Atomic mass number: 214 208 4 The decay process 214 (b) Charge: 90 88 2 84Po → 208Pb 82 4 is not possible. 2 Atomic mass number: 230 226 4 The decay process 230 (c) Charge: 27 28 0 90Th → 88 226Ra 4 is possible. 2 Atomic mass number: 60 60 1 The decay process 27 60Co → 60 28Ni 1n is not possible. 0 Practice Problems Determine whether these decay processes are possible. 210Rn 4 2 0 233U 1 1H 212Po → 86 84 233Pa → 92 91 14C → 7 6 14N 1 2. 3. 1. Answers 1. Impossible 2. Possible 3. Impossible Concept Check Why are electrons not considered when applying the conservation law for atomic mass number? Alpha Decay In 1908, Rutherford showed that alpha particles are helium nuclei spontaneously emitted by unstable large nuclei. In these nuclei, the electromagnetic force repelling the outer protons is almost as great as the attractive strong nuclear force. Such nuclei can spontaneously emit alpha particles. Because a cluster of two protons and two neutrons forms a highly stable helium nucleus, these unstable large nuclei decay by emitting alpha particles rather than separate protons and neutrons. The emission of an alpha particle decreases the atomic number by 2 and the atomic mass number by 4. For example, alpha decay of uranium-238 produces thorium: 238 92U → 90 234Th 4 2 In this example, uranium is the parent element and thorium is the daughter element. Applying the conservation laws gives this general form for alpha decays: A ZX → A4 Z2Y 4 2 parent element: the original element in a decay process daughter element: the element produced by a decay process where X is the chemical symbol for the parent element and Y is the symbol for the daughter element. Here, A is the atomic mass number of the parent element and Z is its atomic number. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 799 16-Pear
sonPhys30-Chap16 7/24/08 4:32 PM Page 800 Example 16.6 Practice Problems Write the -decay process for these elements, and name the parent and daughter elements. 1. 2. 3. 230Th 90 238U 92 214Po 84 Answers 1. 90 2. 92 3. 84 230Th → 226 238U → 90 214Po → 82 88Ra 4 ; thorium, radium 2 234Th 4 ; uranium, thorium 2 210Pb 4 ; polonium, lead 2 Predict the daughter element that results from alpha decay of radium-226. Analysis and Solution From a periodic table, you can see that the atomic number for radium is 88. So, the parent element is 226 Since the alpha particle carries away four nucleons, including two protons, A decreases by 4 and Z decreases by 2: ZX → A4 A So, the daughter element is 882 The periodic table shows that the element with Z 86 is radon. 2264Y 222 Z2Y 88Ra. 86Y. 4 2 Paraphrase For alpha decay, the daughter element of radium-226 is radon-222. Energy Released During Alpha Decay You can apply the concepts of energy conservation and mass-energy equivalence to alpha decay, using a method similar to the calculation of nuclear binding energy. The mass-energy of the parent nucleus is equal to the sum of the mass-energy and the kinetic energies of both the daughter nucleus and the alpha particle: mparentc2 mdaughterc2 mc2 E The difference in energy, E, appears as the total kinetic energy of the alpha particle and of the daughter nucleus. If the parent nucleus was at rest, the law of conservation of momentum requires the momentum of the alpha particle to be equal in magnitude and opposite in direction to the momentum of the daughter nucleus. Usually, the mass of the daughter nucleus is much greater than the mass of the alpha particle. So, the speed of the alpha particle is correspondingly greater than the speed at which the daughter nucleus recoils: mv mdaughtervdaughter v mdaughtervdaughter m 800 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 801 The kinetic energy of the alpha particle is also correspondingly greater than the kinetic energy of the daughter nucleus: 1 E mv 2 2 1 m 2 mdaughter m mdaughter m mdaughtervdaughter m 2 mdaughterv 2 daughter
1 2 Edaughter Concept Check Explain why E must be positive in order for -decay to occur. Example 16.7 Show that -decay of radium-226 is possible, and estimate the maximum kinetic energy of the emitted alpha particle. Given Parent atom is radium-226. Required maximum kinetic energy of the alpha particle Practice Problems Calculate the energy released during -decay of these nuclei: 1. 2. 3. 230Th 90 238U 92 214Po 84 Answers 1. 7.641 1013 J 2. 6.839 1013 J 3. 1.255 1012 J Analysis and Solution Example 16.6 showed that the daughter element is radon-222. The energy released is equivalent to the difference between the mass of the parent atom and the total mass of the products. m mparent Table 7.5 on page 881 lists the atomic masses for radium-226, radon-222, and helium-4. As in section 16.1, you can use atomic masses instead of nuclear masses because the masses of the electrons will balance out. A radon nucleus has over 50 times the mass of an alpha particle. So, the alpha particle will have over 98% of the total kinetic energy, E. m m226 mproducts 88Ra (m 222 m4 ) 2 226.025 410 u 222.017 578 u 4.002 603 u 0.005 229 u 86Rn E 0.005 229 u 1.492 1010 J 1 u 7.802 1013 J or 0.005 229 u 4.871 MeV 931.5 MeV 1 u Paraphrase Since E 0, alpha decay of radium-226 is possible. The maximum kinetic energy of the alpha particle when emitted is about 7.802 1013 J or 4.871 MeV. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 801 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 802 THEN, NOW, AND FUTURE Ionization Smoke Detectors Most household smoke detectors (Figure 16.7) contain a small amount of americium-241. This isotope emits -particles, which ionize air molecules between two metal plates within the smoke detector. One of the plates has a positive charge, and the other plate has a negative charge. The plates attract the ions, so a small current flows between the plates. If smoke particles enter the smoke detector, they
absorb some of the -particles. So, the alpha radiation ionizes fewer air molecules Figure 16.7 This smoke detector uses alpha radiation to sense smoke particles. and the current between the metal plates decreases. This drop in current triggers the alarm circuit in the smoke detector. Questions 1. Why is it safer for a smoke detector to use alpha radiation, instead of beta or gamma radiation? 2. Suggest reasons why most manufacturers of smoke detectors recommend replacing them after 10 years. beta-negative () decay: nuclear decay involving emission of an electron beta () particle: electron emitted by a nucleus Beta Decay Sometimes, a nucleus decays by emitting an electron. This process is termed beta-negative or decay. During decay, a neutron in the nucleus transforms into a proton, electron, and an extremely small neutral particle known as antineutrino, symbol ¯ (Figure 16.8). So, the atomic number of the atom increases by 1, but the atomic mass number does not change. Charge is conserved because the charge on the new proton balances the charge on the electron emitted from the nucleus. This electron is often called a beta () particle, a name that originates from the 0 in equaearly classification of types of radiation. It is often written as 1 tions. For example, decay of thallium-208 produces lead, and the equation is: 208Tl → 81 208Pb 82 0 υ– –1 n e p υ Figure 16.8 During decay, a neutron changes into a proton, electron, and antineutrino. Concept Check Why is the mass of the neutron slightly larger than the sum of the proton and electron masses? 802 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 803 Example 16.8 What element will the decay of thorium produce? Analysis and Solution A periodic table shows that the atomic number for thorium is 90. decay increases the atomic number by 1, so Adaughter The element with an atomic number of 91 is protactinium, the element immediately after thorium in the periodic table. 91. Paraphrase For decay of thorium, the daughter element is protactinium. Practice Problems 1. Find the elements produced by decay of (a) 228 88Ra (b) 212 82Pb Answers 1. (a) 228 (b) 212 89Ac 83Bi As with alpha decays, you can use atomic masses to calculate how much
energy a beta decay will release. Example 16.9 How much energy would you expect the decay of a thorium-234 nucleus to release? Given Parent element is 234 90Th. Required Energy released by decay (E) Practice Problems 1. (a) What element does the decay of cobalt-60 produce? (b) How much energy would you expect the decay of a cobalt-60 nucleus to release? Answers 1. (a) 60 28Ni (b) 2.823 MeV Analysis and Solution As shown in Example 16.8, the daughter element is protactinium. However, this daughter atom has only the 90 electrons from the original thorium atom because the electron emitted by the thorium nucleus leaves the atom as beta 91Pa. The energy released radiation. The result is a positive ion, 234 is equivalent to the difference between the mass of the parent atom and the total mass of the decay products. Together, the masses of the protactinium ion and the beta particle equal the mass of a neutral protactinium atom. Table 7.5 on page 881 lists the atomic masses. m mparent m 234 m 234 91 Pa 234.043 601 u 234.043 308 u 0.000 293 u mproducts (m 234 m 234 m 0 1 90 Th 90 Th 91 Pa ) 1 u is equivalent to about 931.5 MeV, so E 0.000 293 u 931.5 MeV 1 u 0.2729 MeV Paraphrase The decay of a 234 90Th nucleus should release 0.2729 MeV. PHYSICS INSIGHT In calculating energy produced in nuclear decay, it is common to use atomic masses because these data are readily available. You see this being done in Examples 16.9 and 16.10. In both of these examples, as an intermediate step an ion notation has been used to account for the change in nuclear charge that happens during beta decay. In reality, in beta decay it is most likely that the atom will not end up ionized. The atom will either lose or gain an electron as appropriate. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 803 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 804 info BIT The name neutrino comes from the Italian word for “little, neutral one.” The word was coined by Enrico Fermi, a renowned physicist who developed a theory to explain beta
decay. neutrino: an extremely small neutral subatomic particle e WEB To learn more about the Sudbury Neutrino Observatory, follow the links at www.pearsoned.ca/school/ physicssource. info BIT Each second, more than 100 trillion neutrinos pass through your body! Almost all of these neutrinos were formed by nuclear reactions in the core of the Sun. weak nuclear force: fundamental force that acts on electrons and neutrinos antimatter: form of matter that has a key property, such as charge, opposite to that of ordinary matter ): an antipositron (e or 0 1 electron; a positively charged particle with its other properties the same as those of an electron The Elusive Neutrino Since the daughter nucleus has vastly more mass than an electron, there is practically no recoil of the daughter nucleus during beta decay. Consequently, physicists expected that virtually all of the energy released during decay would appear as the kinetic energy of the electron emitted by the nucleus. However, measurements found that most electrons emitted during decay had somewhat less kinetic energy than expected, and a few had almost no kinetic energy. During decay, small portions of the mass of the parent nuclei seemed to just disappear! In 1930, the Austrian physicist Wolfgang Pauli (1900–1958) suggested that the missing energy in beta decay was carried away by a tiny, as-yetundiscovered neutral particle, now called the neutrino,. Neutrinos are so small that physicists have yet to determine their size and mass. These “ghost-like” particles can pass through Earth with only a slight chance of being absorbed! Indeed, it was 1956 before an experiment using the intense radiation at a nuclear power plant finally proved conclusively that neutrinos actually exist. Eventually physicists discovered that there are actually two kinds of neutrinos given off in beta decay. In decay an antineutrino is released. As you will soon see, in decay a neutrino is released. The neutrino and antineutrino are identical in all respects except for their opposite spins. Many astrophysicists now think that neutrinos play a critical role in the cores of stars and perhaps in the structure of the cosmos as well. Concept Check How did physicists know that the neutrino must be neutral? Beta Decay, the Weak Nuclear Force, and Antimatter Careful study of beta decays revealed two further important differences from alpha decay. First, the transformation of
a neutron into a proton involves a fundamental force called the weak nuclear force. Although it is less powerful than the strong nuclear force, the weak nuclear force acts on electrons and neutrinos, whereas the strong nuclear force does not. The second difference is that beta decay involves antimatter. An antimatter particle has a key property, such as charge, opposite to that of the corresponding particle of ordinary matter. For example, an anti0), has a positive charge but the same mass electron, or positron (e or 1 as an electron. Section 17.2 presents antimatter in more detail. In decay, the transformation of a neutron into a proton produces an antineutrino rather than a neutrino: n → p 1 0 where is the symbol for the antineutrino. Thus, decays have the general form ZX → A A Z1Y 1 0 (Z increases by 1) 804 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 805 A second form of beta decay also produces an antiparticle. In decay, a proton transforms into a neutron, and the parent nucleus emits a positron and a neutrino: beta-positive () decay: nuclear decay involving emission of a positron ZX → A A Z1Y 0 (Z decreases by 1) 1 Sometimes, you will see the electron in these decay processes represented by the symbol e. To distinguish this electron from those orbiting the 0 to represent an electron nucleus, this chapter uses the symbol 1 0 is used to represent an emitted by a nucleus. Similarly, the symbol 1 emitted positron. Example 16.10 Nitrogen-13 (13 by decay. 7N) transmutes into carbon-13 (13 6C) 13N → 7 13C 6 0 1 Calculate the energy released if the atomic masses are 13.005 739 for nitrogen-13 and 13.003 355 for carbon-13. Given Nitrogen-13 transmutes into carbon-13 by decay. Atomic masses: 13.005 739 for nitrogen-13, 13.003 355 for carbon-13 Required Energy released in the decay Analysis and Solution The energy released is equivalent to the difference between the mass of the parent atom and the total mass of the products. Practice Problems 1. (a) What isotope will decay of thallium-202 produce? (b) Write the process for this decay. (c) How much energy will be
released by the decay of the thallium-202 nucleus if the mass of the thallium nucleus decreases by 0.001 463 u? Answers 1. (a) mercury-202 81Tl → 80 (b) 202 (c) 0.3400 MeV 202Hg 0 1 m mparent m 13 7N m 13 7N mproducts 6C m 0 (m 13 m 0 (m 13 6C 1 ) m 0 1 Note that again we use an ion notation indicating the presence of a carbon ion. In fact, at the end of the decay process, the carbon ion will lose an electron, and its mass can be written as (m 13 ) as shown above. ) 1 m 0 1 6C Since electrons and positrons have the same mass, m 0 1 Therefore, m m 13 7N 2m 0 1 (m 13 6C ) 13.005 739 u [13.003 355 u 2(0.000 549) u] 0.001 286 u m 0 1. 1 u is equivalent to 931.5 MeV, so E 0.001 286 u 931.5 MeV 1 u 1.198 MeV Paraphrase The decay of a 7 13N nucleus should release 1.198 MeV of energy. PHYSICS INSIGHT In Example 16.10, the energy released when a nitrogen-13 nucleus decays to form carbon-13 is calculated to be 1.198 MeV. Most nuclear decay data tables, however, will indicate that the total energy released in this decay is 2.221 MeV. Both are correct! When a decay occurs, a positron is emitted. This positron could combine with an electron to release the energy equivalence of 2 electron masses, an additional 1.023 MeV. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 805 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 806 Gamma Decay (-decay) Many nuclei have a series of energy levels that correspond to different configurations of the nucleons. In the excited states, the nucleons are farther apart. As a result, their binding energy is less than when in the ground state, and the total energy of the nucleus is greater. When making a transition to a lower-energy state, a nucleus emits a gamma-ray photon, similar to the photon emitted when an electron in an atom moves to a lower energy level (Figure 16.
9). However, the difference in energy is much greater for a nucleus. Gamma () decay does not change the atomic number or the atomic mass number. Gamma decays can be written using this general form: A AX Z ZX* → where * indicates an excited state and represents a gamma ray. Often, alpha or beta decay leaves the daughter nucleus in a highly excited state. The excited nucleus then makes a transition to its ground state, and emits a gamma ray. For example, when decay of boron-12 produces carbon-12, the carbon nucleus is highly excited and quickly emits a gamma ray: 12 5B → 6 6C* → 6 12 12C* 0 1 12C The energy of a gamma ray depends on the energy levels and the degree of excitation of the particular nucleus. Gamma rays can have energies ranging from thousands to millions of electron volts. Stability of Isotopes Figure 16.10 shows that stable isotopes form a relatively narrow band when plotted by their proton and neutron numbers. Other than hydrogen, all stable isotopes have at least as many neutrons as protons. As Z increases, the isotopes require an increasing ratio of neutrons to protons in order to be stable. There are no completely stable isotopes with more than 83 protons. The stable isotopes have greater binding energies than the unstable isotopes. Radioactive decay transmutes unstable nuclei into nuclei with higher binding energies. For example, heavy nuclei above and to the right of the stable band will emit alpha particles (larger red arrows), heavy nuclei below and to the right of the band will emit positrons, or particles (small red arrows), and lighter nuclei to the left of the band will emit electrons, or particles (blue arrows). All of these decay processes produce isotopes that are either in the stable band or closer to it. A nucleus may undergo several successive decays before it reaches the stable band 15 10 5 0 15.1 12.7 9.64 7.65 4.44 ground state Figure 16.9 Nuclear energy levels for carbon-12: How do these energy levels differ from those for electrons in hydrogen? gamma () decay: emission of a high-energy photon by a nucleus e WEB To learn more about nuclear energy levels, follow the links at www.pearsoned.ca/ school/physicssource. transmute: change into a different element α decays β decays N Z β decays 160 150 140 130 120 110 100 90
80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 Atomic Number, Z 90 100110 Figure 16.10 The black dots represent the band of stable isotopes. 806 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 807 Radioactive Decay Series Often, a radioactive nucleus will decay into a daughter nucleus that is itself radioactive. The daughter nucleus may then decay into yet another unstable nucleus. This process of successive decays continues until it creates a stable nucleus. Such a process is called a radioactive decay series. β decay α decay 238 234 230 226 222 218 214 210 206 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra 89 Ac 90 Th 91 Pa 92 U Atomic Number, Z Figure 16.11 How many different decay paths are there from uranium-238 to lead-206? Radioactive decay series beginning with 238 92U and ending with 206 82Pb. The dots in Figure 16.11 represent nuclei that are part of the decay series. A decay series can have several branches that lead to the same final product. Figure 16.11 shows that 218 84Po by three different combinations of decays. All of the intermediate isotopes in a decay series are unstable, but the degree of instability is different for each isotope. For example, 218 86Rn usually lasts for only a fraction of a second whereas 222 90Th takes thousands of years. Although not shown in Figure 16.11, many of the intermediate isotopes undergo gamma decay. 86Rn takes several days to decay and 230 84Po can transmute into 214 Concept Check Explain why gamma decays cannot be shown as paths on a decay series graph like the one in Figure 16.11. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 807 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 808 Potential Hazards of Nuclear Radiation Alpha, beta, and gamma radiation are all invisible, and most of their effects on the human body are not immediately apparent. As a result, it was not until years after the discovery of radioactive decay that researchers realized how dangerous radiation can be. Radiation poses two major types of risk: • Radiation Sickness: Radiation can ionize cellular material. This ionization disrupts the intricate biochemistry of the body, resulting in radiation sickness. Large doses of ionizing radiation can kill cells. Blood cells and
the lining of the intestine are particularly vulnerable. Symptoms include nausea, vomiting, diarrhea, headache, inflammation, and bleeding. Severe radiation sickness is often fatal. • Genetic Damage: High-energy particles and gamma rays can alter DNA, and lead to the development of cancers or harmful mutations. These effects often appear 10 to 15 years after radiation exposure. Everywhere on Earth, there is some naturally occurring radiation from cosmic rays and from radioisotopes in the ground. This background radiation causes some minor damage, but normally the body can repair such damage without any lasting harm. The effect of radiation on living organisms depends on the energy it carries, its ability to ionize atoms and molecules, and the depth to which it can penetrate living tissue. The charge and energy of the radiation determine how ionizing it is. The energy also affects how far the radiation can penetrate. The energy that a radiation has depends on the process that produces it. Table 16.2 compares the hazards posed by typical radiations from natural sources. Table 16.2 Radiation Hazards from Natural Sources Outside the Body Radiation Typical Penetration Ionization Hazard alpha beta gamma Travels about 5 cm in air. Cannot penetrate skin. high Travels about 30–50 cm in air. Penetrates about 1 cm into the body. moderate Travels great distances in air. Penetrates right through the body. low low low high Although and particles are much less penetrating than gamma radiation, they can still be extremely harmful if emitted by material absorbed into the body, because the nearby tissue has a continuing exposure to the radiation. For example, health scientists have calculated that breathing in a speck of dust containing just 1 g of plutonium is virtually certain to cause lung cancer within 30 years. The introduction of radioactive isotopes into the food chain is also a serious concern because these materials can accumulate in the body. For example, strontium-90, a by-product of nuclear weapons and power reactors, is absorbed into bones because it is chemically similar to calcium. Radiation from strontium damages bone marrow, reduces the production of blood cells, and can lead to bone cancer and leukemia. info BIT Both Marie and Pierre Curie suffered from radiation sickness. Some of Marie’s laboratory notebooks are still dangerously radioactive. radioisotope: an isotope that is radioactive 808 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 809 Despite its potential hazards, nuclear radiation is not always harmful. As you will see in section 16.
