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C 2:15 5 of 8 Nuclear 2019 Done SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. [5 marks] b) Give an overview of the shell model of the nucleus. Include in your discussion the nuclear potential, angular momentum and spin, and energy level splitting. Illustrate your answer with sketches as necessary. (Shells are found in the Appendix.) [9 marks] c) In the spin orbit coupling term the dot product L S appears. Derive a formula for its expectation value, and hence calculate the difference in energy levels induced in the shell model by this term. [6 marks] d) Give the configuration of 10In, and hence find the state J". [5 marks] Turn over Page 6 SPA5302 (2019) 2:15 Nuclear 2019 4 of 8 Done Turn over Page 4 SPA5302 (2019) SECTION B Answer TWO questions from Section B Question B1 a) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A)=ay A-asò/³ – ac² Z(Z-1) (A-2Z)² A1/3 QA + 8(Z, A). A Give a discussion of the origin of the last term in this expression. [5 marks] b) Starting from the Pauli exclusion principle, justify the asymmetry term in the SEMF. [5 marks] c) Derive an expression for the constant in the Coulomb term in the SEMF, ac, based on the electrostatic formula for the potential energy of a sphere radius R with charge Q, 3 Q2 54%EOR Use your formula to estimate the theoretical value of ac and compare it to its measured value. [7 marks] d) Show that the values of N where the minimum mass value roughly occurs when A=N+Z is constant is given by You may neglect the 5 term. N20+acA2/3 A 40+ ac²/3 Use this to argue whether heavy nuclei have more neutrons or more protons. How would this change if the Coulomb term was zero? [8 marks] SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. C [5 marks]

C 2:15 5 of 8 Nuclear 2019 Done SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. [5 marks] b) Give an overview of the shell model of the nucleus. Include in your discussion the nuclear potential, angular momentum and spin, and energy level splitting. Illustrate your answer with sketches as necessary. (Shells are found in the Appendix.) [9 marks] c) In the spin orbit coupling term the dot product L S appears. Derive a formula for its expectation value, and hence calculate the difference in energy levels induced in the shell model by this term. [6 marks] d) Give the configuration of 10In, and hence find the state J". [5 marks] Turn over Page 6 SPA5302 (2019) 2:15 Nuclear 2019 4 of 8 Done Turn over Page 4 SPA5302 (2019) SECTION B Answer TWO questions from Section B Question B1 a) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A)=ay A-asò/³ – ac² Z(Z-1) (A-2Z)² A1/3 QA + 8(Z, A). A Give a discussion of the origin of the last term in this expression. [5 marks] b) Starting from the Pauli exclusion principle, justify the asymmetry term in the SEMF. [5 marks] c) Derive an expression for the constant in the Coulomb term in the SEMF, ac, based on the electrostatic formula for the potential energy of a sphere radius R with charge Q, 3 Q2 54%EOR Use your formula to estimate the theoretical value of ac and compare it to its measured value. [7 marks] d) Show that the values of N where the minimum mass value roughly occurs when A=N+Z is constant is given by You may neglect the 5 term. N20+acA2/3 A 40+ ac²/3 Use this to argue whether heavy nuclei have more neutrons or more protons. How would this change if the Coulomb term was zero? [8 marks] SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. C [5 marks]

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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C 2:15 5 of 8 Nuclear 2019 Done SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. [5 marks] b) Give an overview of the shell model of the nucleus. Include in your discussion the nuclear potential, angular momentum and spin, and energy level splitting. Illustrate your answer with sketches as necessary. (Shells are found in the Appendix.) [9 marks] c) In the spin orbit coupling term the dot product L S appears. Derive a formula for its expectation value, and hence calculate the difference in energy levels induced in the shell model by this term. [6 marks] d) Give the configuration of 10In, and hence find the state J". [5 marks] Turn over Page 6 SPA5302 (2019)
Transcribed Image Text:C 2:15 5 of 8 Nuclear 2019 Done SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. [5 marks] b) Give an overview of the shell model of the nucleus. Include in your discussion the nuclear potential, angular momentum and spin, and energy level splitting. Illustrate your answer with sketches as necessary. (Shells are found in the Appendix.) [9 marks] c) In the spin orbit coupling term the dot product L S appears. Derive a formula for its expectation value, and hence calculate the difference in energy levels induced in the shell model by this term. [6 marks] d) Give the configuration of 10In, and hence find the state J". [5 marks] Turn over Page 6 SPA5302 (2019)
2:15 Nuclear 2019 4 of 8 Done Turn over Page 4 SPA5302 (2019) SECTION B Answer TWO questions from Section B Question B1 a) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A)=ay A-asò/³ – ac² Z(Z-1) (A-2Z)² A1/3 QA + 8(Z, A). A Give a discussion of the origin of the last term in this expression. [5 marks] b) Starting from the Pauli exclusion principle, justify the asymmetry term in the SEMF. [5 marks] c) Derive an expression for the constant in the Coulomb term in the SEMF, ac, based on the electrostatic formula for the potential energy of a sphere radius R with charge Q, 3 Q2 54%EOR Use your formula to estimate the theoretical value of ac and compare it to its measured value. [7 marks] d) Show that the values of N where the minimum mass value roughly occurs when A=N+Z is constant is given by You may neglect the 5 term. N20+acA2/3 A 40+ ac²/3 Use this to argue whether heavy nuclei have more neutrons or more protons. How would this change if the Coulomb term was zero? [8 marks] SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. C [5 marks]
Transcribed Image Text:2:15 Nuclear 2019 4 of 8 Done Turn over Page 4 SPA5302 (2019) SECTION B Answer TWO questions from Section B Question B1 a) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A)=ay A-asò/³ – ac² Z(Z-1) (A-2Z)² A1/3 QA + 8(Z, A). A Give a discussion of the origin of the last term in this expression. [5 marks] b) Starting from the Pauli exclusion principle, justify the asymmetry term in the SEMF. [5 marks] c) Derive an expression for the constant in the Coulomb term in the SEMF, ac, based on the electrostatic formula for the potential energy of a sphere radius R with charge Q, 3 Q2 54%EOR Use your formula to estimate the theoretical value of ac and compare it to its measured value. [7 marks] d) Show that the values of N where the minimum mass value roughly occurs when A=N+Z is constant is given by You may neglect the 5 term. N20+acA2/3 A 40+ ac²/3 Use this to argue whether heavy nuclei have more neutrons or more protons. How would this change if the Coulomb term was zero? [8 marks] SPA5302 (2019) Question B2 Page 5 a) Explain the limitations of the liquid drop model and the semi-empirical mass formula. Your discussion should include at least one graph of neutron or proton separation energies. C [5 marks]
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