Page 2 2:15 Nuclear 2019 Done SPA5302 (2019) SECTION A Answer ALL questions in Section A Question A1 Aluminium-27 may be written as Al. State the mass number, and the number of neutrons and the number of protons of Aluminium-27. Silicon lies immediately to the right of Aluminium on the periodic table. How many neutrons does 28 Si have? [5 marks] Question A2 Sketch a graph of the table of nuclides with N, the number of neutrons, along the horizontal axis and Z, the number of protons, along the vertical axis. On this diagram sketch the line N = Z. With reference to this line, sketch the area of known nuclides, indicating the area where stable nuclei are found. Indicate the directions of isotopes, isotones and isobars. [5 marks] Question A3 Define the binding energy of a nucleus in terms of the nuclear atomic mass, and the masses of the constituent particles. Sketch a plot of the binding energy per nucleon as a function of the mass number. Question A4 Give 5 features of the nuclear force. Question A5 [5 marks] [5 marks] Sketch energy level diagrams using the shell model for the mirror nuclei O and F, clearly labelling each energy level. Give the ground state spin and parity on both cases. [5 marks] Question A6 A nuclide Th decays to 228 Ra which subsequently decays to 225 Ac. State the decay mechanism for each decay. Write down the reactions involved. Question A7 [5 marks] Give the radioactive decay law for a material of N(t) nuclei, with mean lifetime 7, as a function of timet. What is the half-life in terms of 7? [5 marks] SPA5302 (2019) Question A8 Page 3 Sketch a mass chain for an odd-valued A. Illustrate how ẞ-decay leads to the valley of stability. Question A9 Explain why odd-A nuclei with an odd number of neutrons such as 23, 25, 2P, Pu are 'fissile', while even-A nuclei such as C [5 marks] 2:15 3 of 8 Nuclear 2019 Done SPA5302 (2019) Question A8 Page 3 Sketch a mass chain for an odd-valued A. Illustrate how ẞ-decay leads to the valley of stability. Question A9 Explain why odd-A nuclei with an odd number of neutrons such as 233U, 235, 230 Pu, 239p Pu are 'fissile', while even-A nuclei such as are not. 28Th, U, 200 Pu, Pu [5 marks] Question A10 [5 marks] The figure below shows the relative abundance of the elements in the Solar System as a function of atomic number. Explain why there are peaks at Carbon, Nitrogen and Oxygen, as well as at Iron and Nickel. Explain the reason there is an alternating pattern as we move through atomic number. 1012 1010 He 100 1006 1004 1002 1000 Be 10-02 Page 4 Si Na ΑΙ 12345678 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 [5 marks] Turn over 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 R(ZA) 12/3 Z(Z-1) (A-2Z)²