3, nuclear radiation has many beneficial industrial and medical applications. Measuring Radiation Exposure The effects of a given dose of radiation depend on the type of radiation. For example, a dose of infrared radiation that delivered 1 J/kg to living tissue would do little more than heat the tissue slightly. The same quantity of energy from X rays would ionize some molecules within the tissue, whereas the same quantity of energy from alpha radiation would be far more ionizing and disruptive. For this reason, SI has two units for measuring radiation exposure: The gray is the unit for absorbed dose and the sievert is the unit for equivalent absorbed dose. Gray (Gy): 1 gray is the dose of ionizing radiation that delivers 1 J of energy to each kilogram of material absorbing the radiation. Sievert (Sv): 1 sievert is the absorbed dose of ionizing radiation that has the same effect on a person as 1 Gy of photon radiation, such as X rays or gamma rays. The absorbed dose in sieverts is equal to the dose in grays multiplied by the relative biological effectiveness (RBE), a measure of how harmful the particular kind of radiation is. For example, the RBE for high-energy alpha particles is about 20, so an absorbed dose of 1 Gy of alpha radiation is equivalent to 20 Sv. An equivalent dose of 6 Sv in a short time is usually fatal. Typical radiation exposure for North Americans is less than 0.5 mSv annually. Table 16.3 summarizes some common sources of radiation exposure. Table 16.3 Common Sources of Radiation Exposure relative biological effectiveness (RBE): a factor indicating how much a particular type of radiation affects the human body Source Natural Artificial Total Radon from ground Cosmic rays Radioactive rocks/minerals, common building materials Ingested from natural sources Medical/dental X rays Nuclear weapons testing Consumer products All other Typical Exposure (Sv/year) 200 44 40 18 73 4 1 2 <400 Figure 16.12 Dosimeters: How do these devices measure exposure to radiation? Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 809 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 810 16.2 Check and Reflect 16.2 Check and Reflect Knowledge 1. What are the three basic radioactive decay processes and how do they differ from each other? 2. What is the ratio of neutrons to protons for the heaviest stable isotopes? 3. (a) Write the
alpha-decay process for 234 91Pa. (b) Identify the parent and daughter nuclei in this decay. 4. (a) Which type of beta decay transmutes carbon-14 into nitrogen? 11. Identify each type of decay in this series, and name the parent and daughter elements. (b) (a) 232 (d) 228 90Th → 228 22Na → 10 11 88Ra* → 228 (c) 228 88Ra → 228 89Ac → 228 90Th → 224 228 0n 1p → 0 (e) 228 (g) 0 (f) 88Ra* 4 22Ne 2 0 1 88Ra 0 89Ac 1 90Th 1 0 88Ra 4 2 0 1 (b) Write the process for this decay. Extensions 5. (a) Which type of beta decay transmutes the sodium isotope 11 22Na into 10 (b) Write the process for this decay. 22Ne? 6. Explain why the daughter nucleus in an alpha decay often emits a gamma ray. 7. Which form of radioactive decay has the 12. In a process called electron capture, a nucleus absorbs an electron and emits a neutrino. (a) What effect does electron capture have on the atomic number? (b) Use nuclear notation to write the general form for electron capture. greatest penetrating power? (c) Compare electron capture with beta decay. 13. Devise an experiment to test the hypothesis that gamma rays are emitted by nucleons jumping from higher energy levels to lower ones, similar to the energy-level transitions of electrons in an atom. What would you expect the spectrum of gamma rays emitted by a nucleus to look like? 14. Use library or Internet resources to learn how radon forms in the ground. Explain how radon can accumulate in basements in some areas. Why is this accumulation a health concern? e TEST To check your understanding of radioactive decay, follow the eTEST links at www.pearsoned.ca/school/physicssource. Applications 8. How much energy is released when 22Ne? The mass of 11 22Na decays to 10 11 is 21.994 436 u and the mass of 10 21.991 385 u. 22Na 22Ne is 9. Explain whether the atomic number can increase during nuclear decay. Support your answer with an example. 10. Compare the annual average radiation exposure from natural sources with the dose you would receive from a dental X ray. 810 Unit VIII Atomic Physics 16-PearsonPhys30-
Chap16 7/24/08 4:32 PM Page 811 16.3 Radioactive Decay Rates How can an archaeologist confidently tell you that a bison head found in southern Alberta provides evidence that First Nations peoples were here more than 5000 years ago? Why do doctors sometimes inject patients with radioactive dyes? In this section, you will be introduced to the concepts of radioactive decay rate and half-life, and begin to see how understanding the behaviour of radioactive elements can provide us with a glimpse into the past or give us powerful techniques to diagnose and combat disease. 16-3 QuickLab 16-3 QuickLab Simulating Radioactive Decay Problem How can decay rates of atoms be predicted? Materials container with 100 pennies graph paper Procedure Work in groups of two or three. 1 (a) Pour the pennies onto a flat surface and spread them out. Put aside any pennies that are tails up. These pennies have “decayed.” (b) Count the remaining pennies and put them back into the container. Record this count in a table. 2 Predict how many pennies will remain if you repeat step 1 two more times. 3 Repeat step 1 a total of eight times. 4 Pool your results with the other groups in the class. 5 Use the pooled data to draw a graph of how the number of pennies remaining varies with time. Questions 1. How many pennies were left after you had done step 1 three times? Does this result match your prediction? 2. If you repeat the experiment, will you get exactly the same results each time? Explain. 3. Suppose that step 1 takes 2 min each time. (a) How long would it take for the number of pennies remaining to decrease by half? How long will it take until only about an eighth of the pennies remain? How are these two time intervals related? (b) Try to find a formula to predict how many pennies will remain at any given time. Activity and Decay Constant The radioactive decay of a specific nucleus is unpredictable. The nucleus could decay in the next minute, or tomorrow, or thousands of years from now. However, you can accurately predict how many nuclei in a sample will decay in a given time. The decay constant () is the probability of any given nucleus decaying in a unit of time. The decay constant is a property of each particular isotope. For example, radium-226 has a decay constant of 1.4 1011 s1, indicating that each individual nucleus in a sample
of radium-226 has a probability of 1.4 1011 of decaying in 1 s. The greater the decay constant, the faster an isotope will decay. decay constant: probability of a nucleus decaying in a given time Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 811 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 812 activity or decay rate: the number of nuclei in a sample that decay within a given time becquerel (Bq): unit of activity, equal to 1 decay per second The activity (A) or decay rate is the number of nuclei in a sample that decay within a given time. Activity is usually measured in decays per second, or becquerels (Bq). A highly radioactive sample has many radioactive decays each second. Activity and the decay constant are related by this formula: A N t N where N is the number of radioactive nuclei, t is the time interval, and is the decay constant. Example 16.11 Carbon-14 has a decay constant of 3.8 1012 s1. What is the activity of a sample that contains 2.0 1015 carbon-14 nuclei? Practice Problems 1. Cobalt-60 has a decay constant of 4.1 109 s1. Find the activity of a sample containing 1.01 1022 cobalt-60 atoms. 2. A sample containing 5.00 1020 atoms has an activity of 2.50 1012 Bq. Find the decay constant of this sample. Answers 1. 4.1 1013 Bq 2. 5.00 109 s1 Given 3.8 1012 s1 N 2.0 1015 atoms Required activity (A) Analysis and Solution Substitute the given values into the formula for activity: A N (3.8 1012 s1)(2.0 1015) 7.6 103 Bq The negative sign indicates that the number of carbon-14 nuclei is decreasing. Paraphrase The initial activity of the sample is 7.6 kBq. The activity of a radioactive material decreases over time. The reason is simple: Radioactive decay “uses up” the unstable nuclei in the sample. Half-life Half-life is the time required for one-half of the radioactive nuclei in a sample to decay. For example, to diagnose thyroid problems, doctors sometimes inject patients with the radioactive isotope iodine-131, which has a
half-life of about 192 h. Out of a dose of 20 g of iodine-131, 10 g will decay within 192 h. Only 5 g of iodine-131 will remain after the next 192 h, then 2.5 g after the next 192 h, and so on (see Figure 16.13). A common symbol for half-life is t1/2. half-life: the time it takes for half of the radioactive nuclei in a sample to decay e SIM To see a simulation of half-life, follow the links at www.pearsoned.ca/ school/physicssource. 812 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 813 The number of nuclei of the original radioisotope left in a sample is given by the equation where t is the time elapsed, N0 is the number of nuclei of the original radioisotope when t 0, is the half-life of the isotope. and t1/2 N N0 t t1 /2 1 2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0. half-life 0 5 10 15 Time (days) Figure 16.13 A graph showing the radioactive decay of iodine-131 Example 16.12 Carbon-14 has a half-life of 5730 years. How long will it take for the quantity of carbon-14 in a sample to drop to one-eighth of the initial quantity? 5730 years Given t1/2 N 1 N0 8 Required time (t) Analysis and Solution N N0 1 N0 8 1 2 t t1 /2 In 3 half-lives, N will decrease to N0 t 3 Therefore, t1 /2 t 3t1/2 3 5730 years 1.719 104 years N0 1 2 1 2 1 8 1 2 Practice Problems 1. Astatine-218 has a half-life of only 1.6 s. About how long will it take for 99% of a sample of astatine-218 to decay? 2. Radium-226 has a half-life of 1600 years. What percentage of a sample of radium-226 will remain after 8000 years? Answers 1. about 11 s 2. 3.125% Paraphrase It will take just over 17 thousand years for the amount of carbon-14 in
a sample to drop to one-eighth of its original value. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 813 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 814 Example 16.13 Radon-222 has a half-life of 3.82 days. What percent of a sample of this isotope will remain after 2 weeks? Practice Problems 1. Strontium-90 has a half-life of 29.1 years. What percent of a sample of this isotope will be left after 100 years? 2. Tritium (3 1H) has a half-life of 12.3 years. How much of a 100-mg sample of tritium will be left after 5.0 years? Answers 1. 9.24% 2. 75% Given t1/2 3.82 days t 14 days Required percent remaining after 14 days Analysis and Solution The percent remaining is calculated from the ratio N N0 t t1 /2 1 2 N N0. N0 4 1.8 2 3 1 2 1 2 3.66 N0 0.079N0 N N0 0.079 or 7.9% Note that you can use the exponent or ^ key on a scientific or graphing calculator to evaluate powers of enter (1/2)^(14/3.82). 1 2. On a graphing calculator, you could Paraphrase Only 7.9% of a sample of radon-222 will remain after 2 weeks. Applications of Radiation The Rutherford gold-foil experiment that you learned about in Chapter 15 was one of the first examples of the use of nuclear energy (the release of alpha particles in the decay of radium nuclei) to study the inner working of atoms. Scientists apply radioactive decay in many other fields of scientific research, including archaeology. Radioactive compounds also have numerous industrial applications and are routinely used to diagnose and treat diseases. 814 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 815 THEN, NOW, AND FUTURE Radiotherapy During their first experiments with radium, Pierre and Marie Curie noticed that its radiation could burn the skin, but the wound would heal without forming scar tissue. They realized that radium could therefore be used to treat cancer. To ensure that this treatment was readily available to cancer patients, the Curies refused to patent their discovery
. Radiotherapy is particularly useful for treating cancer because cancer cells are more susceptible to the effects of radiation than healthy tissue is. Also, the radiation is concentrated on the cancer, and kept away from the surrounding tissue as much as possible (Figure 16.14). γ rays Figure 16.14 Rotating the radiation source around the patient minimizes damage to normal tissue. There is now a wide variety of radiation treatments. Often, a carefully focussed beam of gamma rays is directed at the tumour. Another common method is to inject the tumour with a short-lived radioisotope that emits alpha-particles. Questions 1. Give two reasons why gamma rays are used for the beam type of radiotherapy. 2. Why does injected radiotherapy use an isotope that undergoes alpha decay rather than one that gives off beta or gamma radiation? Radioactive Dating Nearly 6000 years ago, First Nations people of southwestern Alberta devised an ingenious method for hunting the vast herds of bison on the plains. By setting up barriers along a carefully chosen route, the First Nations people funnelled the bison toward a hidden cliff and then drove them over the edge. There were about 150 buffalo jumps in Alberta. The most famous, Head-Smashed-In Buffalo Jump, is now a United Nations World Heritage Site (see Chapter 2, Figure 2.68). By carefully measuring the ratio of carbon-12 to carbon-14 in bones found at this site, archaeologists have shown that it was used continuously for over 5500 years. e MATH To plot the decay rate of carbon–14 and other radioactive elements, and to learn how to mathematically determine a radioactive sample’s age based on the percentage of the sample remaining, visit www.pearsoned.ca/school/ physicssource. How did this carbon ratio indicate the age of these bones? High-energy neutrons in cosmic rays produce the radioisotope carbon14 by colliding with nitrogen atoms high in the atmosphere: 7N → 1n 14 0 14C 6 1H 1 This carbon-14 diffuses throughout the atmosphere. Some of it is absorbed by plants and enters the food chain. So, a small proportion of all the carbon metabolized by plants and animals is carbon-14. Carbon-14 undergoes decay to form nitrogen-14, whereas carbon-12 is completely stable. When living matter dies, it stops absorbing carbon, and the proportion of carbon-14 gradually decreases as it decays (see Figure 16.15). The
half-life of carbon-14 is 5730 years 100 90 80 70 60 50 40 30 20 10 0 t1 2 t1 2 10 000 t1 2 t1 2 20 000 Time (years) 30 000 40 000 Figure 16.15 Carbon-14 content as a function of the age of an artifact Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 815 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 816 e WEB To learn more about radioisotope dating, follow the links at www.pearsoned.ca/ school/physicssource. For archaeologists, bone fragments and other artifacts found at Head-Smashed-In Buffalo Jump are like clocks that show when the living matter stopped absorbing carbon. Suppose, for example, that the proportion of carbon-14 in a bone fragment is about 40% 1.32 40%, the carbon-14 has been of that in living tissue. Since decaying for about 1.3 half-lives, provided that the ratio of carbon-14 to carbon-12 in the atmosphere is the same now as when the buffalo was alive. Thus, the age of the bone fragment is roughly 1.3 5730 7500 years. Accurate estimates require more detailed calculations that take into account factors such as variations in the proportion of carbon-14 in the atmosphere through the ages. 1 2 Geologists estimate the age of rocks and geological formations with calculations based on isotopes with much longer half-lives. Such calculations are one of the methods that scientists use to estimate the age of Earth. Industrial Applications Manufacturers of sheet materials such as paper, plastics, and metal foils often monitor the thickness of the material with a gauge that measures how much of the beta radiation from a calibrated source passes through the material. Unlike mechanical thickness gauges, such gauges need not touch the material they measure, so they do not get worn down and have less risk of marking the material. Gamma rays can pass through thick metal parts to expose a photographic plate. The resulting image can reveal hidden air bubbles or hairline cracks, similar to the way X rays produce images of the inside of a patient’s body. Gamma-ray photographs are a non-destructive way of testing items that X rays cannot penetrate, including structural materials, jet engines, and welded joints in pipelines. Radioactive tracers are also used in pipelines to measure flow and to detect underground leaks. Some uses of radiation are controversial
. For example, beta radiation from tritium powers runway lights and emergency exit signs that require no electricity. However, several people have received harmful doses of radiation when tritium lights have been damaged. Critics of these lights argue that other technologies can provide reliable lighting during power failures without any risk of radiation exposure. Perhaps the most controversial application is the irradiation of food to kill bacteria, insects, and parasites. Although this process sterilizes the food and thereby prolongs its shelf life, there are concerns that the radiation might also alter the food in ways that make it harmful or less nutritious. Concept Check Why is beta radiation used for measuring the thickness of sheet materials, whereas gamma radiation is used for testing structural materials? 816 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 817 16.3 Check and Reflect 16.3 Check and Reflect Knowledge 1. What fraction of a radioactive material remains after four half-lives? 2. How many decays per second occur in a radioactive sample containing 6.4 1023 atoms of a material that has a decay constant of 5.8 1012 s1? 3. Which has the greater activity, 1 g of material with a half-life of 1 ms or 1 g of material with a half-life of 1 year? Explain your answer. Applications 4. Analysis of a rock sample shows that only of the original amount of chlorine-36 1 16 remains in the rock. Estimate the age of the rock given that the half-life of chlorine-36 is 3.0 105 years. 5. A radioactive tracer used in a medical test has a half-life of 2.6 h. What proportion of this tracer will remain after 24 h? 6. An archaeologist finds a wooden arrow shaft with a proportion of carbon-14 that is about 25% of that in a living tree branch. Estimate the age of the arrow. 7. A radioactive sample has an activity of 2.5 MBq and a half-life of 12 h. What will be the activity of the sample a week later? 8. Graph the data in this table. Then use your graph to estimate (a) the half-life of the material (b) the activity of the sample at time t 0 Time (h) Activity (decays/min) 1 2 4 6 8 10 3027 2546 1800 1273 900 636 Extensions 9. A dealer in antiquities offers to sell you an �
�authentic” dinosaur bone for a mere $100. He shows you a certificate indicating that carbon-14 dating determined that the bone is 65 million years old. Why should you be suspicious? 10. Do a Web search on use of irradiation in food production and distribution. Prepare a summary of the arguments for and against this technology. 11. (a) What is depleted uranium? (b) Why is depleted uranium used in armour-piercing shells and in ballast for aircraft? (c) Why are these applications controversial? e TEST To check your understanding of radioactive decay, follow the eTEST links at www.pearsoned.ca/school/physicssource. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 817 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 818 Figure 16.16 The doomsday clock from the Bulletin of the Atomic Scientists 16.4 Fission and Fusion In 1945, a group of the scientists who had designed and built the atomic bomb founded a magazine as part of an ongoing campaign to prevent this weapon from ever being used again. The Bulletin of the Atomic Scientists features a doomsday clock that symbolizes their estimate of the risk of a nuclear war (Figure 16.16). Since 2002, the clock has showed just seven minutes to midnight — a sobering reminder of the dangers posed by the enormous energy that nuclear reactions can release. The graph in Figure 16.4 (page 796) shows that binding energy per nucleon has a maximum value of about 8.7 MeV when the atomic mass number, A, is from 58 to 62 — the values for isotopes of iron and nickel. Up to this maximum, the binding energy per nucleon generally increases as A increases. Then, as A increases further, the binding energy per nucleon gradually decreases. The shape of this graph indicates that two distinct types of reactions can release energy from nuclei. Fission: When a nucleus with A > 120 splits into smaller nuclei, they have greater binding energy per nucleon. This fission reaction gives off energy equal to the difference between the binding energy of the original nucleus and the total binding energy of the products. Fusion: When two low-mass nuclei combine to form a single nucleus with A < 60, the resulting nucleus is more tightly bound. This fusion reaction gives off energy equal to the difference between the total binding energy of the original nuclei and the binding energy of the product
. For both nuclear fission and fusion, the energy released, E, is E Ebf (net change in mass defect) c2 Ebi where Ebi is the total binding energy of the original nucleus or nuclei, and Ebf is the total binding energy of the product(s). Since the binding energies correspond to the mass defects for the nuclei, the energy released corresponds to the decrease in the total mass defect. This change in the total mass defect equals the change in the total mass. Thus, the energy released corresponds to the mass that the reaction transforms into energy: mi) c2 E (mf where mi is the total mass of the original nucleus or nuclei, and mf is the total mass of the product(s). Concept Check Why does a nuclear reaction that increases the binding energy per nucleon release energy? Use an analogy to help explain this release of energy. 818 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 819 Nuclear Fission Often, fission results from a free neutron colliding with a large nucleus. The nucleus absorbs the neutron, forming a highly unstable isotope that breaks up almost instantly. Figure 16.17 shows one of the ways that uranium-235 can split into two lighter nuclei. In the next example, you will calculate the energy released during a fission reaction. 1 0 n compound nucleus 141 56 Ba 235 92 U 236 92 Figure 16.17 in a CANDU nuclear reactor. Absorbing a neutron causes uranium-235 to undergo fission 92 36 Kr Example 16.14 Calculate the energy released by the fission reaction 92Kr 3 0 92U 235 1n → 141 0 56Ba 1n. 36 Given Initial mass: 235 Final mass: 141 92U plus one neutron 56Ba, 36 92Kr, and three neutrons Required energy released (E) Analysis and Solution First, use the atomic mass data on page 881 to calculate the net change in mass resulting from the reaction. mi mf mi U mn m 235 92 235.043 930 u 1.008 665 u 236.052 595 u m 141 56 140.914 412 u 91.926 156 u 3(1.008 665 u) 235.866 563 u mf 0.186 032 u 236.052 595 u 235.886 563 u 3mn m 92Kr 36 Ba Practice Problems 1. Calculate the energy
released by the reaction 92U 1 235 0n → 94 40Zr 139 52Te 3 1 0n. 35Br), a 2. A uranium-235 nucleus absorbs a neutron and then splits into a bromine nucleus (87 146La), and lanthanum nucleus ( 57 additional neutrons. How many neutrons are released in this fission reaction? Express this reaction as a balanced equation. 3. How much energy is released in the reaction in question 2? Answers 1. 172.9 MeV 92U 1 2. 235 3. 167.8 MeV 0n → 87 35Br 146 57La 3 1 0n Now, use mass-energy equivalence to calculate the energy released. 1 u is equivalent to 931.5 MeV, so 931.5 MeV 1 u E 0.186 032 u 173.3 MeV Paraphrase The fission of an atom of uranium-235 into barium-141 and krypton-92 releases 173.3 MeV of energy. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 819 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 820 Comparing Chemical Energy with Nuclear Energy When you sit by a campfire, the warmth that you feel is due to the chemical energy released by the combustion of wood. All chemical processes, including combustion, involve electrons moving from one energy level to another. In Chapter 15, you learned that such transitions typically release no more than a few tens of electron volts. Example 16.15 shows that a nuclear process can release a vastly greater amount of energy. Example 16.15 Burning 1 kg of gasoline releases about 4.4 107 J. Compare this energy to the energy released by the fission of 1 kg of uranium-235 into barium-141 and krypton-92. Practice Problems 1. A typical family car requires approximately 1600 MJ of energy to travel 500 km. (a) How many kilograms of gasoline does it take to provide this energy? (b) What mass of uranium-235 would provide the same energy? Answers 1. (a) 36 kg (b) 22 mg Given chemical energy content of gasoline 4.4 107 J/kg Required ratio of the energy content of gasoline to that of uranium-235 Analysis and Solution From Example 16.14, you know that uranium-235 has about 173.3 MeV of nuclear potential energy per atom, assuming fission into barium and krypt
