30_InstSolManual_PDF_Part1

30_InstSolManual_PDF_Part1 - NUCLEAR AND HIGH-ENERGY...

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Unformatted text preview: NUCLEAR AND HIGH-ENERGY PHYSICS 30 8. B 9. D 10. E 11. B 12. A 13. B 14. B 15. A Answers to Multiple-Choice Problems 1. A 2. C 3. A, C, D 4. C, D 5. D 6. A, D 7. A, D Solutions to Problems 30.1. Set Up: In the symbol AEl, Z is the number of protons and A is the number of nucleons. The number of Z neutrons is N 5 A 2 Z. Solve: (a) Z 5 10. N 5 21 2 10 5 11. There are 10 protons and 11 neutrons. (b) Z 5 30. N 5 65 2 30 5 35. There are 30 protons and 35 neutrons. (c) Z 5 47. N 5 108 2 47 5 61. There are 47 protons and 61 neutrons. Solve: (a) 21Ne: A 5 21. R 5 1 1.2 3 10215 m 2 1 21 2 1/3 5 3.3 3 10215 m. 10 65 215 m 2 1 65 2 1/3 5 4.8 3 10215 m. 30Zn: A 5 65. R 5 1 1.2 3 10 108 215 m 2 1 108 2 1/3 5 5.7 3 10215 m. 47Ag: A 5 108. R 5 1 1.2 3 10 4 21 215 3 243 3 (b) 10Ne: V 5 3 p 1 3.3 3 10 m 2 5 1.5 3 10 m . 4 65 215 m 2 3 5 4.6 3 10243 m3. 30Zn: V 5 3 p 1 4.8 3 10 4 108 215 m 2 3 5 7.8 3 10243 m3. 47Ag: V 5 3 p 1 5.7 3 10 227 Amp 3m p Amp 3 1 1.67 3 10 kg 2 5 5 2.3 3 1017 kg / m3 5 (c) r 5 4 3 5 4 3 4pR03 4p 1 1.2 3 10215 m 2 3 3 pR 3 pR0 A R0 5 1.2 3 10215 m. Density is r 5 30.2. Set Up: R 5 R0 A1/3, with R0 5 1.2 3 10215 m. V 5 4 pR 3. r 5 M / V, with M 5 Amp. mp 5 1.67 3 10227 kg. 3 30.3. Set Up: The volume of a sphere is V 5 4 pR 3. The empirical formula for the radius is R 5 R0 A1/3 where 3 m . m 5 1.67 3 10227 kg Vp Solve: (a) V 5 4 pR 3 5 4 pR03A, so V is proportional to A. 3 3 (b) Neutrons and protons have very similar masses and A is the total number of neutrons and protons in the nucleus. 3mp m pA 3 1 1.67 3 10227 kg 2 (c) r 5 4 5 , which is independent of A. r 5 5 2.3 3 1017 kg / m3 3 3 4pR0 4p 1 1.2 3 10215 m 2 3 pR0 A 3 This is 2.0 3 1013 times the density of lead and is similar to the density of a neutron star. Reflect: The mass of an atom is close to the mass of the nucleus but the volume of the nucleus is much less than the volume of the atom, so the average density of the atom is much less than the density of the nucleus. Neutron stars are thought to be composed of nuclear matter; they are essentially one very large nucleus. 30-1 ...
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This note was uploaded on 03/06/2009 for the course PHYS 114 taught by Professor Shoberg during the Spring '07 term at Pittsburg State Uiversity.

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