Quantum Physics

Answers to Quick Quizzes, Odd-Numbered Conceptual Questions and Problems A.31ton has spin (intrinsic angular momentum) and is involvedin electromagnetic interactions, while the neutrinohas spin /2, and is closely related to beta decays.15. Since the two samples are of the same radioactive nuclide,they have the same half-life; the 2:1 difference in activityis due to a 2:1 difference in the mass of each sample. After5 half lives, each will have decreased in mass by a power of2 5 32. However, since this simply means that the massof each is 32 times smaller, the ratio of the masses will stillbe (2/32) : (1/32), or 2:1. Therefore, the ratio of theiractivities will always be 2:1.PROBLEMS1. A 2, r 1.5 fm; A 60, r 4.7 fm; A 197, r 7.0 fm;A 239, r 7.4 fm3. 1.8 10 2 m5. (a) 27.6 N (b) 4.16 10 27 m/s 2 (c) 1.73 MeV7. (a) 1.9 10 7 m/s (b) 7.1 MeV931979. 8.66 MeV/nucleon for 41 Nb , 7.92 MeV/nucleon for 79 Au11. 3.54 MeV2313. 0.210 MeV/nucleon greater for 11 Na , attributable to lessproton repulsion15. 0.46 Ci17. (a) 9.98 10 7 s 1 (b) 1.9 10 10 nuclei19. 1.0 h21. 4.31 10 3 yr23. (a) 5.58 10 2 h 1 , 12.4 h (b) 2.39 10 13 nuclei(c) 1.9 mCi208 95 14425. , 37 Rb81 Tl , 60 Nd40 94 427. , ,29. e 42 Mo56decay, 27 Co2 He20 Ca: 5626 Fe e 31. (a) cannot occur spontaneously(b) can occur spontaneously33. 18.6 keV35. 4.22 10 3 yr3037. (a) 15 P (b) 2.64 MeV21 14439. (a) 10 Ne (b) 54 Xe (c) X e , X 13 1041. (a) 6 C (b) 5 B19719843. (a) 79Au n : 80 Hg e (b) 7.88 MeV145. (a) 0 n (b) Fluoride mass 18.000 953 u47. 18.8 J49. 24 d51. (a) 8.97 10 11 electrons (b) 0.100 J (c) 100 rad53. 46.5 d55. Q 3.27 MeV 0, no threshold energy required57. (a) 2.52 10 24 (b) 2.29 10 12 Bq (c) 1.07 10 6 yr59. (a) 4.0 10 9 yr (b) It could be no older. The rock couldbe younger if some 87 Sr were initially present.61. 54 Ci63. 2.3 10 2 yr65. 4.4 10 8 kg/hChapter 30QUICK QUIZZES1. (c)2. (a)3. (b)4. (d)CONCEPTUAL QUESTIONS1. The experiment described is a nice analogy to the Rutherfordscattering experiment. In the Rutherford experiment,alpha particles were scattered from atoms and the scatteringwas consistent with a small structure in the atom containingthe positive charge.3. The largest charge quark is 2e/3, so a combination of onlytwo particles, a quark and an antiquark forming a meson,could not have an electric charge of 2e. Only particlescontaining three quarks, each with a charge of 2e/3, cancombine to produce a total charge of 2e.5. Until about 700 000 years after the Big Bang, the temperatureof the Universe was high enough for any atoms thatformed to be ionized by ambient radiation. Once theaverage radiation energy dropped below the hydrogenionization energy of 13.6 eV, hydrogen atoms could formand remain as neutral atoms for relatively long period oftime.7. In the quark model, all hadrons are composed of smallerunits called quarks. Quarks have a fractional electric1charge and a baryon number of 3. There are six flavors ofquarks: up (u), down (d), strange (s), charmed (c), top(t), and bottom (b). All baryons contain three quarks,and all mesons contain one quark and one antiquark. Section30.12 has a more detailed discussion of the quarkmodel.9. Baryons and mesons are hadrons, interacting primarilythrough the strong force. They are not elementary particles,being composed of either three quarks (baryons) ora quark and an antiquark (mesons). Baryons have a1 3nonzero baryon number with a spin of either2or2.Mesons have a baryon number of zero and a spin of either0 or 1.11. All stable particles other than protons and neutrons havebaryon number zero. Since the baryon number must beconserved, and the final states of the kaon decay containno protons or neutrons, the baryon number of all kaonsmust be zero.13. Yes, but the strong interaction predominates.15. Unless the particles have enough kinetic energy to producea baryon–antibaryon pair, the answer is no. Antibaryonshave a baryon number of 1, baryons have abaryon number of 1, and mesons have a baryon numberof 0. If such an interaction were to occur and produce abaryon, the baryon number would not be conserved.17. Baryons and antibaryons contain three quarks, whilemesons and antimesons contain two quarks. Quarks havea spin of 1/2; thus, three quarks in a baryon can onlycombine to form a net spin that is half-integral. Likewise,two quarks in a meson can only combine to form a netspin of 0 or 1.19. For the first decay, the half-life is characteristic of thestrong interaction, so the 0 must have S 0, and strangenessis conserved. The second decay must occur via theweak interaction.PROBLEMS1. 1.1 10 16 fissions3. 126 MeV5. (a) 16.2 kg (b) 117 g7. 2.9 10 3 km (1 800 miles)9. 1.01 g811. (a) 4Be (b) 12 C (c) 7.27 MeV613. 3.07 10 22 events/yr15. (a) 3.44 10 30 J (b) 1.56 10 8 yr17. (a) 4.53 10 23 Hz (b) 0.622 fm