on. Use the atomic mass of uranium-235 to calculate the number of atoms in 1 kg of this isotope. Then calculate the potential energy per kilogram for comparison with gasoline. m235 92 U 235.043 930 u 1.660 539 1027 kg 1 u 3.902 996 1025 kg Number of atoms in 1 kg of 235 92U 1 kg 3.902 996 1025 kg Energy content of 235 92 U (2.562 134 1024 atoms kg )(173.3 MeV atom ) 2.562 134 1024 4.4402 1026 MeV/kg 4.4402 1032 eV kg 019 J 1 1.60 V e 1 7.10 1013 J/kg Energy content of 235 Energy content of gasoline 92U 7.10 1013 J/kg 4.4 107 J/kg 1.6 106 Paraphrase The nuclear potential energy of 1 kg of uranium-235 is about 1.6 million times greater than the chemical potential energy of 1 kg of gasoline. 820 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 821 Concept Check A nucleus is much smaller than an atom. How does this difference in size make nuclear reactions much more energetic than chemical reactions? Fusion What powers the Sun? The discovery of the nucleus and of mass-energy equivalence provided the key to this question, which had puzzled scientists for thousands of years. In the early 1920s, the British-American astrophysicist Cecilia Payne-Gaposchkin (1900–1979) showed that the Sun consists primarily of hydrogen (about 73%) and helium (about 27%). Noting that four protons have 0.7% more mass than a helium nucleus, the British astrophysicist Arthur Stanley Eddington (1882–1944) suggested that a fusion process might power the stars. In the 1930s, the young German physicist Hans Bethe (1906–2005) worked out the details of how hydrogen nuclei could release energy by fusing together to form helium. In the Sun and smaller stars, the process, called the proton-proton chain (Figure 16.18), has four steps. First, two hydrogen nuclei combine to form deuterium (an isotope of hydrogen with one neutron), an antielectron, and a neutrino. Next, another hydrogen nucleus combines with the deuterium nucleus to produce a helium-3 nucleus
and a gamma ray. Then, two of the helium-3 nuclei combine to produce a helium-4 nucleus, two hydrogen nuclei, and a gamma ray. In the final step, annihilation of two positron-electron pairs occurs. Each of these annihilations produces a pair of gamma photons. In order for these reactions to occur, the nuclei must have enough kinetic energy to overcome the electrostatic repulsion between them. Step Reaction Energy Released info BIT In the mid-1930s, Hans Bethe won a $500 prize for a paper on fusion in stars. He used the money to get his mother out of Nazi Germany. Bethe won the Nobel Prize for physics in 1967 and helped found the Bulletin of the Atomic Scientists. proton-proton chain: fusion process in which four hydrogen nuclei combine to form a helium nucleus 1H → 1 2H 0 1 (twice) 0.42 MeV (twice) (twice) 5.49 MeV (twice) 1 2 3 4 Total 1 2 1 1H 2 3 2H → 3 1 2He 2He 2 1 2He → 4 0 1 1H → 4 4 1 0 1 → 2 2He 2 0 1 neutrino positron H2 1 H2 1 positron neutrino 1H (twice) 2 7 ray He3 2 He3 2 ray 12.85 MeV 1.02 MeV (twice) 26.71 MeV ray He4 2 Figure 16.18 The protonproton chain Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 821 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 822 Example 16.16 The Sun radiates about 4 1026 W and has a mass of 1.99 1030 kg. Astronomers estimate that the Sun can convert only the innermost 10% of its hydrogen into helium. Estimate how long the Sun can continue to shine at its present intensity. Given Power 4 1026 W Hydrogen available for conversion 10% of total hydrogen 1.99 1030 kg mSun Required Time the Sun will take to convert 10% of its hydrogen into helium (t) Analysis and Solution The fusion of four hydrogen atoms produces 26.71 MeV. To find the rate at which helium nuclei are produced, divide the Sun’s power by the energy released during the formation of each helium nucleus: Rate of helium production power of Sun energy released
per helium atom Practice Problems 1. (a) How many helium nuclei does a star with a power of 1.6 1025 W produce every second? (b) Estimate how much helium this star has produced if it is 4 billion years old. Answers 1. (a) 4.1 1036 (b) 3.4 1027 kg 4 1026 W 26.71 MeV/atom J 4 1026 s V1.60 26.71 0 1 e M V e M 1 m to a 13 J 9.36 1037 atoms/s Since 4 hydrogen atoms are needed for each helium produced, multiply by 4 to find the rate at which the Sun converts hydrogen atoms into helium. Then, convert this rate to mass per second by multiplying it by the mass of a hydrogen atom: k g ms1.67 1027 Rate of hydrogen conversion 49.36 1037 ato o at s m 6.25 1011 kg/s Hydrogen makes up 73% of the mass of the Sun, but only 10% of this hydrogen can be converted into helium. The lifespan of the Sun approximately equals the amount of hydrogen that can be converted divided by the conversion rate. t amount of hydrogen available rate of conversion 1.99 1030 kg 73% 10% 6.25 1011 kg/s 2.32 1017 s or about 7 109 years Paraphrase The Sun can continue to produce energy at its present rate for about 7 billion years. 822 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 823 Concept Check Why can fusion reactions occur only at extremely high temperatures? The cores of massive stars can reach temperatures high enough for helium nuclei to combine to form carbon and oxygen. In some stars, these elements can undergo further fusion. The extent of this nucleosynthesis depends on the star’s density, temperature, and the concentration of the various elements. Current theory suggests that synthesis of elements heavier than iron and nickel occurs only during the explosion of supernovae. Such explosions distribute these elements throughout the cosmos. So, the uranium fuel for today’s nuclear power stations may have come from the explosion of a massive star billions of years ago. A hydrogen-fusion reactor might be an almost ideal energy source. Hydrogen is the most abundant of elements, and the end product, helium-4, is harmless. However, controlling and sustaining a fusion reaction for generating power is extremely difficult. To start the
fusion process, the hydrogen has to be heated to a temperature between 45 million and 400 million kelvins, depending on which isotopes are used. Then, this extremely hot gas has to be contained so that the fusion reactions can continue. Some researchers are using powerful lasers to generate the necessary temperatures and magnetic fields to contain the fusion reactions. However, the latest experiments have sustained fusion for only a few seconds and produced only slightly more energy than it took to run the reactor (see Figure 16.19). It will take major technological advances to make fusion power practical. nucleosynthesis: formation of elements by the fusion of lighter elements supernova: sudden, extremely powerful explosion of a massive star e WEB To learn more about fusion reactors, follow the links at www.pearsoned.ca/school/ physicssource. Figure 16.19 The Joint European Toroid (JET) fusion reactor Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 823 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 824 Concept Check There are concerns that tritium could leak from a fusion reactor. Why would tritium be a serious environmental hazard? 16.4 Check and Reflect 16.4 Check and Reflect Knowledge 1. (a) Complete this nuclear reaction: 235 92U → 54 140Xe? 2 0 1n (b) Does this reaction involve fission or fusion? Justify your answer. 2. What happens to the binding energy per nucleon in a nuclear reaction that releases energy? 3. An iron nucleus of binding energy 492 MeV fuses with a silicon nucleus of binding energy 237 MeV to form a nucleus with binding energy 718 MeV. Will this reaction release energy? Explain why or why not. 4. (a) Which elements are most likely to undergo fission? (b) Which elements are most likely to undergo fusion? 5. A neutron is emitted when aluminium-27 absorbs an alpha particle. (a) What isotope does this reaction create? (b) Write the process for the reaction. Applications 6. (a) Write the reaction formula for the fusion of helium-4 with oxygen-16. (b) How much energy does this reaction release? 7. (a) What particle is emitted when 1H) and tritium (3 deuterium (2 fuse to form helium? 1H) (b) How much energy does this reaction release? 8. A CANDU
-6 nuclear reactor can generate 700 MW of electrical power. A CANDU power plant transforms about 27% of its nuclear energy into electrical energy, with the rest being lost primarily as heat. 824 Unit VIII Atomic Physics (a) If the plant uses uranium-235 as fuel and the average energy released per uranium nucleus is 200 MeV, how many nuclei undergo fission each second when the reactor is running at full power? (b) Estimate how many kilograms of uranium-235 a CANDU-6 reactor uses in a year. List any assumptions you make. Extensions 9. (a) In stars much more massive than the Sun, iron-56 will eventually be produced in their centres. Suppose that two iron-56 nuclei fuse. Complete the following reaction and identify the element produced: 56 26Fe → (b) The element formed in the reaction 26Fe 56 in (a) has a mass of 111.917 010 u. Show that this reaction absorbs rather than releases energy. (c) Explain why stars like the Sun do not produce elements heavier than iron. 10. (a) Research the radioactive wastes produced by nuclear reactors. List the major isotopes produced and their half-lives. (b) Briefly outline some of the methods for storing and disposing of these wastes. 11. Compare and contrast the risks and benefits of generating electricity with coal and with nuclear reactors. e TEST To check your understanding of fission and fusion, follow the eTest links at www.pearsoned.ca/school/physicssource. 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 825 CHAPTER 16 SUMMARY Key Terms and Concepts femto proton neutron nucleon atomic number neutron number atomic mass number isotope atomic mass unit (u) strong nuclear force binding energy mass defect alpha radiation beta radiation gamma radiation transmute parent element daughter element beta-negative () decay beta () particle neutrino weak nuclear force antimatter ) positron (e or 0 1 beta-positive () decay gamma () decay radioactive decay series radiation sickness genetic damage radioisotope gray (Gy) sievert (Sv) relative biological effectiveness (RBE) decay constant activity (A) or decay rate becquerel (Bq) half-life fission fusion proton-proton chain nucleosynthesis supernova Key Equations Binding energy: Eb Enucleons Enucleus decay: A ZX → A4 Z
2Y 4 2 decay: A ZX* → AX Z Activity: A N t N Nuclear energy released: E (mi mf) c2 Mass defect: m mnucleons mnucleus Nmneutron matom Zm1 1H decay: A ZX → A Z1Y 1 0 decay: A ZX → A 1 Half-life: N N0 Z1Y 0 t t1 /2 1 2 Conceptual Overview Summarize this chapter by copying and completing this concept map. nuclear structure nuclear notation mass-energy equivalence types of radiation nuclear decay binding energy conservation laws discovery of neutrino decay constant decay rate activity half-life mass defect fission fusion Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 825 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 826 CHAPTER 16 REVIEW Knowledge 1. (16.1) Do all nuclei contain more neutrons than protons? Justify your answer. 2. (16.1) Is the atomic mass number for an atom always greater than the atomic number? Justify your answer. 3. (16.1) What is the term for elements that have the same atomic number but different neutron numbers? 4. (16.1) Explain how these nuclei are similar and how they differ: 233 92U, 92 235U, 238 92U. 17. (16.2) Compare the radiation dose that North Americans typically receive each year from radon and from diagnostic X rays. Which of these sources poses the greater health hazard? 18. (16.3) What is the activity of a sample that contains 1.5 1020 nuclei of an element with a decay constant of 1.2 1012 s1? 19. (16.3) After 1.5 h, the number of radioactive nuclei in a sample has dropped from 5.0 1020 to 2.5 1020. How many of these nuclei will remain after another 6 h? 20. (16.3) Explain why carbon-14 dating is not 5. (16.1) How many neutrons are in a nucleus useful for determining the age of a rock sample. of 115 55Cs? How many protons? 21. (16.4) Why do all of the elements used as fuel in 6. (16.1) Convert 50 MeV to joules. nuclear power plants have A > 200
? 7. (16.1) Calculate the energy equivalent for 22. (16.4) What is the primary energy source for 1 g of matter. most stars? 8. (16.1) Calculate the energy equivalent for 23. (16.4) List the steps in the proton-proton chain. Applications 24. Calculate the binding energy per nucleon for the following nuclei: (a) 4 (b) 28 (c) 58 (d) 235 2He 14Si 26Fe 92U 25. (a) Write the process for the decay of 52 26Fe. (b) Show that this process conserves charge and atomic mass number. 26. (a) What parent element decays into lead-208 by emitting an alpha particle? (b) Estimate the kinetic energy of the alpha particle. 27. (a) Write a complete decay process for the transmutation of 30 15P into 30 14Si. (b) Calculate the energy released in this decay. 28. In the oldest campsites yet discovered in Alberta, archaeologists have found materials that contain about a quarter of their original carbon-14. Estimate the age of these campsites. Give your answer to two significant digits. 2.3 u of mass. 9. (16.1) Calculate the mass equivalent for 300 MeV. 10. (16.1) Calculate the binding energy for a nucleus that has a mass defect of 0.022 u. 11. (16.2) Which decay processes do not change the atomic number of a nucleus? 12. (16.2) What is the charge on (a) a beta particle? (b) an alpha particle? (c) a gamma ray? 13. (16.2) Explain how each of these decay processes changes nuclear structure: (a) alpha decay (b) beta decay (c) gamma decay 14. (16.2) Describe this decay in words, identifying the parent element, the daughter element, and 19K → 43 the type of decay: 43 15. (16.2) Which of,, and radiation is the most penetrating, and which is the least penetrating? 20Ca 1 0. 16. (16.2) Explain why physicists think that radioactivity originates from nuclei. 826 Unit VIII Atomic Physics 16-PearsonPhys30-Chap16 7/24/08 4:32 PM Page 827 29. Until the early 1950s, a
paint containing radium-226 was used to make the dials on some clocks, watches, and aircraft instruments glow in the dark. Radium-226 has a decay constant of 1.98 1011 s1. (a) If the activity of one of these clocks is 0.10 MBq, how many atoms of radium-226 are on the dial? (b) Calculate the mass of radium on the dial. (c) The half-life of radium is 1600 years. Calculate the activity that the clock will have in 5000 years. 30. Graph the data in this table. Use your graph to estimate (a) the activity of the sample when t 5 h (b) the half-life of the radioactive material in the sample Time (h) 0 2 4 6 8 10 12 Activity (Bq) 1000.0 697.7 486.8 339.6 236.9 165.3 115.3 Time (h) Activity (Bq) 14 16 18 20 22 24 80.5 56.1 39.2 27.3 19.1 13.3 31. Calculate the energy released when three helium-4 nuclei combine to form a carbon-12 nucleus. 32. You are designing a thermoelectric power supply for a space probe. The probe will need 20 W of electricity for 14.5 years. The efficiency of thermal to electrical energy conversion is 15%. You are considering using polonium-208 as the fuel for the power supply. (a) What is the key advantage of polonium over a chemical fuel? (b) How much polonium will you need? Polonium-208 has a decay constant of 7.57 109 s1 and a half-life of 2.9 years. 84Po decays into 204 208 82Pb. Extensions 33. In 1918, Rutherford observed that bombarding nitrogen atoms with alpha particles produced oxygen and hydrogen. Use nuclear notation to write two reactions that could account for these products. Which reaction is more likely to occur? Explain your reasoning. How could you check your conclusion? 34. There have been over 2000 tests of nuclear weapons, including 711 conducted in the atmosphere or in the ocean. What radioactive products did these tests release? What health hazards result from this radioactive fallout? 35. Research nucleosynthesis in stars. List a sequence of fusion reactions that produces iron-56, and explain why smaller stars do not complete this sequence. How are the fusion reactions in the
Sun likely to end? Consolidate Your Understanding 1. Explain how atomic number, atomic mass number, and neutron number are related to the structure of the nucleus. 2. Use the concept of binding energy to explain why some nuclei are more stable than others. 3. Describe the differences between the alpha, beta, and gamma decays. 4. Explain how you can use conservation principles to predict the daughter elements created by a radioactive decay. 5. Distinguish between nuclear fission and nuclear fusion, and explain how to calculate the energy yield from either process. Think About It Review your answers to the Think About It questions on page 789. How would you answer each question now? e TEST To check your understanding of nuclear reactions, follow the eTEST links at www.pearsoned.ca/school/physicssource. Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. 827 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 828 C H A P T E R 17 Key Concepts In this chapter, you will learn about: charge-to-mass ratio quantum mechanical model standard model of matter Learning Outcomes When you have completed this chapter, you will be able to: Knowledge explain the discovery and identification of subatomic particles explain why high-energy particle accelerators are required describe the modern model of the proton and neutron compare and contrast elementary particles and their antiparticles describe beta decays Science, Technology, and Society explain the use of concepts, models, and theories explain the link between scientific knowledge and new technologies Skills observe relationships and plan investigations analyze data and apply models work as members of a team apply the skills and conventions of science 828 Unit VIII The development of models of the structure of matter is ongoing. Antimatter, quarks, particles appearing out of nowhere! Although these concepts may seem like science fiction, they are crucial for understanding the nature of matter. You are about to enter the world of undetectable particles that blink in and out of existence. You will see that a calculation by a theoretical physicist in the 1920s led to sophisticated new medical technology that uses a previously unknown form of matter (Figure 17.1). You will learn about the peculiar properties of quarks, the elusive building blocks for protons, neutrons, and many other subatomic particles. Quantum effects can make the subatomic world seem very strange indeed. This chapter introduces some of the most unusual and challenging ideas in all of physics. You will
learn that experiments are showing that in some profound ways the universe is stranger than anyone could have imagined a century ago. The theories that you will explore next are exhilarating, difficult, weird, and yet elegant. They are a key to the next century of atomic physics. ▲ Figure 17.1 Recent findings in atomic physics may seem strange, but they have led to amazing advances in technology, as well as better models of the structure of matter. 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 829 17-1 QuickLab 17-1 QuickLab Particle Tracking Simulation Problem What can magnetic tracking reveal about the properties and collisions of objects? Materials lid from shirt box or shoe box magnetic metal marbles glass marbles iron filings metre-sticks or wood slats iron filings box top metre-stick supports magnetic or glass marble ▲ Figure 17.2 Procedure 1 Turn the lid upside down and use metre-sticks or wood slats to support it above a smooth surface such as a tabletop. The gap should allow the marbles to roll freely under the lid. 2 Spread iron filings evenly over the lid (Figure 17.2). 3 Roll a glass marble and a magnetic marble under the lid and observe how they affect the filings. 4 Set the lid aside and place a line of five magnetic marbles spaced about 3 cm apart across the middle of the space between the supports. Estimate what percentage of glass marbles rolled between the supports will hit one of the five magnetic marbles. 5 Shake the lid to spread the filings evenly again and put it back on the supports. Then, roll glass marbles under the lid at least 10 times. After each collision, put the magnetic marbles back in line and spread the filings evenly. Note the number and shape of any tracks resulting from collisions between the glass marbles and the magnetic ones. Watch for any pattern in the formation of the tracks. Questions 1. What can you conclude about the magnetic field from the glass marbles? 2. Calculate the percentage of glass marbles that appeared to collide with the magnetic marbles in step 5. How close was your estimate? Account for any difference between your estimate and your observations. 3. Did any factor appear to affect the length of the collision tracks? 4. How would you expect the tracks to change if you repeated step 5 using round plastic beads instead of glass marbles? 5. How could you use the electric field from charged particles to detect these particles? How could you detect uncharged
particles? Think About It 1. How can you tell if a particle is fundamental? 2. What did the measurement of beta decays reveal about the structure of matter? 3. How many fundamental particles are there? Discuss your answers in a small group and record them for later reference. As you complete each section of this chapter, review your answers to these questions. Note any changes in your ideas. Chapter 17 The development of models of the structure of matter is ongoing. 829 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 830 17.1 Detecting and Measuring Subatomic Particles A skilled wilderness guide can tell a great deal about an animal from its tracks, not just identifying the animal but also estimating its age and how fast it was moving (Figure 17.3). In a similar way, physicists use tracks left by subatomic particles to identify the particles, study their interactions, and deduce the structure of matter (Figure 17.4). cloud chamber: a device that uses trails of droplets of condensed vapour to show the paths of charged particles ▲ Figure 17.3 Tracks of an adult snowshoe hare. What do these tracks tell you about the hare’s speed? ▲ Figure 17.4 Tracks of subatomic particles. The heavier particles have straighter tracks. Cloud Chambers and Bubble Chambers A cloud chamber contains dust-free air supersaturated with vapour from a liquid such as water or ethanol. The amount of vapour air can hold depends on temperature and pressure. Air is supersaturated when it contains more vapour than it would normally hold at a given temperature and pressure. So, the liquid and vapour in a cloud chamber are not in equilibrium, and a tiny disturbance can trigger condensation of vapour into droplets of liquid. A charged particle speeding through the supersaturated air will ionize some molecules along its path. The ions trigger condensation, forming a miniature cloud along the trajectory of the speeding particle. This cloud track shows the path of the particle the way a vapour trail formed by condensing exhaust gases shows the path of a jetliner through the sky. Figure 17.5 One of Charles ▲ Wilson’s cloud chambers. The glass sphere is an expansion chamber used to lower the pressure in the cylindrical cloud chamber. 830 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 831 Charles Thomson Rees Wilson
