1718 H2 Nuclear Physics tutorial with soln

9749 H2 Physics Tutorial Nanyang Junior College 1 Chapter 20 NUCLEAR PHYSICS Self-Attempt Questions 1 (a) The figure below shows three alpha particles approaching a heavy stationary nucleus N. (i) Complete the diagram to show the paths of alpha particles as they pass by, and move away from N. (Particle C shows most deflection, follow by B, then A) (ii) The nucleus N could be one of several different isotopes of gold. 1 State what is meant by the term isotope. Isotopes are nuclei of atoms of a particular element containing the sa me number of protons but different number of neutrons. 2 Suggest, with an explanation, whether different isotopes of gold would give rise to different deviations of a particular α-particle. All isotopes of gold have the same number of protons, hence the same charge. There will be no difference in the deviations of the α-particle. (b) Classical experiments on alpha particle scattering were performed by Rutherford, Geiger and Marsden. State the experimental observation obtained from such experiments that proves that (i) the nucleus is small, Most of the alpha particles pass straight through the gold foil without being deflected. This shows that the nucleus is small and the atom is largely empty space.

9749 H2 Physics Tutorial Nanyang Junior College 2 (ii) the nucleus is massive and charged. Some alpha particles were scattered significantly and a very small number (about 1 in 8000) were deflected by more than 90°. This shows that the nucleus is positively charged, and that the nucleus is massive with the mass of the atom concentrated at the nucleus. 2 State what is meant by (a) relative atomic mass, The relative atomic mass is the ratio of the mass of one atom of the substance to 1/12th the mass of a carbon-12 atom. (b) nuclear binding energy. The nuclear binding energy of a nucleus is define d as the energy needed to completely separate the nucleons in the nucleus. (It is also defined as the energy released when a nucleus is formed from its constituent nucleons.) 3 The decay of 238 92U to 239 93Np by β-emission is not possible because A 239 93Np is not a stable isotope. B mass number cannot increase in a β-decay process. C atomic number cannot decrease in a β-decay process. D mass number and atomic number must both decrease in a β-decay process. Ans: B 4 Complete the following representations of nuclear transformation: (a) 9 12 4 6 1 0Be C n  (b) 13 14 6 7C p N    (c) 15 12 27 4 6N p C He  

9749 H2 Physics Tutorial Nanyang Junior College 3 5 The nuclide 238 92U decays to a final stable product 210 84Po through a series of radioactive nuclides. At each stage, an alpha or beta particle is emitted. Determine the number of alpha and beta particles emitted during the complete decay process. after chain decay238 210 92 84U Po Since the mass number decreases by 28, the number of alpha particles emitted = 28 / 4 = 7. Thus the atomic number should decrease by 2 x 7 = 14. However the atomic number only decreases by 8. Therefore, 6 beta particles must be released. 238 210 4 0 92 84 2 1U Po 7 He 6 e    6 Antimony-124 undergoes radioactive decay, with a half -life of 60 days, to become tin -124. Tin-124 is stable. Initially, a sample of antimony-124 contains no tin-124. For this sample, after what period of time will the ratio number of tin-124 nuclei number of antimony-124 nuclei be equal to 6? A between 60 days and 120 days C between 120 days and 180 days B 120 days D 180 days Ans: C Let initial number of antimony -124 nuclei be X o. Let number of antimony -124 nuclei and tin-124 nuclei at time t be X and T respectively. T + X = Xo XT 1X X o      ln2 60 ln2 60 t o t o X X e X eX              Hence  ln2 60T 1X t e        ln2 606 1 168.4 days t e t       

9749 H2 Physics Tutorial Nanyang Junior College 4 ATOMIC STRUCTURE AND NUCLEUS 1 (a) In an experiment, 13 6C was bombarded by proton s of kinetic energy 2.00 MeV to produce 13 7N . By using the masses of the isotopes given below, determine wheth er this process is possible. [mass of 13C = 13.003355 u; 1H = 1.007825 u; 13N = 13.005739 u; 14N = 14.003074 u; 1 0n = 1.008665 u; 17O = 16.999134 u] 13 1 13 1 6 1 7 0C H 2.00 MeV N n    Total mass of 13 6C and 1 1H = 13.003355 u + 1.007825 u + 6 19 8 2 27 2.00 10 (1.6 10 ) (3.0 10 ) (1.66 10 )       u = 14.013322 u Total mass of 13 7N and 1 0n = 13.005739 u + 1.008665 u = 14.014404 u Total mass of reactant < Total mass of products This process is not possible. (b) 14 4 17 1 7 2 8 1N He O H   In the nuclear reaction represented by the above equation, nitrogen was bombarded with α-particles of kinetic energy 7.68 MeV. The oxygen nucleus and the proton produced have kinetic energy of 0.56 MeV and 5.93 MeV respectively. Calculate the mass of the α-particle. By conservation of energy, 2 2 2 2 O H He O H N2 6 19 8 2 27 27 27 (K K K ) (m m m ) (0.56 5.93 7.68) 10 1.60 10 (3.00 10 ) (16.999134 1.007825 14.003074) (1. 66 10 ) 4.002611 1.66 10 6.64 10 kg N He He O O H H He m c m c K m c K m c K m c                               

9749 H2 Physics Tutorial Nanyang Junior College 5 2 (a) Identify the numbers and symbols represented by the letters, q, r, s, t, u and v in the nuclear equation    3 2 4 t 1 r s vq H He u 17.5 MeV q = H (tritium), r = 1 (atomic no. of deuterium), s = 2 (atomic no. of helium) From conservation of mass number, 3 + 2 = 4 + t  t = 1 From conservation of atomic number, 1 + 1 = 2 + v  v = 0 Therefore u = n (neutron) (b) The product particles each have a greater mass than when at rest. Account for this and calculate the overall difference in mass in this nuclear reaction. Assume that energy released in this nuclear reaction is in the form of kinetic energy of the product particles. From Einstein’s mass-energy relation, the mass of the particles increased when they have additional energy. The kinetic energy possessed by the particles (due to release of energy) contributed to the larger mass. 17.5 MeV = Δm c2   6 19 29 28 17.5 10 (1.60 10 ) 3.11 10 kg 3.00 10 m        (c) If 200 kg of mixed material (denoted by ‘q’ and H) were used each year to fuel a fusion power station with an overall conversion efficiency of 10%, estimate the electrical power output and the waste heat produced. Assume 1 mole of ‘q’ & H weigh 5.0 g together, and there are equal numbers of ‘q’ and H in the mixed material. 200 kg will contain 3 4200 10 4.00 10 moles5    of ‘q’ & H. No. of pairs of ‘q’ & H in 200 kg = 4 × 104 (6.02 x 1023) = 2.41 × 1028 Total energy produced = 2.41 × 1028 (17.5 × 106 × 1.60 × 10-19) = 6.74 × 1016 J Total power (each year) = 16 96.74 10 2.14 10 W3600 24 365     Useful power output = 0.10 × 2.14 × 109 = 2.14 × 108 W Waste heat produced = 0.90 × 2.14 × 109 = 1.92 × 109 W

9749 H2 Physics Tutorial Nanyang Junior College 6 3 The energy of the sun produced by the thermonuclear reaction represented by 1 4 0 1 2 14 H He 2 e particle x   The masses of 1 1H and 4 2He are 1.00813 u and 4.00386 u respectively. (a) State the name of particle x. neutrino (b) If the mean earth-sun distance is 1.5 × 1011 m and the energy of the sun falling on a unit area of the earth per second is 1.35 kW m -2, determine the rate that hydrogen is converted to helium on the sun. [The mass and energy of the positrons, e0 1 and