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Sample student answers A2 Unit G485: Fields, particles and frontiers of physics Module 6: Nuclear physics Question 1 Total marks: 10 A certain carbon (C) nuclide and a certain oxygen (O) nuclide each decay to form the same nitrogen (N) nuclide. These two decay reactions are represented by the arrows in the figure. (a) Write down the symbols for the nuclei of each of these nuclides. Marks available: 2 Student answer: (a) Examiner comments: (a) Good, straightforward answer © Pearson Education Ltd 2009 This document may have been altered from the original 1 (b) Write down the equations for each of the decay reactions: (i) carbon decay; and (ii) oxygen decay. Marks available: 2 Student answer: (b) (i) (ii) Examiner comments: (b) Always be careful to add the neutrinos or antineutrinos, and if writing an equation with mass and proton numbers included, always show mass and charge of electron or positron. (c) Use your answer to (b) to deduce, in their simplest form, the quark equations which occur in these decay reactions. Show all the steps in your deduction. Do not neglect leptons in your equations. Marks available: 4 Student answer: (c) (i) Carbon decay is a beta minus decay, where a neutron decays into a proton, an electron and an antineutrino: n → p + e− + In terms of quarks a neutron is udd and a proton is uud. Therefore carbon decay is: d → u + e− + (ii) Oxygen decay: u → d + e+ + Examiner comments: (c) Good answer, but always remember that when the question asks you to deduce the simplest quark equation, you would lose marks if you only wrote the final equation. So (ii) should start like this: Oxygen decay is a positron decay, where a proton decays into a neutron, a positron and a neutrino: p → n + e+ + Therefore: u → d + e+ + © Pearson Education Ltd 2009 This document may have been altered from the original 2 (d) The axes shown here can be used to plot a graph of the variation of nuclear mass with proton number. The nuclear mass scale does not start from zero. Mark points on a copy of this graph showing possible positions for the carbon, oxygen and nitrogen nuclei involved in the above reactions. Label your points C, O and N respectively. Explain how you arrived at your answer. Assume that the mass of the electron is negligible. Marks available: 2 Student answer: (d) When decay occurs, the final rest mass is always less than the original rest mass. © Pearson Education Ltd 2009 This document may have been altered from the original 3 Module 6: Nuclear physics Question 2 Total marks: 11 This question is about the formation and decay of plutonium-239, isotope of plutonium. , which is a fairly stable Natural uranium is a mixture of the nuclides and . When this natural uranium is exposed to neutrons, one of the heavier nuclei can absorb a neutron. The resulting nucleus then undergoes two decay reactions, resulting in the formation of a nucleus. (a) Write nuclear equations to represent these three reactions. The nuclide formed in the second reaction is an isotope of neptunium (Np). Marks available: 4 Student answer: (a) Reaction 1: Reaction 2: + Reaction 3: + Examiner comments: (a) Good, you have again remembered the antineutrino. © Pearson Education Ltd 2009 This document may have been altered from the original 4 (b) A physicist prepares a sample of the neptunium isotope, which decays to plutonium-239. She measures the activity of the sample over a period of 5.0 days. She then plots this graph of the variation with time of the activity of the sample. (i) Find the half-life in seconds of the neptunium isotope. (ii) Show that the decay constant of the neptunium isotope is 3.4 × 10−6 s−1. (iii) Deduce the number of nuclei of the neptunium isotope that are present after 2.00 days. Marks available: (i) 2 (ii) 1 (iii) 3 Student answer: (b) (i) From the graph, T1/2 = 2.36 days = 2.36 × 24 × 3600 = 2.04 × 105 s (ii) λ = ln 2/T1/2 = 0.693/(2.04 × 105) = 3.4 × 10−6 s−1 (iii) A = λN A = 2.8 × 1012 s−1 Therefore N = 2.8 × 1012/(3.4 × 10−6) = 8.24 × 1017 Examiner comments: (b) Make sure that in the exam you draw the line on the graph to show how you found the halflife. © Pearson Education Ltd 2009 This document may have been altered from the original 5 (c) The physicist then measures the activity of a sample of plutonium-239 over the same period. Sketch a graph of activity against time (in days) that she might obtain. Marks available: 1 Student answer: (c) © Pearson Education Ltd 2009 This document may have been altered from the original 6