(1869–1969) made the first observations of particle tracks in a cloud chamber in 1910 (Figure 17.5). For the next 50 years, cloud chambers were the principal tools of atomic physics. They are to atomic physics what telescopes are to astronomy. The bubble chamber (Figure 17.6) was developed in 1952 by the physicist Donald Glaser (b. 1926). It contains a liquefied gas, such as hydrogen, helium, propane, or xenon. Lowering the pressure in the chamber lowers the boiling point of this liquid. When the pressure is reduced so that the boiling point is just below the actual temperature of the liquid, ions formed by a charged particle zipping through the liquid cause it to boil. Thus, the particle forms a trail of tiny bubbles along its path. Bubble chambers reverse the process used in cloud chambers: particle tracks are formed by a liquid turning into vapour instead of a vapour turning into liquid. info BIT Charles Wilson built the first cloud chamber in 1894 to study how clouds form. He shared a Nobel Prize for his contribution to particle physics. Wilson was a renowned meteorologist and an avid mountaineer. bubble chamber: a device that uses trails of bubbles in a superheated liquid to show the paths of charged particles info BIT CERN stands for Conseil Européen pour la Recherche Nucléaire. It is the world’s largest particle physics laboratory. ▲ Figure 17.6 One of the large bubble chambers at the CERN laboratory near Geneva, Switzerland Neutral particles will not create tracks in a cloud or bubble chamber. However, it is possible to calculate some of the properties of neutral particles from the tracks of charged particles that interact with them. Concept Check Outline possible reasons why neutral particles will not show up in a bubble chamber. How could you tell if a neutron were involved in a particle collision in a bubble chamber? e SIM To see an animation of particle tracks, follow the links at www.pearsoned.ca/ school/physicssource. Chapter 17 The development of models of the structure of matter is ongoing. 831 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 832 17-2 Inquiry Lab 17-2 Inquiry Lab Building a Cloud Chamber Question Can types of radiation be identified by the characteristics of their tracks? Hypothesis Since alpha, beta, and gamma radiations have different properties, the tracks they produce in a cloud chamber will be different
. Materials and Equipment clear glass container flat glass or plastic cover black blotting paper to fit the bottom of the container dry ice (frozen carbon dioxide) reagent grade ethanol (ethyl alcohol) foam plastic insulation tape silicone grease lamp with reflector radiation sources CAUTION: The temperature of dry ice is 78 °C. Handle it only with tongs or thick gloves. Be careful not to damage the casing on the radioactive samples. Variables Identify the manipulated, responding, and controlled variables in this experiment. Procedure Work with a partner or a small group of classmates. 1 Cut a piece of black blotting paper to fit the bottom of the glass container. 2 Saturate this blotting paper with alcohol, but avoid having a pool of alcohol in the container. 3 Cover the container using silicone grease to ensure a good seal between the cover and the container. 4 Use a piece of foam plastic insulation as the base for your cloud chamber. Place a piece of dry ice at least 2.5 cm thick in the centre of this base, then put the 832 Unit VIII Atomic Physics Required Skills Initiating and Planning Performing and Recording Analyzing and Interpreting Communication and Teamwork glass container on top of the dry ice. Placing more insulation around the sides of the dry ice will make it last longer. 5 Position the lamp so it shines down from the side of the chamber (Figure 17.7). Darken the room and wait several minutes. Note any changes that you observe in the cloud chamber. 6 Now tape an alpha-radiation source onto the inside of the container near the bottom. Write a description of any tracks that appear. If the tracks have a consistent shape or pattern, sketch a typical track. 7 Repeat step 6 with beta- and gamma-radiation sources. transparent cover T18-01 lamp glass container radiation source blotting paper foam plastic insulation dry ice ▲ Figure 17.7 A simple cloud chamber Analyzing and Interpreting 1. Were all of the tracks you observed produced by the three radiation sources? What else could produce tracks in your cloud chamber? Explain your reasoning. 2. Describe any relationship you see between the appearance of the tracks and the type of radiation that produced them. 3. Suggest improvements to the design of this experiment. Forming Conclusions 4. Do your observations support the hypothesis? If so, which properties of the radiation might be responsible for any differences in the tracks? 5. Under what conditions will subatomic particles travelling through the ethanol cloud not produce observable tracks? 17
-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 833 Extending 6. Hold a strong magnet against the side of the cloud chamber and observe the magnetic field’s effect on tracks from the three radiation sources. Explain whether you could use the magnet to help distinguish between different types of radiation. 7. Make a hypothesis about how taping the radiation sources to the outside of the glass container would affect the tracks produced by each source. Test your hypothesis. Could your results help you distinguish between different types of radiation? What other methods could you use? Analyzing Particle Tracks Physicists use cloud and bubble chambers as a key part of a controlled environment for studying subatomic particles. Applying a magnetic field across the chamber causes charged particles to follow curved or spiral paths. Measurements of the resulting tracks can be used to determine the mass and charge of the particles. For example, Figure 17.8 shows the path of a particle moving in a cloud chamber in which a magnetic field is coming out of the page. The particle entered the chamber from the left. Applying the right-hand rule to this track shows that the particle must have a positive charge. Often, a photograph of a cloud or bubble chamber will show tracks from a number of particles entering the chamber. Once in a while, a single track will suddenly branch into several diverging tracks, as shown in Figure 17.9. Such tracks suggest that the original particle has transformed into two or more different particles. B v F ▲ Figure 17.8 The right-hand rule shows that the particle must have a positive charge. Orient your right hand as shown and then rotate your hand so that your fingers point out of the page. Your palm points in the same direction as the force on a positively charged particle. ▲ Figure 17.9 These tracks suggest that a particle interaction can form two or more different particles. The following example demonstrates how a particle’s track can reveal its charge-to-mass ratio. Example 17.1 Assume that the tracks shown in Figure 17.10 were made by particles moving at a speed of 0.10c through a uniform magnetic field of 30 mT [out of the page]. The initial radius of each track is 5.7 mm. Determine the charge-to-mass ratio for the particles. Then, make a hypothesis about what the particles are. What is unusual about this pair of particles? ▲ Figure 17.10 Why are these particle tracks spiral rather than
circular? Chapter 17 The development of models of the structure of matter is ongoing. 833 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 834 Given v 0.10c 3.0 107 m/s 30 mT 0.030 T B r 5.7 mm 0.0057 m Required q m identification of each particle Analysis and Solution • Applying the right-hand rule shows that the particle spiralling clockwise has a positive charge. Similarly, the left-hand rule shows that the particle spiralling counterclockwise has a negative charge. • Since there was no track before the two particles appeared, they must have originated from a photon or a neutral particle. For charge to be conserved, the net charge on the two new particles must be zero. Therefore, these particles must have equal but opposite charges. • The charge-to-mass ratio for a particle moving perpendicular to a PHYSICS INSIGHT The tesla is a derived unit that can be expressed in terms of SI base units: k g 1 T 1 s2 A • m magnetic field can be derived from F F c v2 qv • Since the values of q, v, r, and B are the same for both particles, their masses must also be equal. Practice Problems Substituting the known values gives 1. Measurement of a particle track shows a radius of deflection of 8.66 104 m for a proton travelling at a speed of 4.23 105 m/s perpendicular to a 5.10-T magnetic field. Calculate the charge-to-mass ratio for a proton. 2. Determine the radius of the path of an electron moving at a speed of 3.2 105 m/s perpendicular to a 1.2-mT magnetic field. Answers 1. 9.58 107 C/kg 2. 1.5 mm q m 3.0 107 m/s 0.030 T 0.0057 m 3.0 107 m/s g k 0.0057 m 0.030 s2 A • 1.8 1011 A•s/kg 1.8 1011 C/kg The charge-to-mass ratio for an electron is 1.60 1019 C 9.11 1031 kg 1.76 1011 C/kg. The ratios for protons or small ions are about four orders of magnitude smaller. Paraphrase The charge-to-mass ratio of the negative particle is 1.8
1011 C/kg. Since this ratio matches the ratio for an electron, this particle very likely is an electron. However, the other particle has a charge-to-mass ratio of 1.8 1011 C/kg. This particle appears to be a positron, an antimatter particle. 834 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 835 Concept Check Can you tell whether momentum was conserved in the subatomic process in Example 17.1? Explain your reasoning. Example 17.1 illustrates how a conservation law can be a powerful tool for understanding the interactions of subatomic particles. Physicists often apply the conservation laws for charge, momentum, and mass-energy in this way. Experiments and theoretical calculations have shown that several other quantities are also conserved when particles interact. 17.1 Check and Reflect 17.1 Check and Reflect Knowledge 1. Compare the process for forming tracks in a cloud chamber with the process in a bubble chamber. 2. (a) List two subatomic particles that will leave tracks in a bubble chamber. (b) List two subatomic particles that will not leave tracks in a bubble chamber. 3. (a) Why does applying a magnetic field cause the particle tracks in a cloud or bubble chamber to curve? (b) What can the curvature of a particle’s track in a magnetic field reveal about the particle? Applications 4. Will X-ray photons produce tracks in a bubble chamber? Justify your answer. 5. (a) Determine the type of charge on each particle moving through the magnetic field in this diagram. (b) What information would you need to determine which particle is moving faster? 6. Describe and explain the differences in the tracks made in a bubble chamber by the particles in each pair: (a) protons and alpha particles (b) protons and electrons 7. In this bubble-chamber photograph, a particle enters from the bottom and collides with a helium nucleus. (a) Use conservation of momentum to show that the incoming particle was an alpha particle rather than a proton. (b) Describe how you could show that the particles have a positive charge. Extension 8. Bubble chambers have replaced cloud chambers in many research laboratories. What advantages do bubble chambers have over cloud chambers? e TEST To check your understanding of methods for detecting and measuring subatomic particles, follow the eTest links at www.pearsoned.ca/school
/physicssource. Chapter 17 The development of models of the structure of matter is ongoing. 835 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 836 17.2 Quantum Theory and the Discovery of New Particles fundamental particle: a particle that cannot be divided into smaller particles; an elementary particle Early in the 20th century, many scientists thought that there were just three fundamental particles: the electron, the proton, and the neutron. However, developments in quantum theory in the 1920s and 1930s suggested the possibility of other subatomic particles, some with peculiar properties. The Discovery of Antimatter In 1928, British physicist Paul Adrien Maurice Dirac (1902–1984) predicted the existence of peculiar particles such as the positive electron in Example 17.1 (pages 833–834). Dirac combined Einstein’s theory of relativity with Schrödinger’s wave equation (described in section 15.5). Dirac’s calculations, with the resulting relativistic wave equation, predicted that antimatter could exist. As mentioned in section 16.2, a particle of antimatter has a key property, such as charge, that is opposite to that of the corresponding particle of ordinary matter. In 1932, the American physicist Carl Anderson (1905–1991) provided the first evidence that antimatter really does exist. He photographed a cloud chamber track of a positron, as shown in Figure 17.11. For this achievement, Anderson won the Nobel Prize for physics in 1936. Concept Check How could Anderson tell that the particle track in Figure 17.11 showed a positively charged particle going down rather than a negative particle going up? His ingenious solution was to pass the particle through a thin lead plate. This plate slowed the particle a bit. Explain how Anderson could use this change in speed to confirm that the particle had positive charge. (Hint: The magnetic field for the cloud chamber in the photograph was directed into the page.) Quantum theory predicts that each kind of ordinary particle has a corresponding antiparticle. One of the startling properties of antimatter is that a collision between a particle and its antiparticle can annihilate both particles and create a pair of high-energy gamma-ray photons travelling in opposite directions. For example, an electronpositron collision can be written as e e → 2 Such electron-positron annihilations are part of the nuclear processes in stars. Note that e is the symbol for a positron. In
general, charged antiparticles are represented by simply reversing the sign of the charge on the symbol for the corresponding ordinary particles. Antiparticles for neutral particles are indicated by adding a bar over the symbol for the corresponding ordinary matter. Thus, the symbol for an antineutron is n. ▲ Figure 17.11 A picture worth a Nobel Prize: Anderson’s photograph provided evidence for the existence of the positron. Anderson used this path (the white streak in the photo) to show that the particle that made it had a positive charge but a mass equal to that of the electron. annihilate: convert entirely into energy 836 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 837 Concept Check Consider the example of a head-on collision between a positron and an electron travelling at equal speeds. Explain why momentum would not be conserved if all the energy of the two particles transformed into a single photon. Scientific Knowledge Can Lead to New Technologies The discovery of the positron made it possible to develop a powerful new medical diagnostic instrument. Positron emission tomography (PET) is an imaging technique that uses gamma rays from electron-positron annihilations to produce images of cross sections through a patient’s body. A computer can then generate a three-dimensional image by combining successive plane images (Figure 17.12). The patient receives an injection of a radioactive tracer containing an isotope, usually fluorine-18, that gives off positrons as it decays. As these positrons meet electrons within the patient’s body, they create pairs of gamma-ray photons. Several rings of gamma-ray detectors rotate around the patient. As the photon pairs register on diametrically opposite detectors, a computer builds up an image of the location and concentration of the radioactive tracer. These images can show a wide variety of vital information, such as blood flow, brain function, and the location of tumours. Quantum Field Theory By 1930, Dirac, Heisenberg, Born, and others had established the foundations of quantum field theory. In this theory, mediating particles are the mechanism by which the fundamental forces act over the distance between particles. Particles that mediate a force exist for such a brief time that they cannot be observed. For these virtual particles, energy, momentum, and mass are not related as they are for real particles. To help understand this concept, imagine two people tossing a ball back and forth while standing
on a very slippery surface, such as a smooth, wet sheet of ice. Throwing and catching the ball pushes the two people farther and farther apart (Figure 17.13(a)). In this analogy, the people correspond to ordinary particles and the ball corresponds to a mediating particle. For an attractive force, picture the same two people handing a somewhat sticky candy apple back and forth. The force that each person exerts to free the candy apple from the other person’s hand pulls the two people toward each other (Figure 17.13(b)). Note, however, that quantum field theory is a complex mathematical model with aspects that cannot be explained by such analogies. (a) (b) ▲ Figure 17.12 A PET scanner e WEB To learn more about PET scanners, follow the links at www.pearsoned.ca/ school/physicssource. quantum field theory: a field theory developed using both quantum mechanics and relativity theory mediating particle: a virtual particle that carries one of the fundamental forces virtual particle: a particle that exists for such a short time that it is not detectable Figure 17.13 (a) Throwing ▲ a ball back and forth while on a slippery surface pushes these people apart. (b) Handing a sticky object back and forth pulls them together. Chapter 17 The development of models of the structure of matter is ongoing. 837 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 838 quantum electrodynamics: quantum field theory dealing with the interactions of electromagnetic fields, charged particles, and photons gluon: the mediating particle for the strong nuclear force graviton: the hypothetical mediating particle for the gravitational force Project LINK For your unit project, you may want to describe the search for gluons and gravitons. The concept of mediating particles was first applied to the electromagnetic force, in a theory called quantum electrodynamics. This theory states that virtual photons exchanged between charged particles are the carriers of the attractive or repulsive force between the particles. For example, consider the electromagnetic repulsion between two electrons. One electron emits a virtual photon in the direction of the other electron. According to Newton’s third law, the first electron will recoil and its momentum will change by an amount opposite to the momentum of the photon. Similarly, when the second electron absorbs the photon, this electron will gain momentum directed away from the first electron. You can think of the photon for an attractive
force as acting a bit like the shared electron holding two atoms together in a covalent chemical bond. In the latter part of the 20th century, calculations using a refined version of quantum electrodynamics gave results that matched observed values with amazing accuracy — sometimes to 10 significant digits. Mediating Particles By 1970, research with high-energy particle accelerators led physicists to suggest that the strong nuclear force is mediated by zero-mass particles called gluons. So far, there is only indirect evidence for the existence of gluons. Advances in quantum theory also led to the conjecture that the weak nuclear force is mediated by three particles, designated W, W, and Z0. Experiments using extremely powerful accelerators detected these three particles in 1983. Some physicists think that the gravitational force also has a mediating particle, which they call the graviton. As yet, there is no experimental evidence that gravitons exist. Table 17.1 summarizes the current thinking about mediating particles. ▼ Table 17.1 The Fundamental Forces and Their Mediating Particles Force Range Relative Strength for Protons in Nucleus Particles Mediating Particle Observed? Electromagnetic infinite Weak nuclear <0.003 fm Strong nuclear <1 fm Gravitational infinite 102 106 1 1038 photons W, W, Z0 yes yes gluons indirectly gravitons no 838 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 839 17.2 Check and Reflect 17.2 Check and Reflect Knowledge 1. Describe the difference between ordinary matter and antimatter. 2. Outline how Anderson provided evidence for the existence of the positron. 3. (a) Which fundamental force is the strongest over large distances? (b) Which fundamental force is the weakest at nuclear distances? 4. (a) List the mediating particle for each of the fundamental forces. (b) Which of these mediating particles has not been detected at all? 5. Explain why a PET scan is like being X-rayed from the inside out. Applications 6. (a) What event is represented by the equation e e → 2? (b) Why is the event e e → not possible? 7. (a) Under what conditions will two protons attract each other? (b) Under what conditions will they repel each other? 8. The tracks in this diagram show the creation of two particles in a bubble chamber. Initially,
the two particles have the same speed. (a) What evidence suggests that a photon created the two particles? (b) Describe the path of this photon. (c) Which of the tracks shows the path of a positively charged particle? (d) Give two reasons why the other track must show the path of a negatively charged particle. (e) How are the mass and charge of the two particles related? (f) Why is it likely that the interaction involves an antiparticle? 9. Explain how the stability of helium nuclei demonstrates that the electromagnetic force is weaker than the nuclear forces. Extension 10. Research the Lamb shift and the Casimir effect at a library or on the Internet. Explain how these phenomena support the quantum field theory. e TEST To check your understanding of quantum theory and antimatter, follow the eTest links at www.pearsoned.ca/school/physicssource. Chapter 17 The development of models of the structure of matter is ongoing. 839 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 840 17.3 Probing the Structure of Matter Our understanding of the structure of matter comes from a series of remarkable technological advances over the past century. For example, the first circular particle accelerator (Figure 17.14(a)) was about 12 cm in diameter and generated particles with energies up to 13 keV. Now, the most powerful accelerators are up to 8.5 km in diameter and can reach energies of a teraelectron volt (1012 eV). This huge increase in energy reflects an interesting overall trend: To probe matter at smaller and smaller scales, physicists need bigger and bigger machines! This trend results from the nature of matter: All of the fundamental forces become markedly stronger at distances less than the diameter of a nucleus. ▲ Figure 17.14 (a) The first circular particle accelerator (b) Fermilab near Chicago, Illinois. Its Tevatron accelerator ring is 2 km in diameter. Energy Requirements 13.6 eV is sufficient to ionize a hydrogen atom. With energies of a few hundred electron volts, you can study electron shells of atoms and of molecules (using a spectrograph, for example). To determine the size of a nucleus, you need charged particles with enough energy to get close to it despite strong electrostatic repulsion. For his ground-breaking scattering experiment, Rutherford used alpha particles with energies in the order of 10 MeV. To examine the structure of the nucleus,
the energy requirements are much greater because the probe particles have to overcome the strong nuclear force. Within the nucleus, this short-range force is about a hundred times stronger than the electromagnetic force. The fundamental forces within individual subatomic particles are stronger still. So, probing the structure of stable particles such as protons and neutrons requires even more energy. With early, relatively low-energy accelerators, physicists could conduct experiments in which accelerated particles scattered from nuclei or split nuclei into lighter elements (hence the nickname “atom-smasher”). With high-energy particles, physicists can also study interactions that create new types of particles. Producing some of the heavier particles requires a minimum of several gigaelectron volts. 840 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 841 Natural Sources of Energetic Particles Some naturally radioactive isotopes emit particles that are useful for probing the structure of the atom. For example, Rutherford used polonium and radium as particle sources for his experiments. However, the maximum energy of particles from natural radioactive decay is roughly 30 MeV, which is not enough to probe the structure of nuclei. The other major natural particle source is cosmic radiation. Cosmic rays are high-energy particles that stream into Earth’s atmosphere from outer space. Astronomers are not certain about the origin of these particles. Some of them may come from solar flares and from distant supernovae. About 90% of cosmic rays are protons and most of the rest are alpha particles with a few electrons, positrons, antiprotons, and other particles. The energies of these particles range from roughly 102 to 1014 MeV. The particles from space (primary cosmic rays) rarely reach the ground because they interact with atoms in the atmosphere, producing less energetic secondary cosmic rays. Particle Accelerators The first particle accelerators were built around 1930. These accelerators, and the much more powerful ones developed since then, use electric and magnetic fields to accelerate and direct charged particles, usually in a vacuum chamber. Here is a brief description of some of the major types of particle accelerators. • Van de Graaff: A moving belt transfers charge to a hollow, conductive sphere, building up a large potential difference. This potential difference then propels ions through an accelerator chamber. • Drift Tube: An alternating voltage accelerates charged particles through a series of electrodes shaped like open tubes. The applied voltage reverses as the
