Nuclei

Nuclei explores the tiny, dense core of the atom, which contains almost all its mass and is the source of nuclear energy in reactors and stars. In this chapter you will learn about atomic masses measured in atomic mass units, the composition of the nucleus in terms of protons and neutrons, and the meaning of atomic number Z, mass number A, isotopes, isobars and isotones. You will study the size of the nucleus, R = R0 A^(1/3), and show that nuclear density is nearly the same for all nuclei and enormously larger than ordinary matter. You will apply Einstein's mass-energy relation E = mc^2 to calculate the mass defect and binding energy of nuclei, and interpret the curve of binding energy per nucleon against mass number, which peaks near iron. The chapter explains the properties of the nuclear force, which is strong, short-ranged and nearly independent of charge. Finally, you will see how the binding energy curve explains the release of energy in nuclear fission of heavy nuclei and nuclear fusion of light nuclei.

Detailed Worksheet: Nuclei Section A - Definitions (10 marks) 1. Define atomic mass unit. Write its value in kg and its energy equivalent in MeV. (2 marks) 2. Distinguish between isotopes and isobars with one example of each. (2 marks) 3. Define mass defect and binding energy of a nucleus. (2 marks) 4. State three properties of the nuclear force. (2 marks) 5. Distinguish between nuclear fission and nuclear fusion. (2 marks) Section B - Calculations and Applications (15 marks) 6. Using R0 = 1.2 fm, find the radius of the nucleus of iron-56. Find the ratio of the nuclear radii of tellurium-125 and aluminium-27. (3 marks) 7. Show that nuclear density is independent of mass number and calculate its value (mass of nucleon = 1.66 x 10^-27 kg, R0 = 1.2 fm). (3 marks) 8. Calculate the mass defect, binding energy and binding energy per nucleon of oxygen-16, given: mass of O-16 atom = 15.99492 u, mass of H-1 atom = 1.00783 u, mass of neutron = 1.00867 u, 1 u = 931.5 MeV/c^2. (3 marks) 9. Calculate the energy equivalent of 1 g of matter. For how long could this energy run a 100 W bulb? (3 marks) 10. Each fission of uranium-235 releases about 200 MeV. Calculate the energy released by the fission of 1 kg of U-235 (NA = 6.023 x 10^23 mol^-1, 1 MeV = 1.6 x 10^-13 J). (3 marks) Section C - Diagrams (10 marks) 11. Draw the graph of binding energy per nucleon against mass number. Mark the peak near A = 56 and the regions where fission and fusion release energy. (4 marks) 12. Draw the graph of potential energy between two nucleons against their separation, showing the attractive region and the repulsive core. (3 marks) 13. Draw a labelled schematic diagram of a nuclear chain reaction in uranium-235 initiated by a slow neutron. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Explain, using the binding energy curve, why energy is released when a heavy nucleus splits into two medium nuclei and when two light nuclei fuse. Why is iron the most stable nucleus? (5 marks) 15. Calculate the energy released in the fusion reaction 2H + 2H -> 3He + n, given masses: 2H = 2.014102 u, 3He = 3.016029 u, n = 1.008665 u. Explain why fusion needs extremely high temperatures and where it occurs naturally. (5 marks) 16. Explain why the nuclear force must be much stronger than the electrostatic force and why it must be short-ranged. Explain why heavy nuclei have more neutrons than protons. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use 1 u = 931.5 MeV/c^2 and show all steps. Draw neat, labelled graphs.