NYJC_EJC 2026 Nuclear Physics Tutorial

9814 H3 Physics (2026) Nuclear Physics Tutorial 1 Atomic Structure 1. (a) Explain what is meant by binding energy of a nucleus. Use the following values of masses to calculate the binding energy per nucleon in a 56 26Fe nucleus. Give your answer in MeV per nucleon. neutron mass = 1.0087 u; proton mass = 1.0073 u; mass of 56 26Fe nucleus = 55.9207 u [6] (b) An approximate formula for the radius R of a nucleus of nucleon number (mass number) A is R ≈ (1.2 x 10 –15) A1/3 Where R is expressed in metres. (i) Use this formula to calculate the approximate radius of a 56 26Fe nucleus. (ii) Assuming the nucleus to be a uniform sphere, estimate the density of nuclear matter in the iron nucleus. (iii) Sketch a graph to show how the density of nuclear matter depends on the nucleon number A of the nucleus. [6] (c) The mass of 1 m3 of iron is 8 x 10 3 kg. There is a general trend for the densities of solid elements to increase with increasing nucleon number. Comment on these two pieces of information in relation to your answers in (b) (ii) and (iii) and suggest an explanation for any difference between the behaviour of the density of solid elements and the density of nuclear matter. [3] 2. (a) The binding energy B of a nucleus may be expressed as B = 931.4 (1.008665 N + 1.007825 Z – M) In this equation, B is expressed in MeV and M is the atomic mass, expressed in u. (i) What do the symbols N and Z represent? Why are they multiplied by the numbers 1.008665 and 1.007825 respectively? (ii) Show how the number 931.4 arises.

9814 H3 Physics (2026) Nuclear Physics Tutorial 2 (b) Figure 2.1 lists the atomic mass M and the binding energy B of some nuclides. Nuclide M / u B / MeV 15 7N 15.00011 115.5 16 8 O 15.99492 127.6 18 8 O 17.99916 139.8 19 9F 18.99841 147.8 23 11Na 22.98777 186.6 24 12Mg 23.98505 198.3 40 18 Ar 39.96238 343.8 40 20 Ca 39.96259 342.0 44 20 Ca 43.95549 380.9 45 21Sc 44.95592 387.8 46 22Ti 45.95263 398.2 Fig. 2.1 (i) In nuclear physics, nuclei with equal nucleon numbers but different proton and neutron numbers are called isobars. Identify two isobars in Fig.2.1. [1] (ii) Although isobars must have the same nucleon number, their atomic masses can differ because of a difference in binding energy. Confirm that, for the two isobars you have identified in (i), the heavier nuclide of the pair has a smaller binding energy than the lighter one. [1] (iii) Would it be possible for the heavier nuclide of a pair of isobars to have a greater binding energy than the lighter one? Explain your answer. [2] (iv) Suppose that a single proton were removed from each of the following nuclei: 168O, 199F, 2412Mg, 4521Sc, 4622Ti. Use information from Fig. 2.1 to calculate the energy required in each case. What trend, if any, can you detect in the va