particles pass through each tube, so the particles are always attracted to the next tube in the line. • Cyclotron: A magnetic field perpendicular to the paths of the charged particles makes them follow circular paths within two hollow semicircular electrodes. An alternating voltage accelerates the charged particles each time they cross the gap between the two electrodes. The radius of each particle’s path increases with its speed, so the accelerated particles spiral toward the outer wall of the cyclotron. • Synchrotron: This advanced type of cyclotron increases the strength of the magnetic field as the particles’ energy increases, so that the particles travel in a circle rather than spiralling outward. Some of the largest and most powerful particle accelerators are synchrotron rings. Concept Check Explain the advantages and disadvantages of studying nuclei with protons from a large accelerator as opposed to alpha particles produced by radioactive decay. primary cosmic rays: high-energy particles that flow from space into Earth’s atmosphere secondary cosmic rays: the shower of particles created by collisions between primary cosmic rays and atoms in the atmosphere Chapter 17 The development of models of the structure of matter is ongoing. 841 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 842 e WEB To learn more about particle accelerators, follow the links at www.pearsoned.ca/ school/physicssource. info BIT Marietta Blau published a number of papers on cosmic rays in the 1920s and 1930s. She was nominated for the Nobel Prize several times. muon: an unstable subatomic particle having many of the properties of an electron but a mass 207 times greater pion: an unstable subatomic particle with a mass roughly 270 times that of an electron lepton: a subatomic particle that does not interact via the strong nuclear force hadron: a subatomic particle that does interact via the strong nuclear force meson: a hadron with integer spin baryon: a hadron with halfinteger spin spin: quantum property resembling rotational angular momentum fermion: particle with halfinteger spin boson: particle with integer spin PHYSICS INSIGHT How Small Are Electrons? Experiments have shown that electrons are less than 1018 m across, while protons are roughly 1.6 1015 m in diameter. Leptons might be mathematical points with no physical size at all! 842 Unit VIII Atomic Physics Although particle accelerators were originally developed for pure research, they now
have medical and industrial uses as well. Many hospitals use accelerated particles for generating intense beams of X rays that can destroy cancerous tumours. Bombarding elements with particles from cyclotrons produces radioactive isotopes for diagnostic techniques, radiation therapy, testing structural materials, and numerous other applications. Particle accelerators can make a variety of specialized industrial materials by, for example, modifying polymers and implanting ions in semiconductors and ceramics. Accelerators are also powerful tools for analyzing the structure and composition of materials. Particle accelerators have even been used to verify the authenticity of works of art. The Subatomic Zoo In 1937, Carl Anderson and Seth Neddermeyer used a cloud chamber to discover muons in cosmic rays. These particles behave much like electrons, but have a mass 207 times greater and decay rapidly. Ten years later, Cecil Frank Powell discovered π-mesons, or pions, by using a photographic technology that Marietta Blau had developed. This method records tracks of particles on a photographic plate coated with a thick emulsion containing grains of silver bromide. Pions are much less stable than muons, and have some properties unlike those of electrons, protons, or neutrons. Improved particle accelerators and detectors led to the discovery of many more subatomic particles. Over 300 have now been identified. Most of these particles are highly unstable and have lifetimes of less than a microsecond. Studies of the interactions and decays of these particles show that there are two separate families of particles: leptons, which do not interact by means of the strong nuclear force, and hadrons, which do. The term lepton comes from leptos, a Greek word for “thin” or “small,” and hadron comes from hadros, a Greek word for “thick.” The diameters of leptons are much smaller than those of hadrons. The hadrons are divided into two subgroups, mesons (from meso, Greek for “middle”) and baryons (from barus, Greek for “heavy”). One of the key quantum properties for classifying particles is their spin. This property is like angular momentum from rotation of the particle. The spin of a particle can be either an integer or half-integer multiple of Planck’s constant divided by 2. Particles that have half-integer spin or 3 (such as 1 ) are called fermions, while
those that have integer spin 2 2 (such as 0, 1, or 2) are called bosons. Leptons and baryons are fermions. Mesons and mediating particles are bosons. Spin can affect the interactions and energy levels of particles. ▼ Table 17.2 Classification of Subatomic Particles Leptons Hadrons Meditating Particles Fermions all leptons Bosons baryons mesons all mediating particles 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 843 There are far more types of hadrons than types of leptons. In fact, physicists have found only six leptons plus their corresponding antiparticles. Table 17.3 compares the mass and stability of the leptons and some of the more significant hadrons. You are not required to memorize this table. Its purpose is to show a tiny set of the dozens of particles that physicists had discovered by the 1960s. What they were desperately seeking, and what you will learn about in the next section, was an underlying theory that could help make sense of this “subatomic zoo.” ▼ Table 17.3 An Introduction to the Subatomic Zoo Particle Symbol Mass (MeV/c2) Lifetime (s) Leptons electron electron neutrino muon muon neutrino tauon tauon neutrino Mesons pions kaons psi upsilon Baryons proton neutron lambda sigma xi omega.511 < 7 106 106 < 0.17 1777 < 24 140 135 494 498 3097 9460 938.3 939.6 1116 1189 1192 1315 1321 1672 stable stable? 2.2 106 stable? 2.9 1013 stable? 2.6 108 8.4 1017 1.2 108 9 1020 8 1021 1.3 1020 1031? 885* 2.6 1010 8 1011 7.4 1020 2.9 1010 1.6 1010 8.2 1011 *lifetime for a free neutron; neutrons in nuclei are stable Units for Subatomic Masses Note that Table 17.3 lists masses in units of MeV/c2. The kilogram is not always the most convenient unit for expressing the mass of subatomic particles. Physicists often deal with transformations between mass and energy using Einstein’s famous equation E mc2. Rear
ranging E. It follows that mass can be expressed in this equation gives m 2 c energy terms of units of speed of light squared. info BIT A pion will decay in the time it takes light to travel across a classroom. e MATH To better understand the relative sizes of subatomic particles, visit www.pearsoned.ca/school/ physicssource. Particle physicists find it convenient to use a factor of c2 to relate mass to electron volts, the traditional energy unit for particle physics. Conversion factors for such units are 1 eV/c2 1.7827 1036 kg 1 MeV/c2 1.7827 1030 kg 1 GeV/c2 1.7827 1027 kg Chapter 17 The development of models of the structure of matter is ongoing. 843 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 844 For example, the mass of a proton expressed in these units is mp 1.6726 1027 kg 938.23 MeV/c2 1 MeV/c2 1.7827 1030 kg The masses of the known subatomic particles range from 0.5 MeV/c2 to 10 GeV/c2, so exponent notation is usually not necessary with these units. Table 17.4 compares subatomic masses expressed in several common units. ▼ Table 17.4 Comparison of Mass Units for Subatomic Particles (to Five Significant Digits) Particle Mass (kg) Mass (u) Mass (MeV/c2) Electron Proton Neutron 9.1094 1031 5.4858 104 0.511 00 1.6726 1027 1.6749 1027 1.0073 1.0087 938.23 939.52 17.3 Check and Reflect 17.3 Check and Reflect Knowledge 1. Why do physicists require extremely highenergy particles for studying the structure of nucleons? 2. List two natural sources of energetic particles. 3. What is the advantage of high-altitude locations for performing experiments with cosmic rays? 8. (a) Find the energy equivalent of the mass of an electron. (b) The mass of a psi particle is 3.097 GeV/c2. Express this mass in kilograms. 9. Calculate the conversion factor between atomic mass units and MeV/c2. Give your answer to four significant digits. 4. List two uses of particle accelerators in Extensions
10. How has the development of superconducting electromagnets aided research into the structure of matter? 11. (a) What relativistic effect limits the energy of particles accelerated in an ordinary cyclotron? (b) Describe three different ways this limit can be overcome. e TEST To check your understanding of particle accelerators and subatomic particles, follow the eTest links at www.pearsoned.ca/school/physicssource. (a) medicine (b) industry 5. Identify a major difference that distinguishes (a) leptons from hadrons (b) mesons from baryons Applications 6. Can alpha particles from the radioactive decay of polonium be used to probe the nucleus? Explain your answer. 7. Calculate the momentum and kinetic energy of a proton that is accelerated to a speed of (a) 0.01c (b) 5.0 105 m/s 844 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 845 17.4 Quarks and the Standard Model By 1960, physicists faced a large and growing menagerie of subatomic particles. Since the leptons are small and there are only a few types of them, it seemed likely that they were fundamental particles. However, the number of hadrons was a puzzle: Could there really be a hundred or more fundamental particles? info BIT Gell-Mann coined the term “quark” from an obscure line in a novel by the Irish writer James Joyce. Zweig had called the new fundamental particles “aces.” The Quark Model In the 19th century, chemists studied the properties and reactions of the elements. The patterns observed in these properties led to the development of the periodic table and an understanding of the electron structure in atoms. Physicists searched for similar patterns in the properties and interactions of subatomic particles. In 1963, Americans Murray Gell-Mann (b. 1929) and George Zweig (b. 1937) independently proposed that all hadrons are composed of simpler particles, which Gell-Mann called quarks. By grouping the subatomic particles into distinct classes and families, Gell-Mann and Zweig showed that all the hadrons then known could be made from just three smaller particles and their antiparticles. These three particles are now called the up quark, the down quark, and the strange quark.
This theory required that the quarks have fractional charges that are either one-third of the charge on an electron or two-thirds of the charge on a proton. Understandably, many physicists had trouble accepting this radical concept. Using the quark model, Gell-Mann accurately predicted not only the existence of the omega (Ω) particle, but also the exact method for producing it. The quark model also accurately predicted key aspects of electronpositron interactions. Stronger evidence for the quark theory came in 1967 when Jerome Friedman, Henry Kendall, and Richard Taylor used the powerful Stanford Linear Accelerator to beam extremely high-energy electrons at protons. The electrons scattered off the protons, somewhat like the alpha particles that scattered off the gold nuclei in Rutherford’s scattering experiment (Figure 17.15). The pattern of the scattered electrons suggested that the mass and charge of a proton are concentrated in three centres within the proton. Later experiments confirmed these results and showed a similar pattern for scattering from neutrons. In the quark model, protons and neutrons contain only up and down quarks. The strange quark accounts for the properties of strange particles, hadrons that decay via the weak nuclear force even though they originate from and decay into particles that can interact via the strong nuclear force. In 1974, the discovery of the psi meson confirmed the existence of a fourth quark, the charm quark. Then, in 1977, the heavy upsilon meson was detected and found to involve a fifth quark, the bottom quark. Since there are six leptons, physicists wondered if there might be an equal number of quarks. In 1995, a large team of researchers at Fermilab found evidence for the top quark. This discovery required a huge accelerator because the top quark is about 40 000 times heavier than the up quark. quark: any of the group of fundamental particles in hadrons info BIT Richard Taylor was born in Medicine Hat and became interested in experimental physics while studying at the University of Alberta. In 1990, he shared the Nobel Prize in physics with Friedman and Kendall ▲ Figure 17.15 Scattering of high-energy electrons from a proton strange particle: a particle that interacts primarily via the strong nuclear force yet decays only via the weak nuclear force e WEB To learn more about the strange particles, follow the links at www.pearsoned.ca/ school/physicssource. Chapter 17 The development
of models of the structure of matter is ongoing. 845 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 846 THEN, NOW, AND FUTURE Small Particles and Big Science In the summer of 1936, Carl Anderson and his first graduate student, Seth Neddermeyer, lugged a cloud chamber and photographic equipment to the summit of Pikes Peak in Colorado, about 4300 m above sea level. They chose this location because the cosmic rays at that altitude were then the only source of the high-energy particles needed for their research. The work was lonely, uncomfortable, and poorly funded. It was also highly successful. Anderson and Neddermeyer discovered the muon with the cloud chamber photographs they took during their summer on Pikes Peak. Flash forward 60 years. How particle physics has changed! In 1995, the Fermi National Accelerator Laboratory (Fermilab) near Chicago, Illinois, announced that a team of researchers there had discovered the elusive top quark. In all, 450 people worked on this project. A key member of the team was Melissa Franklin (Figure 17.16), who has worked for over 18 years on the collider detector at Fermilab, a machine for studying the interactions resulting from colliding highenergy protons and antiprotons. A graduate of the University of Toronto and Stanford University, she is now a professor of physics at Harvard. Franklin is seeking to understand the structure of matter at the smallest scale, as Anderson did. However, Franklin collaborates with physicists from around the world and uses particle accelerators and detectors costing hundreds of millions of dollars. Although her work centres on tiny particles, she practises science on a big scale! Questions 1. What other fields of scientific research require huge budgets and international cooperation? 2. What are some advantages and drawbacks of “big science”? 3. Teamwork skills are becoming increasingly important in many areas of research. What other skills would be useful for a career in science? ▲ Figure 17.16 Melissa Franklin Table 17.5 compares some properties of the six quarks. The mass of an individual quark cannot be measured directly. The masses given here were derived mainly by taking the total mass of various particles and subtracting estimates of the mass-energy the quarks gain from motion and interactions via the strong nuclear force within the particles. For each quark there is a corresponding antiquark with the opposite charge. ▼ Table 17.5 Some Properties of Qu
arks Generation Name Symbol Mass (MeV/c2) Charge First up down Second strange Third charm bottom (or beauty) top (or truth) u d s c b t 1.5–4* 4–8 80–130 1.15–1.35 103 4.1–4.9 103 1.7–1.9 104 Some physicists think the up quark may be essentially massless. info BIT To name quarks, physicists chose words that would not be mistaken for visible physical properties. In Europe, physicists commonly call the top quark “truth” and the bottom quark “beauty.” 846 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 847 Individual quarks probably cannot be observed. The strong nuclear force binds the quarks in a particle very tightly. The energy required to separate quarks is large enough to create new quarks or antiquarks that bind to the quark being separated before it can be observed on its own. Composition of Protons and Neutrons The proton and the neutron contain only first-generation quarks. As shown in Figure 17.17, the proton consists of a down quark and two e e 2 up quarks. The net charge of these three quarks is 2 3 3 e e. The other quantum properties of the quarks also sum to 1 3 those of a proton. Similarly, a neutron consists of two down quarks and an up quark. In this combination, the positive charge on the up quark exactly balances the negative charge on the two down quarks. Composition of Other Hadrons All of the hadrons discovered in the 20th century can be accounted for with a combination of either two or three quarks: • All the mesons consist of a quark and an antiquark. • All the baryons consist of three quarks. • All the antibaryons consist of three antiquarks. However, experiments in 2003 produced strong evidence that the recently discovered theta particle () consists of five quarks: two up quarks, two down quarks, and an antistrange quark. Table 17.6 gives some examples of quark combinations. ▼ Table 17.6 Some Quark Combinations e WEB To learn more about the difficulties in measuring quarks, follow the links at www.pearsoned.ca/ school/physicssource. 2 3 e u
u 2 3 e Proton Neutron d 1 3 e ▲ Figure 17.17 The quarks making up protons and neutrons Meson Composition Baryon Composition Antibaryon Composition pion () pion (o) pion () kaon () ud uu ud us proton (p) neutron (n) sigma-plus () sigma-minus () uud udd uus dds antiproton (p) antineutron (n) uud udd Describing Beta Decay Using Quarks and Leptons Recall from section 16.2 that during beta decays of elements, the nuclei emit either an electron or a positron. Since both these particles are leptons, beta decay must proceed via the weak nuclear force. In decay of nuclei, a neutron transforms into a proton, an electron, and an antineutrino. Figure 17.18 shows that a neutron consists of an up quark and two down quarks while a proton consists of two up quarks and a down quark. So, the decay can be written as: udd → uud e e Charge is conserved since the difference between the 1 e charge on the 3 down quark and the 2 e charge on the new up quark equals the charge 3 on the electron emitted by the neutron. Physicists think that the down ▲ Figure 17.18 During decay, a down quark changes into an up quark. Chapter 17 The development of models of the structure of matter is ongoing. 847 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 848 quark emits a virtual W particle (a mediator for the weak nuclear force) that then decays into an electron and an antineutrino: d → u [W] e e e WEB To learn more about the decay of subatomic particles, follow the links at www.pearsoned.ca/ school/physicssource. The idea of mediating particles is essential to understanding beta decay and is a central idea in the standard model. Similarly, in decay of nuclei, an up quark in a proton turns into a down quark by emitting a virtual W particle that then decays into a positron and a neutrino: uud → udd [W] e e The Standard Model standard model: the current theory describing the nature of matter and the fundamental
forces The term standard model now refers to a model originally proposed in 1978 to explain the nature of matter and the fundamental forces. Here are some key concepts of this model: electroweak force: a fundamental force that combines the electromagnetic force and the weak nuclear force colour: a quantum property related to the strong nuclear force quantum chromodynamics: quantum field theory that describes the strong nuclear force in terms of quantum colour • All matter is composed of 12 fundamental particles — the 6 leptons and the 6 quarks — plus their antiparticles. • The electromagnetic force and the weak nuclear force are both aspects of a single fundamental force. Sheldon Glashow, Abdus Salaam, and Steven Weinberg developed the theory for this electroweak force in the late 1960s. This theory accurately predicted the existence and masses of the W, W, and Z0 particles. • The electromagnetic and nuclear forces are mediated by virtual particles. As discussed in section 17.2, these mediating particles are the photon, the gluon, and the W, W, and Z0 particles. • All quarks have a quantum property, termed colour, which determines how the strong nuclear force acts between quarks. (Quantum colour is not related to visible colours at all.) The quantum field theory describing the strong nuclear force in this way is called quantum chromodynamics. It is analogous to quantum electrodynamics with colour instead of electric charge and gluons instead of photons. Table 17.7 summarizes the fundamental particles in the standard model. ▼ Table 17.7 Fundamental Particles in the Standard Model Matter Generation First Second Third Quarks Leptons Force Mediating particle(s) up down strange charm bottom top electron electron-neutrino muon muon-neutrino tau tau-neutrino Fundamental Forces Electromagnetic Weak Nuclear Strong Nuclear photon W, W, and Z0 gluon 848 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 849 What’s Next in Quantum Theory? Many theorists are working to combine quantum chromodynamics and the electroweak force theory into a grand unified theory. One such theory suggests that the electromagnetic, strong nuclear, and weak nuclear forces would blend into a single force at distances less than 1030 m, and leptons and quarks could transform from one into the other. However, it would take tremendously high energy to push particles so close together. Although of no relevance for everyday
life, such theories could have a great effect on calculations about the origin of the universe. Another challenge is to develop a theory that unifies gravity with the other three forces. One of the most promising approaches is string theory, which treats all particles as exceedingly tiny vibrating strings of mass-energy. The vibration of the strings is quantized (like standing waves). The various kinds of particles are just different modes of vibration, with the graviton being the lowest mode. At present, these theories are highly speculative. The only thing known for sure is that the people who solve these problems will be in line for a Nobel Prize! grand unified theory: quantum theory unifying the electromagnetic, strong nuclear, and weak nuclear forces string theory: theory that treats particles as quantized vibrations of extremely small strings of mass-energy Project LINK For your unit project, you may want to describe theories that unify the fundamental forces. 17.4 Check and Reflect 17.4 Check and Reflect Knowledge 1. What experimental evidence suggests that the proton contains three smaller particles? 2. Why is it probably impossible to observe an individual quark on its own? 3. Compare the quark composition of a proton to that of a neutron. 4. Describe the difference between mesons and baryons in terms of quarks. 5. State two differences between leptons and hadrons. 6. List the 12 fundamental particles of matter in the standard model. 8. Is the beta decay → e possible? Justify your answer. e 9. Describe what happens in this decay process: uud → udd [W] e e Extension 10. Explain why a grand unified theory could have a great effect on speculations about the origin of the universe. Applications e TEST 7. (a) Using quark theory, write an equation for the beta decay of a neutron. (b) Show that charge is conserved in this decay process. To check your understanding of fundamental particles and the nature of matter, follow the eTest links at www.pearsoned.ca/school/physicssource. Chapter 17 The development of models of the structure of matter is ongoing. 849 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 850 CHAPTER 17 SUMMARY Key Terms and Concepts cloud chamber bubble chamber fundamental particle quantum field theory mediating particle virtual particle quantum electrodynamics gluon graviton primary cosmic rays secondary cosmic rays Van de Graaff accelerator drift
