1718 H2 Nuclear Physics timed practice with soln

9749 H2 PHYSICS Topical Timed Practice Nanyang Junior College 1 Chapter 20 NUCLEAR PHYSICS Name: ___________________________ CT: __________ Duration: 30 minutes Data and Formulae Section A: Multiple Choice Questions (2 marks each) Fill in the answers in the boxes below. 1 2 3 4 5 6 D C D C D C 1 The deviation of α-particles by thin metal foils through angles that range from 0 o to 180o can be explained by A scattering from free electrons. B diffuse reflection from the metal surface. C diffraction from the crystal lattice. D scattering from small but heavy regions of positive charge. Ans: D speed of light in free space c = 3.00 × 108 m s−1 elementary charge e = 1.60 × 10−19 C unified atomic mass constant u = 1.66 × 10−27 kg rest mass of electron me = 9.11 × 10−31 kg rest mass of proton mp = 1.67 × 10−27 kg the Avogadro constant NA = 6.02 × 1023 mol−1 radioactive decay x = xo exp (−λt) decay constant λ = ln2 / t1/2 25

9749 H2 PHYSICS Topical Timed Practice Nanyang Junior College 2 2 A nucleus has a nucleon number A, a proton number Z and a binding energy B. The masses of the neutron and proton are mn and mp respectively, and c is the speed of light. The mass of the nucleus is given by the expression A 2n p BAm Zm c  B 2n p BAm Zm c  C   2n p BA Z m Zm c   D   2n p BA Z m Zm c   Ans: C 3 The rest mass of the deuteron, 2 1H , is equivalent to an energy of 1876 MeV. The rest mass of a proton is equivalent to 939 MeV and the rest mass of a neutron is equivalent to 940 MeV. A deuteron may disintegrate to a proton and a neutron if it A emits a  -ray photon of energy 1 MeV. B captures a  -ray photon of energy 1 MeV. C emits a  -ray photon of energy 3 MeV. D captures a  -ray photon of energy 3 MeV. Ans: D Since Reactants ProductsM M   , a photon must be absorbed whose energy is equal to the difference   2 Products ReactantsM M c  . 4 At time t, a sample of radioactive substance contains N atoms of a particular nuclide. At time (t + Δt), where Δt is a short period of time, the number of atoms of the nuclide is (N – ΔN). Which expression is equal to the decay constant of the nuclide? A N N  B N t   C N N t   D N N t   Ans: C Decay constant  = probability of decay per unit time Probability of decay = N N  Hence N N t   OR Activity A = rate of decay = N t   Since A N => A N N N t   

9749 H2 PHYSICS Topical Timed Practice Nanyang Junior College 3 5 The graph shows how the activities of two isotopes X and Y vary with time. What will be the ratio activity of X activity of Y after each has decayed for 8 hours? A 9 10 B 10 9 C 81 100 D 100 81 Ans: D Isotope X (4) 1 900 1000 0.0263 hr X X e       After 8 hrs, (0.0263)(8)1000 810 BqXA e   Isotope Y (2) 1 900 1000 0.0527 hr Y Y e       After 8 hrs, (0.0527)(8)1000 656 BqYA e   Hence 1001.23 81 X Y A A  

9749 H2 PHYSICS Topical Timed Practice Nanyang Junior College 4 6 A detector of ionising radiation gives a background count rate of 24 per minute. A radioactive source is placed close to the detector and the reading is 532 counts per minute. What will be the reading after two half-lives of the source? A 127 B 133 C 151 D 157 Ans: C 1/ 2 (ln2) t t oC C e        (ln2) 2 (532 24) 127C e     Hence detector reading = 127 + 24 = 151 Section B: Structured Questions (13 marks) 7 (a) Define binding energy. [1] It is defined as the energy needed just to separate completely the nucleons in the nucleus. / It is also defined as energy released when a nucleus is formed by putting all its constituent nucleons together (b) A minimum energy Q is required to remove a neutron from a helium-4 nuclide to form a helium-3 nuclide. The following data is given: Binding energy per nucleon of helium-4 nuclide = 6.8 MeV Binding energy per nucleon of helium-3 nuclide = 2.3 MeV Mass of neutron = 1.0087 u (i) Write the nuclear equation for this reaction. [1] 4 3 1 2 2 0He He n  (ii) Calculate Q. [2]     . . – . . 4 6.8 3 2.3 20.3 MeV reactants productsQ B E B E     (iii) Hence calculate the difference in mass between the helium -3 and helium -4 nuclides. [2]             2 Products Reactants 2 6 19 27 28 By Conservation of Energy, Mass Energy of Reactants + Q = Mass Energy of Products ( ) He-3 He-4 (20.3 10 )(1.60 10 )He-4 He-3 1.0087(1.66 10 ) 3.00 10 M M c Q Qm n m m c m m                27 1.64 10 kg 

9749 H2 PHYSICS Topical Timed Practice Nanyang Junior College 5 8 Strontium-90 decays with the emission of a β-particle to form Yttrium-90. The reaction is represented by the equation 90 90 0 38 39 1Sr Y e 0 55MeV .   The decay constant is 0.025 year-1. (a) Explain what is meant by the decay constant. [1] The decay constant λ is the ratio of the number of decays per unit time to the number of remaining radioactive nuclei. (It represents the probability that a radioactive nucleus will decay in a unit time.) (b) At the time of purchase of a Strontium-90 source, its activity is 3.7 × 106 Bq. (i) Calculate, for this sample of Strontium-90, 1. the initial number of atoms present, [2]   6 15 0 0253 7 10 365 24 3600 4 67 10 A N .. N N .        2. the initial mass. [2] Initial mass = 15 7 23 4 67 10 90 6 98 106 02 10 . ..     g (ii) Determine the activity of the sample 5.0 years after purchase, expressing your answer as a fraction of the initial activity Ao. [2] t oA A e    0 025 5 0 0 882 . . o A e .A   