tube accelerator cyclotron synchrotron muon Key Equations Electron-positron annihilation: e e → 2 Mass units: 1 eV/c2 1.7827 1036 kg pion lepton hadron meson baryon spin fermion boson quark strange particle standard model electroweak force colour quantum chromodynamics grand unified theory string theory decay: udd → uud [W] decay: uud → udd [W] e e e e Conceptual Overview Summarize the chapter by copying and completing this concept map. Nature of Matter involves fundamental particles classed as have corresponding antiparticles leptons quarks generations generations first first second second quark & antiquark have integer spin third third bosons have half-integer spin interact via make up all gluons can interact via 3 quarks fundamental forces mediated by W W Z0 photons gravitons? unified in electroweak unified in 850 Unit VIII Atomic Physics 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 851 CHAPTER 17 REVIEW Knowledge 1. (17.1) How does a bubble chamber detect the path of a charged particle? 2. (17.1) Describe the technological advance in atomic physics made by (a) Charles Wilson (b) Marietta Blau (c) Donald Glaser 3. (17.2, 17.4) (a) In the early 1900s, which three subatomic particles were thought to be the fundamental building blocks of matter? (b) Which of these particles is still thought to be fundamental? 4. (17.2) What theory predicted the existence of antimatter? 5. (17.2) For each of these particles, list the corresponding antimatter particle and explain how it differs from the ordinary matter particle. (a) electron (b) proton 6. (17.2) How does quantum field theory account for fundamental forces acting over a distance? 7. (17.2, 17.3) Describe a similarity and a difference between a muon and a pion. 8. (17.3) What are two advantages of using units of MeV/c2 to express the mass of subatomic particles? 9. (17.3) Compare the size of an electron to that of a proton. 10. (17.4) Describe an experiment that provided evidence for the existence of quarks. 11. (17.4) Give
two reasons why Millikan did not detect any quarks with his oil-drop experiment. 12. (17.4) (a) Why did physicists suspect that there might be a sixth quark? (b) What is the name of this sixth quark? (c) Why was a huge accelerator necessary for the discovery of this quark? 15. (17.4) How does the string theory explain the various kinds of subatomic particles? Applications 16. Sketch the paths that alpha, beta, and gamma radiation would follow when travelling perpendicular to a magnetic field directed out of the page. 17. The red tracks in this diagram show a high- speed proton colliding with a hydrogen atom in a bubble chamber, deflecting downward (toward the bottom of the page), and then colliding with another hydrogen atom. These tracks curve clockwise slightly. (a) In which direction is the magnetic field oriented? (b) What conclusions can you make about the mass, speed, and charge of the particles involved in the first collision? (c) What conclusion can you make about the mass, speed, and charge of the particles that made the small spiral tracks? 18. (a) Write a nuclear decay equation to show how fluorine-18 can produce positrons for use in positron-emission tomography. (b) Describe the role that quarks play in this decay process. (c) Write an equation to describe what happens to the positrons within a patient undergoing a PET scan. 13. (17.4) Compare the quark composition of 19. The mass of a top quark is about 176 GeV/c2. antiprotons and antineutrons. Express this mass in kilograms. 14. (17.4) Which two fundamental forces are united 20. (a) Determine the charge on a particle having in the standard model? the quark composition uus. (b) Estimate the mass of this particle. Chapter 17 The development of models of the structure of matter is ongoing. 851 17-PearsonPhys30-Chap17 7/24/08 4:34 PM Page 852 21. The diagram shows a particle track recorded in a bubble chamber at the CERN particle accelerator. There is good reason to suspect that the particle is either an electron or a positron. The magnetic field in the bubble chamber was 1.2 T directed out of the page. 0 2 4 6 8 10 cm (a) Does the particle have
a positive or negative charge? Explain your reasoning. (b) Estimate the initial radius of the particle’s path. (c) Determine the initial momentum of the particle. Assume that the particle is an electron or a positron. (d) Why does the particle’s path spiral inward? (e) What could cause the short tracks that branch off from the large spiral track? Extension 22. Research Pauli’s exclusion principle at the library or on the Internet. Write a paragraph describing this principle and the classes of particles to which it applies. Consolidate Your Understanding 1. Describe three experiments that discovered new subatomic particles. Explain how these experiments changed physicists’ understanding of the nature of matter. 2. Give two examples of theories that accurately predicted the existence of previously unknown subatomic particles. 3. (a) Why was the quark theory first proposed? (b) Outline the experimental evidence that supports this theory. (c) Explain to a classmate why the standard model now includes six quarks instead of the three originally suggested by Gell-Mann and Zweig. Think About It Review your answers to the Think About It questions on page 829. How would you answer each question now? e TEST To check your understanding of the structure of matter, follow the eTest links at www.pearsoned.ca/school/physicssource. 852 Unit VIII Atomic Physics 18-PearsonPhys30-U8-Closer 7/25/08 7:36 AM Page 853 UNIT VIII PROJECT How Atomic Physics Affects Science and Technology Scenario Atomic physics has enormously influenced the development of modern science and technology. Advances in atomic physics have profoundly changed scientists’ understanding of chemistry, biology, and medicine. A century ago, technology that is taken for granted now would have seemed impossible even in principle. In this project, you will work with two or three classmates to research how the concepts presented in this unit affected an aspect of science or technology. Planning Brainstorm with your classmates to make a list of possible topics. Look for branches of science or technology that apply concepts of atomic physics. Here are some starting points: • medical diagnostic technologies, such as X rays, magnetic resonance imaging (MRI), PET scans, and radioactive tracers • chemistry applications, such as understanding molecular bonds and using spectroscopy to identify compounds • biology topics such as quantum effects in photosynthesis and DNA replication • computer and electronic devices, such as microchips
, tunnel diodes, and quantum computers • nanotechnologies such as nanotubes and atomic force microscopes • power technologies, such as nuclear reactors, tokamaks, and radioisotope thermoelectric generators (RTGs) Decide upon a topic to research. Often, you will find it easier to deal with a specific topic rather than a general one. For example, you could focus on nanotubes rather than trying to cover the whole field of nanotechnology. You may want to do some preliminary research on two or three promising ideas to see how much information is available. Consider the best way to present your findings. You might use a written report, an oral presentation, slides, a poster, a model, a video, or a combination of methods. Consult with your teacher on the format of your presentation. Assessing Results Assess the success of your project based on a rubric* designed in class that considers: research strategies clarity and thoroughness of the written report effectiveness of the team’s presentation Materials • library resources, including books and periodicals • Web browser and Internet connection Check with your teacher about any special resources, such as computer software, that you may need for your presentation. Procedure 1 Assign tasks for each group member. Each member should do part of the research as well as some of the preparation for the presentation, such as writing, preparing graphics, or building a model. Clearly identify who is responsible for each part of your project. 2 Once you have gathered basic information about your topic, consider what further research you need to do. For example, you may be able to interview an expert either in person, or by telephone or e-mail. Many university departments have an outreach program that might suggest an expert you could consult. 3 Check whether the presentation method your group has chosen is suitable for the information you have found during your research. Consult with your teacher if you think you need to change to another type of presentation. If you will be making an oral presentation, practise. Having friends and family critique your presentation can often help you find ways to improve it. Thinking Further • Atomic physics often seems to be too abstract or theoretical to have any relevance to the “real world.” How has your investigation changed your understanding of the relationship between atomic physics and other disciplines? • Does the influence of atomic physics extend beyond science? Can you find ways in which atomic physics has influenced the arts or philosophy? • Science fiction often employs ideas from physics. List several science-fiction
books, movies, or television series that use some of the concepts in this unit. How accurate is their treatment of atomic physics? *Note: Your instructor will assess the project using a similar assessment rubric. Unit VIII Atomic Physics 853 18-PearsonPhys30-U8-Closer 7/25/08 7:36 AM Page 854 UNIT VIII SUMMARY Unit Concepts and Skills: Quick Reference Summary Resources and Skill Building Concepts Chapter 15 cathode rays Electric force and energy quantization determine atomic structure. 15.1 The Discovery of the Electron Thomson’s experiments showed that cathode rays are subatomic particles with a negative charge. charge-to-mass ratio You can use electric and magnetic fields to measure the charge-to-mass ratio of a particle. charge quantization Millikan’s experiment 15.2 Quantization of Charge Electric charge exists only in multiples of the fundamental unit of charge, e. Millikan’s oil-drop experiment measured the charge on an electron and showed that charge is quantized. 15-1 QuickLab Example 15.2 15-2 QuickLab Example 15.3 eSIM of Millikan’s oil-drop experiment classical model of the atom 15.3 The Discovery of the Nucleus Rutherford’s gold-foil experiment led to the solar-system model with electrons orbiting a tiny positively charged nucleus at the centre of the atom. 15-3 QuickLab Example 15.5 spectra Bohr model energy levels 15.4 The Bohr Model of the Atom Elements and compounds have characteristic emission and absorption line spectra. The Bohr model uses energy levels to account for stability of the atom and to explain line spectra. This model accurately predicts many properties of hydrogen, but has several serious failings. 15-4 Design a Lab Example 15.6 An electron in an atom can occupy only orbits that give the electron discrete, quantized amounts of energy that are inversely proportional to the square of the principal quantum number. Example 15.7 15-5 Inquiry Lab quantum mechanical model 15.5 The Quantum Model of the Atom The wave properties of electrons lead to a powerful new model based on probability distributions. Figures 15.24–15.25 Chapter 16 Nuclear reactions are among the most powerful energy sources in nature. nuclear structure 16.1 The Nucleus Nuclei contain protons and neutrons bound together by the strong nuclear force. mass-energy equivalence Mass and energy are equivalent, and the one can be transformed
into the other. binding energy, mass defect The binding energy and mass defect of a nucleus indicate how tightly its nucleons are bound together. nuclear decay, transmutation 16.2 Radioactive Decay Some nuclei spontaneously transmute into a different element by emitting an alpha or beta particle. Nuclei can also give off gamma rays. All three types of radiation can be harmful. Examples 16.1 and 16.2 Example 16.3 Figure 16.3 Example 16.4 Examples 16.5–16.10 16-1 Inquiry Lab 16-2 Design a Lab half-life, activity nuclear reactions 16.3 Radioactive Decay Rates You can use the decay constant and the half-life of a radioisotope to predict the activity of a sample. Examples 16.12 and 16.13 16.4 Fission and Fusion Both the fission of a heavy nucleus into smaller nuclei and the fusion of light nuclei into a single heavier nucleus can release tremendous amounts of energy. Figures 16.17 and 16.18 Examples 16.14–16.16 Chapter 17 The development of models of the structure of matter is ongoing. particle tracks antimatter 17.1 Detecting and Measuring Subatomic Particles The existence and basic properties of subatomic particles can be determined by analyzing the paths of particles in magnetic and electric fields. 17.2 Quantum Theory and the Discovery of New Particles Quantum theory predicted the existence of antimatter, which was confirmed by Anderson’s discovery of the positron. Example 17.1 17-1 QuickLab, 17-2 Inquiry Lab Figure 17.11 quantum field theory According to this theory, the electromagnetic and nuclear forces are mediated by virtual particles. Figure 17.13 particle accelerators families of particles fundamental particles 17.3 Probing the Structure of Matter Particle accelerators produce high-energy particles, which are used to study the structure of matter. Hadrons interact via the strong nuclear force, whereas leptons do not. Bosons have integer spin and fermions have half-integer spin. 17.4 Quarks and the Standard Model The fundamental particles are the six leptons, the six quarks, and their antiparticles. All hadrons consist of a combination of quarks and/or antiquarks. Figure 17.14 Tables 17.2 and 17.3 Tables 17.5,17.6, and 17.7 854 Unit VIII Atomic Physics 18-PearsonPhys30-U8-Closer 7/25/08 7:36
. What is the activity of a sample that contains 1.5 1022 nuclei of an element with a decay rate of 1.5 1013 Bq? 16. Write the decay process for 18 9F, and identify the daughter element. 17. The half-life of sulfur-35 is 87.51 days. How much of a 25-g sample of this isotope will be left after a year? 18. Write the alpha decay process for 228 90Th and 6. Determine whether the charge on this particle is identify the daughter element. positive or negative. 19. Explain the difference between fission and fusion. CHAPTER 17 20. What is a positron? 21. What is a pion? 22. If an electron and positron collide, they annihilate each other and are converted into energy. (a) How much energy does the annihilation of a positron-electron pair produce? (b) Explain why the annihilation must produce two gamma rays with the same wavelength. (c) Estimate the wavelength of these gamma rays. Assume that the kinetic energy of the electron and positron was negligible. 23. What is a quark? 24. Describe this reaction in words: ve p → n e B 7. What is an alpha particle? 8. Here are four energy-level transitions for an electron in a hydrogen atom: 4 → nf ni ni 6 → nf ni ni (a) For which transition(s) does the atom 1 → nf 2 → nf 5 6 1 2 lose energy? (b) For which transition does the atom gain the most energy? 25. Identify the particle formed by each of these (c) Which transition emits the shortest wavelength photon? 9. You are comparing the energy released by two different atomic transitions in a mercury atom. Transition A produces a very bright green line while transition B produces a fainter violetcoloured line. Which of these transitions releases more energy? Explain. 856 Unit VIII Atomic Physics combinations of quarks: (a) uud (c) ud (b) us (d) dds 26. Use quarks to describe how a neutron decays into a proton and an electron. 18-PearsonPhys30-U8-Closer 7/28/08 10:48 AM Page 857 Applications 27. A beam of protons enters a vacuum chamber where the electric field strength is 40 kN/C and the magnetic field strength is 0.55 T.
(a) Sketch an orientation of the electric and magnetic fields that could let the protons pass undeflected through the chamber. (b) What speed must the protons have if they are not deflected by this orientation of the fields? 28. Find the magnetic field strength that will deflect a sodium ion (Na) in an arc of radius 0.50 m when the ion has a speed of 1.0 106 m/s. 29. This diagram shows an electron moving at 2.5 106 m/s through perpendicular electric and magnetic fields. B 0.50 T [out of the page] E 100 N/C [down] v (a) Calculate the electric and magnetic forces acting on the electron. (b) Calculate the net force acting on the particle. 30. An oil droplet with a mass of 1.6 1016 kg is suspended motionless in a uniform electric field of strength 981 N/C [down]. (a) Find the charge on this droplet. (b) How many electrons has the droplet either gained or lost? 31. (a) Find the wavelengths of the first four spectral lines produced by transitions into the n 3 energy level of a hydrogen atom. (b) What part of the electromagnetic spectrum are these lines in? 32. (a) Use the Bohr model to calculate the radius of the n 2 energy level in a hydrogen atom. (b) Find the de Broglie wavelength for an electron in this energy level. (c) Use the formula for the de Broglie wavelength to find the momentum of this electron. (d) Find the electron’s speed and kinetic energy. 33. Calculate the binding energy for 40 20Ca. 34. Identify the nucleus produced in each reaction. (a) (b) (c) 12C →? 6 14N →? n 7 206Tl →? v 81 35. Explain why each of these reactions cannot occur. 5 15C → (a) 6 1H → 3 (b) 3 11Na n → 23 15B ve 2He ve 19F 9 (c) 36. How much energy is released by decay of 16 7N? 37. Some blood-flow tests use iodine-131 as a tracer. This isotope has a half-life of 8.04 days. Estimate the percentage of iodine-131 left after 30 days. 38. How much energy is given off in the alpha decay of neodymium isot
ope 144 element does this decay produce? 60Nd? What daughter 39. A radioactive sample has an activity of 0.50 MBq and a half-life of 6 h. What will the activity of the sample be after 3.0 days? 40. The proportion of carbon-14 in charcoal used in a cave painting is only 12.5% of the proportion in living trees nearby. Estimate the age of this cave painting. 41. Calculate the amount of energy released when a carbon-12 nucleus absorbs an alpha particle and transmutes into oxygen-16. 42. Calculate the energy released by the reaction 2 1H 2 1H → 3 1H 1 1H. 43. (a) What fundamental particles does a neutron contain, according to the standard model? (b) Show that this combination of particles has zero net charge. Unit VIII Atomic Physics 857 18-PearsonPhys30-U8-Closer 7/25/08 7:36 AM Page 858 44. The size of a nucleus is in the order of 1 fm. (a) Calculate the electrostatic force of repulsion between two protons separated by 1 fm. (b) Determine the potential energy of this pair of protons. (c) What keeps a nucleus together despite the electrostatic repulsion between protons? Extensions 45. Two hydrogen atoms in the ground state collide head on and both ionize. Find the minimum speed at which the atoms could have been moving toward each other. 46. (a) Describe the reaction p → 0 p in words. (b) Calculate the minimum energy the photon must have to produce this reaction. 47. In decay, a proton becomes a neutron and the nucleus emits a positron and a neutrino. A proton has less mass than a neutron, and the positron and the neutrino carry away some mass and energy. Explain how such decays conserve mass-energy despite this apparent imbalance. 48. A 5.0-GeV photon creates, via pair-production, an electron and a positron. Calculate the total momentum of the two particles and sketch their motion relative to the path of the original photon. 51. A spill of radioactive material at an industrial site emits 1.25 mGy per hour, measured at a distance of 1.0 m from the spill. The relative biological effectiveness of this radiation is 2. (a) Compare the radiation dose from this spill to exposure from background radiation. (
b) At what distance from the spill would the annual absorbed dose be less than 0.1 mSv? (c) A newspaper headline reads “Dangerous Spill at Local Factory.” Is this description fair? Explain why or why not. 52. (a) What is the fundamental difference between a fusion process and one that combines matter and antimatter? (b) Compare the energy released by the fusion of ordinary hydrogen into helium-4 with the energy released by combining two protons with two antiprotons. (c) Why can antimatter not be used for generating power or propelling a spaceship now? 53. Suppose that an electricity generator powered by 1H 3 the fusion reaction 2 overall efficiency of 20%. How much deuterium and tritium will this generator need to produce 10 MWh of electricity, the annual consumption of a typical home? 0n has an 2He 1 1H → 4 49. Imagine that protons and electrons were not Skills Practice charged but could still form a hydrogen atom through gravitational attraction. Calculate the radius of the ground state. (Hint: Assume that the electron travels in a circular orbit and has a total energy me.) Gm p of 2 r 50. A typical banana contains about 0.40 g of potassium. Naturally occurring potassium is mainly 39 isotope 40 1.8 1017 s1. The average atomic mass for natural potassium is 39.1 u. 19K, but 0.012% of it is the radioactive 19K, which has a decay constant of (a) Calculate the activity of a typical banana. (b) Does the radiation exposure from bananas outweigh their health benefit as a source of potassium, fibre, and vitamins A, B6, and C? Explain your reasoning. 54. After two years, 6% remains of the original radioisotope in a sample. Estimate the half-life of this isotope. 55. A nucleus of boron 10 5B absorbs an alpha particle and emits a proton. Use nuclear notation to write this reaction process, and identify the element that it produces. 56. Does an electron that moves from an energy level of 5.1 eV to an energy level of 6.7 eV emit or absorb a photon? Find the wavelength of the photon. 57. How much energy is produced by the conversion of 0.250 u of matter into energy? 58. Calculate the radius of a hydrogen atom in the n 2 state. 858 Unit
VIII Atomic Physics 18-PearsonPhys30-U8-Closer 7/25/08 7:36 AM Page 859 59. An electron jumping from the n 3 to the n 2 state in a hydrogen atom emits a 656-nm photon. (a) Which state has the greater energy? (b) Find the energy difference between the Self-assessment 64. Outline how you would describe Rutherford’s gold-foil experiment to a friend. Explain why the results were startling for physicists in 1910. two states. 60. Calculate the binding energy for 24 12Mg. 61. Find the parent atom for this decay:? → 14N e v 7 62. Calculate the electrical charge of a particle composed of the quarks uus. 63. Find the activity of a sample containing 1.5 1020 radioactive atoms with a decay constant of 3.5 1015 s1. 65. (a) Explain why classical physics predicts that hydrogen will always produce a continuous spectrum rather than discrete spectral lines. (b) How does the Bohr model explain spectral lines? 66. Draw a concept map of the atomic physics topics that you find the most difficult. If you have trouble completing this concept map, discuss the concepts with a classmate or your teacher. 67. Explain why pair annihilation, such as e e → 2, does not violate the law of conservation of mass. 68. List the four fundamental forces and explain which ones are involved in nuclear binding energy, decays, fission, and fusion. e TEST To check your understanding of atomic physics, follow the eTEST links at www.pearsoned.ca/school/physicssource. Unit VIII Atomic Physics 859 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 860 APPENDIX STUDENT REFERENCES Contents SR 1 SR 2 SR 3 SR 4 SR 5 SR 6 SR 7 Safety.......................................... 861 The Inquiry Process............................... 864 The Problem-Solving Process: GRASP.................. 867 Using Graphic
Organizers........................... 869 Graphing Data................................... 872 5.1 Graphing Techniques......................... 872 5.2 Using the Graphing Tools...................... 874 Math Skills...................................... 875 6.1 Measurement: Accuracy and Precision........... 875 6.2 Mathematical Operations with Data.............. 876 6.3 Exponential Notation and Scientific Notation..... 877 6.4 Unit Conversions (Unit Factor Method).......... 878 6.5 Trigonometry for Solving Right Triangles......... 879 Tables.......................................... 880 7.1 SI Prefixes.................................. 880 7.2 Fundamental Quantities and Base Units.......... 880 7.3 Derived Quantities and Units................... 880 7.4 Numerical Constants.......................... 881 7.5 Atomic Masses of Selected Isotopes............. 881 7.6 Masses of Subatomic Particles..........
........ 881 860 Appendix Student References 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 861 SR 1 Safety In our modern society, safety has become much more than just protecting one’s well being. Issues around safety have become extremely important to industry, business, governments, and all kinds of institutions including educational institutes. The understanding and application of safety in a broad sense has become an industry in itself. Today, even to be considered for many jobs, one must take safety courses or have a variety of safety-training certificates. Now is the time for you to continue developing an attitude and awareness of safety. Safety is everyone’s responsibility. The Provincial Government, the local school board, your teachers, and you all have an important role in keeping a safe environment. Alberta Education has prepared a detailed document, “Safety in the Science Classroom”, outlining safety roles and responsibilities, and providing extensive information on potential hazards and safety procedures. This document is available online; go to www.pearsoned.ca/school/physicssource and follow the link to Safety in the Science Classroom. Of particular interest to you in this physics course is Chapter 6: Physical Hazards. For more technical information on issues, follow the link to Health Canada Index and search the topic alphabetically. In general, your role in maintaining safety is to act responsibly by carefully following directions, learning how to recognize potential safety hazards, and how to respond to potentially unsafe situations and emergencies. If you are unsure about how to proceed, ask your teacher. The Canadian Hazardous Products Act requires chemical manufacturers to include all hazard symbols and the degree of hazard on product labels. You may recognize hazard symbols on many household products. These symbols may indicate hazard(s), precaution, and first-aid treatment. Hazardous Product and WHMIS Symbols Household hazardous product symbols indicate the type of danger and the degree of danger. They appear in either a triangle (which means “caution”), a diamond (which means “warning”), or an octagon (which means “danger”). There are also numerous laboratory and industry hazard symbols in use. Some symbols relevant to Physics 20 and 30 are shown below: Figure SR 1.1 Laboratory and industry hazard symbols Many of the chemical products used in Canadian schools are manufactured in the United States. To standardize the labelling systems, WHMIS (the Work
place Hazardous Materials Information System) was developed. The symbols belonging to this system appear on materials and products used both in workplaces and our schools. Appendix Student References 861 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 862 2. Precautions with Mechanical Hazards a) Rotating machinery or moving devices can catch loose clothing, fingers or hair; therefore, keep a safe distance away from moving parts. b) Strong magnets can snap on ferromagnetic materials and other magnets very quickly. Use caution to avoid pinching skin or cutting clothing. c) Projectile launchers should be used only with appropriate eye protection and a clear “line-of-fire.” Be aware of the potential for a misfire or backfire. d) Model rockets with air, water, or solid-fuel motors can be a hazard. Wear eye protection and stay well clear of the launch area and potential trajectory. Make sure everyone watches for rocket parts falling back to the ground. 3. Precautions with Electrical Sources a) Do not use 110-V AC equipment if it has a damaged plug (e.g., missing the ground pin) or a frayed cord. Always disconnect the cord from the socket by pulling the plug, not the cord. b) Keep water and wet hands away from electrical cords. c) Do not touch a person in contact with live electrical currents. Disconnect the power source first. Then give artificial respiration if necessary. Call for help and treat burns. d) Make sure electrical cords are not placed where someone could trip over them. e) Do not allow a short circuit connection to a dry cell or battery. Dangerous amounts of heat can be generated in the wires and in the cells themselves, potentially causing an explosion or fire. f) Never attempt to recharge a non-rechargeable battery. Never cut open batteries. Their contents can be corrosive and poisonous. g) Keep flammable liquids away from electrical equipment. Sparks, in a motor for example, could ignite flammable vapours. Figure SR 1.2 Laboratory Safety Approach all investigations, especially in the laboratory, with maturity. Before you begin, read the instructions carefully, noting all safety precautions. In addition, your teacher may provide other safety reminders and rules pertaining to the laboratory activity. It is your responsibility to inform your teacher of medical conditions such as possible allergies to materials used (e.g., latex) or by-products of the activity. Inform your teacher if you wear
contact lenses. 1. General Precautions and Safety Equipment a) Identify all safety equipment in the laboratory. b) Know the location of and how to operate safety equipment, including the fire extinguisher, fire blankets, eyewash fountains, sand, and the first-aid kit. c) Know how and where to get help if needed. d) Wear appropriate laboratory apparel, which may include safety goggles, gloves, and/or lab aprons. e) Tie back long hair and secure any loose clothing. 862 Appendix Student References 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 863 b) Never look directly into the beam of an operating laser, even one with a low power. The eye focuses the laser light onto the retina, resulting in a power density of about 50 times that of direct sunlight. This can cause pinpoint burns to the retina. c) Guard against stray reflections and turn the laser off when not in use. d) Use radioactive sources only under the direction of your teacher. e) In all cases, the potential for harm from radiation increases with exposure. Exposure can be minimized by limiting the time of use and maximizing the distance away from the source. h) Spark timers create a very short but high voltage spark, which can give a minor electrical shock to anyone who touches a “live” part of the circuit. Although the shock itself is not dangerous, the surprise and sudden reaction can cause elbows to fly or objects to be dropped. i) Some high voltage devices can cause nasty shocks or skin burns. Be aware of the potential danger of charged capacitors, tesla coils, electrostatic generators, and transformers. Use only under the guidance of your teacher. j) When hooking up circuits, always have your teacher check the circuit before turning on the power. 4. Precautions with Electromagnetic Radiation a) Never look directly into an infrared (IR) or an intense, visible ultraviolet (UV) light source. Intense light can harm the retina. UV and IR radiation are absorbed by the cornea and eye contents, and can cause burning and overheating or other damage. Appendix Student References 863 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 864 SR 2 The Inquiry Process Inquire: to seek knowledge of, to ask about, to investigate, or to seek information by asking. Have you ever seen “sun dogs”? They are
a common occurrence in Alberta, especially in the winter. Often they are coloured and associated with a coloured ring, or halo, around the sun. They seem to occur in thin clouds or in frosty air. You may have noticed that they are always the same distance from the sun and the colours are always in the same order: red closest to the sun and violet farther away. This set of observations can be the focus of an inquiry process. Figure SR 2.1 Prairie sun dogs The inquiry process is a model of learning incorporated in Alberta Education curricula; it is not a separate topic or option. The inquiry process is applicable to all learning, and is especially suited to learning physics. Learning an inquiry approach is more than a way to succeed in physics; it is a useful way to deal with problems and challenging situations throughout any future career. The inquiry process is non-linear (there may be some side-tracks or dead ends), flexible (you can bend the rules or the process), individual (you can develop your own process), and recursive (you will need to revisit or loop through parts of the process as you go). An inquiry process model contains six components that connect together, all around your own thinking or reflection on the process. These components are: • Planning • Retrieving • Processing • Creating • Sharing • Evaluating 864 Appendix Student References Planning In order to inquire, you must have something in mind about which to inquire. Normally, the planning stage involves recognizing a situation, event, topic, or occurrence for which there is some unknown component. This leads to questions. In the planning stage, you (or your teacher) will need to look at the situation at hand and ask a question to be investigated. You may have many questions, but part of the process is to reflect on the situation and narrow (or in some cases, broaden) your question so that it is something you can actually investigate. From there, you will need to develop your process to lead through the other stages of the inquiry process. One way of working through the planning stage is to ask yourself the following questions: • What do I want to know? • What do I think the result might be? • How can I find out? • What do I need to do to find out? • How will I know when I have found out? • What form will my final results take? • How can I best share my results with others? • How can I evaluate what I have done? In this stage, you will need to develop a clear
inquiry question, propose a thesis or hypothesis, identify variables or related factors, create a data or information gathering process (experiment or research strategy), and recognize where your results may end up. Sometimes, this is the most difficult or lengthy part of the entire process, but very important. Retrieving Once you have an inquiry question, a hypothesis to test, and a plan to follow, you can begin the process of retrieving. This may involve experimentation or research. You may be gathering text information or numerical data from measurements. You may be using several different data sources including your own experimental data. In this stage, you may need to revisit Planning if you find difficulties or discrepancies during your information gathering. 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 865 Processing Evaluating The information or data you retrieve must be processed. You must evaluate the information, sort good data from poor data, decide what data is relevant, and perhaps re-identify variables. At this stage, you may find yourself looping through parts of the Planning and Retrieving stages again. Once you have good information, you need to decide how to display and analyze the data. What combination of data tables, graphs or graphic organizers should you use? Is there some mathematical analysis such as finding a slope, modelling a curve with an equation, or some statistical calculations that will be useful? Again, you may want to loop back to Planning, or ahead to Creating and Sharing to decide what detail of analysis you want to perform on your information. Ultimately, you need to be able to answer the question, “What does this information mean?” Creating You have asked a question, retrieved your information, and processed it. Now you must put the package together by creating a final product. Remember to look ahead to Sharing. In this product, you must clearly indicate your initial inquiry, provide a summary of your data or information, explain the meaning of your data, and state some conclusions regarding your inquiry question. At this point, you may find that you have more questions. This could lead you to another inquiry, and another, and another. This is the essence of how scientific knowledge continues to grow. Sharing This stage in the inquiry process is often devalued, yet it is a crucial step in the process. In science, if a new discovery is not communicated, then it is lost. In education, communicating ideas to others is one of the best learning processes. You don’t really know or understand something
until you can share the ideas with others. How you share will depend in part on how you created your final product. There are many modes of sharing: oral presentation, poster display, written report, demonstration, art work, working model, skit… Your job will be to choose a method that best fits you, your results, your classroom situation, and your audience. Again, you may need to loop back to Planning and Creating to get this in the most suitable form. Now is the time to look at the whole process (not just the results or answers). Ask yourself these questions: • What worked well? • What became a challenge? • Is there another or better way of doing any one of the stages in this process? • What parts of the process were easier or more difficult, or more or less effective? • How would I coach someone else to do this same inquiry in a more efficient way? • Are there other questions or situations that might be resolved by the process I followed? • What have I learned (about the inquiry question and about learning)? By critically evaluating what you have done, you will learn process skills beyond physics or science; you will develop skills to last a lifetime. A skeleton of a sample inquiry: Planning Situation: a solar halo display is very clear and colourful in the sky. Question: Where do the sun dog’s colours come from? Hypothesis: This is the same effect as the rainbow. If I spray water into sunlight, then I should be able to see a halo. What to do: Research rainbows and halos in print and online. Do an experiment with light rays and water drops to try to create a halo. How do I know I have the answer: I can create a halo and a rainbow and match them together. My final results: I will have a poster display with photos I have taken, and I will explain the results to my classmates. Retrieving Internet search informs me that halos and rainbows are different. From photos, I see that the colours are reversed. There are different types of halos. Sun dogs are part of ice crystal halos caused by refraction. Revisit planning Question: Does refraction of light through ice or other transparent solid crystals model the position of colours in sun dogs? Appendix Student References 865 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 866 Hypothesis: If I shine a white light beam on a transparent solid crystal,
then I will be able to see colours located in different directions. Experiment: Shine light through ice crystals, prisms, or other transparent solids, and look for colours in different directions. Sharing I will give a short presentation to my class to explain my question and results, and model the path of light with white and coloured yarn through a foam block. Classmates will be able to see “colours” only at certain directions. Evaluating I will look critically at the entire process once I am finished. Processing Can I see colours produced by light passing through the crystals? Is there a way for me to quantify my observations, e.g., can I measure directions? To what degree of accuracy can I measure directions? Do I have enough data? Do I need to look at more variables such as the shape or material of the crystal? How can I record my observations in the most meaningful way for this context? Creating I will summarize my specific question and investigative process. My results include: data tables showing the approximate angles where I see different colours of light refracted through prisms of different shapes; three photos of my apparatus set-up and colours I could see; and internet photos of more sophisticated experiments. I will also create diagrams of what could be seen in my apparatus according to theory, and a poster display of the theory behind the experiment and actual halos. There are other questions arising from my work that I will pose on my poster. For example: What happens to the halo when an ice crystal tips on its side? 866 Appendix Student References 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 867 SR 3 The Problem-Solving Process: GRASP Solving Numerical Problems A significant amount of effort in physics is spent in solving problems that have a numerical component. Often these problems seem more difficult than they really are because they involve physics concepts, principles, and/or laws as well as mathematical operations. Research into the problemsolving abilities of professionals and novices shows that professionals have logical procedures they follow when solving problems while novices who are having difficulty do not. The more methods the problem-solver can apply, the more adept he/she is at problem solving. The approach used in numerical problems throughout the textbook follows four basic steps. These steps are easy to remember and apply because combined, the first letters of the key words spell GRASP. A description of the four steps is provided below. Step 1: List what
is Given The first step in solving numerical problems involves answering the question, “What information are we given?” This is sometimes referred to as data extraction. To answer this question, read the problem carefully, study the information given, and represent physical quantities and numerical data with appropriate symbols, units, and directions (if necessary). Write the data in scientific notation to the correct number of significant digits (SR 6.3). Step 2: List what you are Required to find The second step involves answering the question, “What am I required to find?” To answer this question, identify what the problem is asking you to do. Be sure to note the units requested, if specified, and, for vector quantities, the direction. Answering this question will point you in the right direction and prevent you from being distracted by irrelevant information. Step 3: Analysis and Solution — Analyze the problem carefully and work out the Solution The third step requires a careful analysis of the problem before solving. To analyze the problem you must break it down into a series of logical steps. Begin by sketching a diagram. Many physics problems lend themselves to a diagram and the diagram often provides the key to solving the problem. Write down all the relationships you know involving the givens and the required. Also, write down any assumptions that must be made in order to solve the problem. An assumption is anything that must be taken for granted. Next, start with what you are trying to find, and answer the question, “What additional information do I need to calculate the unknown?” This may be a constant that you have to look up in a reference book or from a table of constants given in the textbook. Organize and sequence the information you have to form the solution. In physics, this often involves substituting appropriate data into an equation. It is good practice to rearrange an equation to solve for an unknown variable in terms of the other variables before substituting to obtain the final answer. Always be on the lookout for errors in the mathematical computations and check that the answer has the correct number of significant digits, and that appropriate units are included. Step 4: Paraphrase the solution The numerical answer should be stated in a form that answers the original question. Since the original question was a sentence, the statement of the final answer should also be a complete sentence. Physical quantities should include units and directions, if appropriate. You can use the following Numerical Problem Checklist to guide your work. Numerical Problem Check
Then brainstorm differences and list these in the non- overlapping sections. Used to clarify concepts and ideas by clustering them Cluster words and/or information around a central object, concept, or idea. Pie Chart Used to estimate the relationship of parts to the whole Estimate/research the importance or amount of proportionate time of each aspect of an event in relation to the whole. Flowchart/Sequence Chart Used to map out your thinking about an issue or to organize ideas for an essay or report Brainstorm aspects of the whole event. Select important aspects and put them into sequential order. Appendix Student References 869 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 870 Type of Graphic Organizer Purpose Method Ranking Ladder Used to rank ideas in order of importance Brainstorm ideas and rank them in order from least important (bottom rung) to most important (top rung). Fishbone Diagram Used to identify cause-and-effect relationships Right-Angle Diagram Used to explore the consequences of an idea and the impact of its application Target Diagram Used to weigh the importance of facts and ideas Identify a problem to be solved. List the “effect” at the head of the fish. Brainstorm “possible causes” in each bone. Rank the causes and circle the most probable ones, justifying your choice. Briefly describe the idea you are exploring on the horizontal arrow. Brainstorm consequences of the idea, and list these to the right of the horizontal arrow. Expand on one consequence, and list details about it along the vertical arrow. Describe social impacts of that trait below the vertical arrow. Brainstorm facts and ideas. Rank their importance and place the most important facts or ideas centrally, and the least important ones toward the outer rings. 870 Appendix Student References 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 871 Type of Graphic Organizer Purpose Method Agree/Disagree Chart Used to organize data to support a position for or against an idea or decision List a series of statements relating to a topic or issue. Survey agree-disagreement before discussion. Survey again after discussion and research. PMI (Plus, Minus, Interesting) Chart Used to summarize the positive and negative aspects of a topic or issue, as well as identify interesting aspects of the topic for possible further research Sort ideas or information about a topic or issue in a three-column chart that has the following headings
: Plus (), Minus (), and Interesting. Gathering Grid Used to make distinctions between ideas or events Concept Hierarchy Diagram Used to identify and sequence the subordinate concepts needed to understand a higher-order concept Gather information on a number of ideas or events and arrange it on a grid. Each idea or event is assigned to a separate row. Analyze the information according to selected criteria in each specific column. Place the higher-order concept at the top of a page. Then consider the question, “What concepts need to be understood before the higher-order concept above can be grasped?” The same question is then asked for each of the subordinate concepts identified and a hierarchy of connected concepts is created. Appendix Student References 871 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 872 SR 5 Graphing Data 5.1 Graphing Techniques Table SR 5.1 Total mass of system as sand is added to a beaker Total Volume of Sand Added V (mL) Total Mass of System m (g) 28 55 84 106 148 174 210 188 258 333 391 500 567 661 Physicists make extensive use of graphs to convey information and to help determine how one physical quantity is affected by another. To review simple graphical analysis techniques, as an example, use the data from a simple measurement experiment where students added given volumes of sand as measured in a graduated cylinder to a beaker on a balance, recording the total volume of sand in the beaker and the total mass of the system as shown on the balance. The Data Table A data table is the most practical way to record quantitative data. Table SR 5.1 above shows the data from the student experiment of adding sand to a beaker on a balance. Note that the name of each variable, the symbol, and the unit of measurement (in round brackets) are recorded at the top of each column. The Title of the Graph Figure SR 5.2 shows a sample graph for a student’s experiment. Every graph needs a title to describe what it is about. The title is placed at the top of the graph or in a box on a clear area above the graph. The Axes of the Graph Plot the independent variable on the horizontal x-axis and the dependent variable on the vertical y-axis. The variable that is changed intentionally is called the manipulated or independent variable. Volume of sand in the beaker was the manipulated or independent variable in the experiment 872 Appendix Student References 800 600
400 200 ) g ( m s s a M 0 0 Total Mass of System vs. Volume of Sand in Beaker m 640 g 165 g 475 g V 200 mL 20 mL 180 mL 100 200 Volume V (mL) 300 Figure SR 5.2 as students chose how much to add for each trial. The mass of the system depended on how much sand was added, thus the mass was the responding or dependent variable. Label each axis with the name, symbol, and unit of the variable being plotted, as shown in Figure SR 5.2. Scales are chosen for each axis to spread the measured values across the graph paper without making the plotting difficult. The maximum values in the data table determine the maximum numbers on the scales of the axes. To set a scale for an axis, analyze the data to be plotted and choose increments appropriate to the data. In Table SR 5.1, the maximum volume value was 210 mL, and the minimum volume value was 28 mL. Increments of 20 mL on the x-axis would be appropriate for the data. As well, the maximum total mass of system was 661 g, and the minimum total mass of system was 188 g. Increments of 50 g on the y-axis would be appropriate for the data. Plotting the Data and Drawing the Line of Best Fit Use a pencil to plot the data points as accurately as possible by making a small visible dot. Accuracy is important. Use the actual data values and make your best estimate of values within the scale grid. Once all of the data points have been plotted, a line of best fit is drawn. A line of best fit is a line that shows the trend of the points. Make the smoothest curve you can, balancing points that do not fit the curve evenly above and 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 873 below the curve. Do not try to have the curve or straight line go through all the dots since most data points have some error. The scatter of the data points from the smooth line indicates the extent of the errors in the data. Where a point is far off the line, a serious error may have been made. If this occurs, measure the data for that point again, if possible. If you believe an error was made, still plot the point, but ignore it while drawing your best fit curve. Interpolating from the Graph Interpolation is the process of estimating a value that is between two directly measured data points of a
variable. To interpolate, first locate the point on the appropriate axis for the value of the variable in which you are interested. Next, draw a line perpendicular to this axis to intercept the line of best fit. From this point on the line of best fit, draw a second line perpendicular to the second axis. Read the value of the second variable from this axis. For example, in Figure SR 5.2, a volume of 70 mL of sand is interpolated to a total mass of 300 g (indicated by the small star). There is some risk of inaccuracy involved in interpolation, since it is assumed that the trend of the line continues between the measured points. This assumption is not always valid. Extrapolating from the Graph Extrapolation is the process of estimating the values of a data point beyond the limits of the known or measured values. However, there is a considerable risk of inaccuracy, because it is assumed that the trend of the curve continues outside the range of the data. When the line is extended, a dotted line is used to show that the extension is little more than guesswork. The arrow in Figure SR 5.2 shows the process of extrapolating the curve to find the mass of the system without any sand in the beaker. What is this value and what does it represent? How valid is the value? Calculating the Slope If the line of best fit is straight, the slope of the line can be found. The slope of the line is defined as the rate of change of one variable with respect to the other and is found by the ratio of the rise to the run. To find the slope, find two points far apart on the line of best fit whose values are easily readable from the scales on the axes. Note that the points used should not be data points (i.e. values that were measured and plotted to draw the line of best fit). On the graph, lightly draw a horizontal line from the lower point and a vertical line from the higher point so that they intersect. Use the axis scale to determine the change in vertical value (rise) and change in horizontal value (run) along these two line segments. In Figure SR 5.2, the rise is shown as 475 g and the run as 180 mL. The slope of this graph is thus: slope rise/run 475 g/180 mL 2.64 g/mL Notice that the slope in this example has units; it also has some physical significance: it represents the density of the
sand. Writing the Equation of the Line If the trend of the curve is a straight line, then changes in the plotted variables are directly proportional to each other. As the change in one variable doubles, the change in the other doubles, and vice versa. The general equation for a straight line is y mx b, where y is the variable on the vertical axis, x is the variable on the horizontal axis, m is the slope of the line, and b is the vertical axis intercept. Figure SR 5.2 shows a straight line for volumes of sand at least up to 210 mL. For this range, the change in mass is directly proportional to the volume of sand added. The general equation for the linear graph in Figure SR 5.2 is: m V b where m is the total mass of the system, is the density of the sand, V is the total volume of sand in the beaker, and b is the mass of the empty beaker. The specific equation for this graph is: m (2.64 g/mL)V 115 g. Using the Equation of the Line It is often more convenient to extrapolate or interpolate from the specific equation than from the graph. For example, the total mass of the system could be determined if 800 mL of sand is added, even though our beaker may not be that big and our graph does not extend that far. To do this, substitute 800 mL for V in the equation and calculate m. The accuracy of this result depends on the accuracy of the equation, which in turn depends on the accuracy of the determination of slope and vertical axis intercept. Appendix Student References 873 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 874 5.2 Using the Graphing Tools Graphing calculators make the process of plotting and interpreting graphs easy and efficient. Data from an experiment can be entered into the calculator and displayed as a scatterplot. The calculator can be used to determine the function that best models a given scatterplot. The information provided for this function can also be used to write the equation that best describes the relationship between the two plotted variables. The graphing calculator can also be used to help us explore the graph of a given equation or relationship. It can be used to interpolate values between the plotted points or to extrapolate values beyond the plotted points. These uses make the graphing calculator a very powerful laboratory tool. Data can also be stored and plotted in a com- puter
spreadsheet such as Microsoft Excel. The eMath activities in this textbook provide opportunities for you to use the graphing calculator or a computer spreadsheet. 874 Appendix Student References 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 875 SR 6 Math Skills 6.1 Measurement: Accuracy and Precision Measurement is a process of comparing some unknown characteristic, attribute, or quantity to some known or accepted scale or standard. Measurement involves tools and technique. If there is a problem with either, there can be problems with the quality of the measured data. A tape measure with the end broken off would give incorrect measurements if the problem was not noticed. Using a metre stick to measure the thickness of a hair would not work well. Forgetting to include the weight of the fuel when weighing in freight to load a plane could be disastrous. At best, a measurement is an estimate; there is always some amount of uncertainty to the value you record. To make a measurement, and to use measured values correctly, we must understand a number of important issues. Accuracy Accuracy is a means of describing the quality of measurements, or how closely a measurement agrees with the accepted or actual value of the quantity being measured. A broken tape measure will not give accurate values for length. The difference between an observed value (or the average of observed values) and the accepted value is called the deviation. The size of the deviation is an indication of the accuracy. Thus, the smaller the error, the greater is the accuracy. The percent deviation is determined by subtracting the accepted value from the measured value, dividing this by the accepted value, and multiplying by 100. Thus, percent deviation (measured value accepted value) accepted value 100% red-heads. The smaller the divisions of its scale, the less uncertainty there will be in reading values. Any measurement that falls between the smallest divisions on the measuring instrument is an estimate. We should always try to read any instrument by estimating tenths of the smallest division. For a ruler calibrated in centimetres, this means estimating to the nearest tenth of a centimetre, or to 1 mm. Using this procedure, the length of the object in Figure SR 6.1 is found to be 6.7 cm. We are certain of the 6, but the 0.7 is an estimate. In reality, it could easily be 0.6 or 0.8. It is however, unlikely that it would be 0.5 10 11 I 6.7 cm Figure SR 6
.1 Figure SR 6.2 shows the measurement of the same object using a ruler calibrated in millimetres. The reading estimated to the nearest tenth of a millimetre appears closest to 6.74 cm. It might be tempting to record the length as either 6.7 cm or 6.8 cm. This would be wrong. We can tell that the length is between the two divisions. The estimated digit is always shown when recording the measurement. The estimated digit in this reading is 0.04 cm 10 11 Precision Precision is the degree of repeatability of measurements; it depends on your care and technique. If the same measurement is carefully made several times independently, we find that we may get variations in the last digit we read. This limitation defines the precision of the measurement. The precision of a measuring instrument depends on how finely the scale is divided. A ruler with mm divisions will not be useful in measuring the difference in hair thickness between blondes and Figure SR 6.2 Figure SR 6.3 shows a different object being measured with a ruler calibrated in centimetres. The length falls exactly on the 6-cm mark. Should the length be recorded as 6 cm or 6.0 cm? Remember that with a centimetre ruler we can estimate to tenths of a centimetre. With this ruler we can therefore distinguish readings of 5.9 cm and 6.1 cm. The object is right on a division mark, Appendix Student References 875 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 876 so the estimated digit is zero-tenths of a centimetre. Zero-tenths is indicated by 0.0 and the correct reading is 6.0 cm, not 6 cm. • All of the digits from one to nine (1, 2, 3, … 9) are significant, so 424.7 m or 0.4247 km each have four significant digits 10 11 Figure SR 6.3 Indicating the Precision of Measured Quantities The precision of a measurement is indicated by the number of decimal places. For example, 2.861 cm is more precise than 581.86 cm even though the latter contains more digits. This is because the three decimal places in 2.861 make it precise to the nearest one-thousandth of a centimetre, while the two decimal places in 581.86 make it precise to the nearest one-hundredth of a centimetre. In this physics
textbook, angle measures will have a precision no better than 0.1° (that is, angle measures are either whole numbers or to one decimal place only). Significant Digits The accuracy of a measurement is indicated by the number of significant digits. Significant digits are the specific number of digits used to communicate the degree of uncertainty in a measurement. When we are expressing a physical quantity as a number, how many significant digits should we indicate? These rules should help you decide. • Numbers obtained by counting are considered to be exact and contain an infinite number of significant digits. For example, if there are 12 stopwatches in a classroom, there are not 11 stopwatches, or 13 stopwatches, or 12.35 stopwatches. There are exactly 12.000… stopwatches. The zeros may be extended to as many decimal places as necessary in calculations. • Numbers obtained from definitions are considered to be exact and contain an infinite number of significant digits. For example, 1 m 100 cm, and 1 kWh 3600 kJ, are definitions of equalities. ( 3.141 592 654) has an infinite number of decimal places, as do numbers in formulae such as P 4s, where P is perimeter of a square, and s is the length of a side. 876 Appendix Student References • All zeros to the left of the first non-zero digit are not significant. For example, 1.4 kg and 0.0014 kg each have two significant digits. • Zeros between other non-zero digits are significant. Therefore, 501.009 s has six significant digits. • Alberta Education Assessment Branch considers all trailing zeros to be significant. Any zero to the right of a non-zero digit is significant. Therefore, the mass of an object written as 2000 kg has four significant digits. If the mass is a stated value, not a measured value, we can indicate that we know it to four significant digits by using scientific notation and writing the mass as 2.000 103 kg. Good measurements have high degrees of both accuracy and precision. In order to assure better accuracy, instruments should be calibrated. Calibration involves making sure the scale divisions are spaced properly and that the zero reading is correct. Better precision is attained by using better tools, those with finer scales. Good technique, of course, is also necessary for both precision and accuracy. 6.2 Mathematical Operations with Data When doing calculations with measured values, never keep more digits in the final answer than in the
least accurate number in the calculation. For example, 0.6 0.32 0.9, not 0.92. This procedure for using only meaningful digits is called rounding off. The procedure for rounding off digits is as follows: • When the first digit discarded is less than five, the last digit retained is left the same. Notice that we start rounding off at the digit immediately after the last digit we are retaining. For example, 14.248 kg rounded to three digits is 14.2 kg, since the fourth digit (4) is less than five. • When the first digit discarded is a five or greater, we increase the last digit retained by one. Therefore, 7.8361 km rounded to three digits is 7.84 km, and 4.255 01 s rounded to three digits is 4.26 s. • Consider numbers that are exact counts to be perfectly precise. For example, the average mass of three cars having masses of 1000 kg, 1250 kg, and 1165 kg is (1000 kg 1250 kg 1165 kg)/3 or 1138 kg. The denominator (3) in this example is an exact count, and therefore the answer includes four significant digits. 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 877 • Consider fractions and defined equalities to be perfectly precise. The fraction 1 in the equa2 1 mv2 does not influence rounding off. tion Ek 2 Neither does the defined equality 10 mm 1 cm. Note: In the examples in this textbook, intermediate steps are shown rounded off to one extra significant digit. In reality, all digits are carried through the calculations until the final answer is reached, at which point the final answer is rounded off appropriately. Rules for Significant Digits in Mathematical Operations Adding or subtracting when it is the only operation: the precision, as shown by the number of decimal places in the values being used, determines the number of significant digits in the answer. Round off the answer to the same precision as the least precise value used. For example, 11.2 kg 0.24 kg 0.336 kg 11.776 kg, is rounded off to 11.8 kg because the least precise value, 11.2 kg, is only given to the first decimal place. Multiplying or dividing when it is the only operation: the value with the least number of significant digits determines the number of significant digits in the answer. For example, a distance of 34.28 m is travelled
in a time of 4.8 s. The average speed is calculated by (34.28 m)/(4.8 s) 7.141 666 m/s, rounded off to 7.1 m/s to two significant digits because the time of 4.8 s has only two significant digits. When a series of calculations is performed, each interim value should not be rounded before carrying out the next calculation. The final answer should then be rounded to the same number of significant digits as are contained in the quantity in the original data with the lowest number of significant digits. For example: In calculating (1.23)(4.321) ÷ (3.45 – 3.21), three steps are required: a. 3.45 – 3.21 = 0.24 b. (1.23)(4.321) = 5.314 83 c. 5.314 83 ÷ 0.24 = 22.145 125 The answer should be rounded to 22.1 since 3 is the lowest number of significant digits in the original data. The interim values are not used in determining the number of significant digits in the final answer. When calculations involve exact numbers (counted and defined values), the calculated answer should be rounded based upon the precision of the measured values. For example: 12 eggs 49.6 g/egg 595.2 g (to one decimal place) Note: In this textbook, in calculations involving angle measurements, the number of significant digits in the angle measurements is not taken into consideration when determining the number of significant digits for the final answer. The rules of operation apply to all other measurements. Answers for angle measurements should be no more precise than the least precise in the given angle data. 6.3 Exponential Notation and Scientific Notation Exponential Notation Exponential notation makes use of powers of ten to write large and small quantities and to convey the number of significant digits. The first part of the number is called the coefficient, and the power of ten is the exponent. The radius of Earth may be written in exponential notation to three significant digits as 638 104 m, 63.8 105 m, 6.38 106 m, or 0.638 107 m. The diameter of a typical atom may be expressed to one significant digit as 1 108 cm or 0.1 107 cm. Scientific Notation Any measurement that consists of a coefficient multiplied by a power of ten is expressed in exponential notation. Both 6.38 106 and 0.638 107 are in exponential notation. Scientific notation
is a special kind of exponential notation. For a number to be in scientific notation, the coefficient must be greater than or equal to 1, and less than 10. This means that 6.38 106 is expressed in scientific notation and 0.638 107 is not. Scientific notation enables us to show the correct number of significant digits. Remember that any zero to the right of the decimal point is significant. Therefore, if all four digits in the measurement 3400 J are significant, then it would be written in scientific notation as 3.400 103 J. However, if only two digits are significant, it would be as 3.4 103 J. Sometimes you may be required to express the results of calculations in scientific notation. This involves moving the decimal point and changing the exponent until the coefficient is between 1 and 9. The exponent is decreased by one for each position the decimal point in the coefficient is moved to the right, and increased Appendix Student References 877 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 878 by one for each position the decimal point is moved to the left. For example, exponent in the answer remains the same as the largest exponent. For example, a) 500 104 5.00 102 104 5.00 1024 5.00 106 b) 0.068 103 6.8 102 103 6.8 102(3) 6.8 105 Exponential Notation and Mathematical Operations Multiplication The product of exponential numbers is determined by multiplying the coefficients and adding the exponents. For example, (3.0 102)(4.0 106) (3.0 4.0)(102 106) 12 102(6) 12 104 1.2 103 Division To divide numbers written in scientific notation, the coefficients are first divided, and then the exponent in the denominator is subtracted from the exponent in the numerator. For example, 3.3 105 6.6 102.50 105(2) 0.50 1052 0.50 107 5.0 106 Addition and Subtraction When the Exponents are the Same When the exponents are the same, the coefficients are added or subtracted as in normal arithmetic. The exponent in the final answer remains the same. For example, (2 104) (3 104) (1 104) (2 3 1) 104 4 104 Addition and Subtraction When the Exponents are Different When the exponents are different, the numbers must first be converted to a form in which
all exponents are the same. The decimal point is moved so that all have the same exponent as the largest number in the group. Then, the coefficients are added or subtracted accordingly. The 878 Appendix Student References (1.00 103) (2.00 104) (400 105) (1.00 103) (0.200 103) (4.00 103) (1.00 0.200 4.00) 103 4.80 103 6.4 Unit Conversions (Unit Factor Method) Conversions are often necessary in both math and science problems. Whether you are working on a problem involving the metric system or converting moles to grams, the unit factor method is a useful tool. The unit factor method is the sequential application of conversion factors expressed as fractions. They are arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained Example 1: Convert a speed of 25 m/s to km/h. The equivalent relationships are: 1000 m 1 km, 60 s 1 min, and 60 min 1 h. Multiplying by unit factors and carefully analyzing the units results in 0 6 k m m 25 1 m n i 0 0 s 10 60 m in m 90 km/h h 1 1 s Example 2: 1 ng 109 g, therefore, 9 g 10 n g 1 1 or 9 g n g 10 This type of relation can be used to convert units from one to another. Example 3: Convert 5.3 mL to L. Multiply by factors of 1 to remove the prefix “m” and to introduce “”. 3 L L 10 5.3 103 L 5.3 mL 6 L 10 m L mL “cancel” as do L, leaving the desired units of L. Subtract the exponents for division: 3 (6) 3 This skill is also useful for drawing scale diagrams. For example, a force of 840 N is to be drawn at a scale of 1 cm 50 N. The scale length, in centimetres, will be found thus, 1 840 N 50 cm 16.8 cm N 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 879 6.5 Trigonometry for Solving Right Triangles A right triangle is a special triangle with one right angle (90°). The side opposite the right angle is always the longest side and
is called the hypotenuse. The other two sides are called the legs. There are several important relationships that allow us to solve right triangles as long as we know the lengths of any two sides, or the length of one side and the measure of one of the acute angles. φ a Figure SR 6.4 c b Pythagorean Theorem The square of the length of the hypotenuse is equal to the sum of the squares of the length of each of the legs. c2 a2 b2 Sine Ratio Sine of one of the acute angles is equal to the ratio of the length of the leg opposite the angle to the length of the hypotenuse. sin opp/hyp sin a/c Cosine Ratio Cosine of one of the acute angles is equal to the ratio of the length of the leg adjacent the angle to the length of the hypotenuse. cos adj/hyp cos b/c θ Tangent Ratio Tangent of one of the acute angles is equal to the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. In general, the relationships are: Angle Sum The angles of a plane triangle add to 180°; the acute angles of a plane right triangle add to 90°. tan opp/adj tan a/b Appendix Student References 879 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 880 SR 7 Tables 7.1 SI Prefixes 7.2 Fundamental Quantities and Base Units Prefix Symbol Scientific Notation yotta- zetta- exa- peta- tera- giga- mega- kilo- hecto- deka- deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto da d c m n p f a z y 1024 1021 1018 1015 1012 109 106 103 102 101 101 102 103 106 109 1012 1015 1018 1021 1024 Quantity Length or Distance Mass Time Electrical current Thermodynamic temperature Quantity of matter Quantity Symbol m t I T n Unit metre kilogram second ampere kelvin mole Unit Symbol m kg s A K mol 7.3 Derived Quantities and Units Quantity Area Volume Speed, Velocity Acceleration Frequency Force Momentum Impulse Quantity Symbol A V v a f F p J Unit square metre cubic metre metre per second metre per second squared hertz newton kilogrammetre
per second newtonsecond Energy, Work E, W Power Electric charge Electric potential Electric resistance Activity Absorbed dose Equivalent absorbed dose P q V R A D E joule watt coulomb volt ohm becquerel gray sievert Unit Symbol Expression in terms of SI Base Units m2 m3 m/s m/s2 Hz N — — — — s1 kgm/s2 kgm/s — Ns J W C V Bq Gy Sv kgm/s kgm2/s2 kgm2/s3 As kgm2/s3A kgm2/s3A2 s1 m2/s2 m2/s2 880 Appendix Student References 19-PearsonPhys-Appendix(SR) 7/25/08 7:35 AM Page 881 7.4 Numerical Constants 7.6 Masses of Subatomic Particles Name Symbol Value Particle Symbol Mass (u) Elementary unit of charge Gravitational constant Coulomb’s constant Atomic mass unit Rest mass of an electron Rest mass of a proton Rest mass of a neutron Speed of light Planck’s constant Rydberg’s constant (hydrogen) e G k u me mp mn c h RH 1.60 1019 C 6.67 1011 Nm2/kg2 8.99 109 Nm2/C2 Electron Proton Neutron me mp mn 5.485 799 104 1.007 276 1.008 665 1.66 1027 kg 9.11 1031 kg 1.67 1027 kg 1.67 1027 kg 3.00 108 m/s 6.63 1034 Js 1.097 107 m1 7.5 Atomic Masses of Selected Isotopes Isotope Symbol Atomic Mass (u) Isotope Symbol Atomic Mass (u) hydrogen deuterium tritium helium-3 helium-4 carbon-12 nitrogen-16 oxygen-16 neon-20 neon-22 sodium-22 sodium-23 magnesium-24 silicon-28 silicon-30 phosphorus-30 potassium-39 potassium-40 calcium-40 iron-56 iron-58 cobalt-60 nickel-60 bromine-87 krypton-92 zirconium-94 H H (or D) H (or T) He He C N O Ne Ne Na Na Mg Si Si P K K Ca Fe Fe Co Ni Br Kr Zr 1

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