Practice Test: 33 marks (43 minutes) Additional Problem: 3 marks (46 minutes). Which of the following causes the greatest number of ionizations as it passes through cm of air? (The total energy of the ionizing radiation is the same.) A. An alpha particle B. A beta particle C. A gamma-ray D. An X-ray 2. The nuclear equation below is an example of the transmutation of mercury into gold. 2 99 97 H + 80Hg 79Au + X The particle X is a A. gamma-ray photon. B. helium nucleus. C. proton. D. neutron. 3. Emission and absorption spectra provide evidence for A. the nuclear model of the atom. C. the existence of isotopes. B. natural radioactivity. D. the existence of atomic energy levels. 4. 2 The difference between the mass of a 6 C nucleus and the sum of the masses of the individual nucleons is 0. u. Which of the following is approximately the binding energy of the nucleus? A. 90 MeV B. 90 MeV c 2 C. 8 MeV D. 8 MeV c 2 5. Which of the following decay sequences would result in the daughter nucleus having the same proton number as the parent nucleus? A. Alpha followed by gamma B. Beta (β ) followed by gamma C. Alpha followed by beta (β ) followed by beta (β ) D. Beta (β ) followed by gamma followed by gamma 6. Data concerning nuclides are plotted using the axes below. What are the axis labels for this graph? Y X A. binding energy per nucleon number of nucleons B. binding energy number of protons C. number of protons binding energy per nucleon D. number of nucleons binding energy 7. The Geiger-Marsden experiment (scattering of alpha particles) provided evidence for A. the nature of alpha particles. B. orbital electrons in the atom. C. very small and relatively massive nucleus. D. the existence of atomic energy levels. /8
8. The relationship between proton number Z, neutron number N and nucleon number A is A. A = Z N. B. Z = A + N. C. N = A Z. D. N = A +Z. 7 9. The binding energy per nucleon of the nucleus Li is approximately 5 MeV. The total energy required to completely separate the nucleons of this nucleus is approximately A. 5 MeV. B. 20 MeV. C. 35 MeV. D. 50 MeV. 0. When the isotope aluminium-27 is bombarded with alpha particles, the following nuclear reaction can take place. 4 27 He + Al X neutron 2 3 + Which of the following correctly gives the atomic (proton) number and mass (nucleon) number of the nucleus X? Proton number Nucleon number A. 5 30 B. 6 3 C. 30 5 D. 3 6. A radio-isotope has an activity of 400 Bq and a half-life of 8 days. After 32 days the activity of the sample is A. 200 Bq. B. 00 Bq. C. 50 Bq. D. 25 Bq. 2. Which of the following is true in respect of both the Coulomb interaction and the strong interaction between nucleons in an atom? 3 Coulomb interaction exists between Strong interaction exists between A. protons only neutrons only B. both protons and neutrons neutrons only C. protons only both protons and neutrons D. both protons and neutrons both protons and neutrons 3. This question is about nuclear physics. (a) Define binding energy of a nucleus. The mass of a nucleus of plutonium ( 94 Pu ) is 238.990396 u. Deduce that the binding energy per nucleon for plutonium is 7.6 MeV. 239 (3) 2/8
(b) The graph shows the variation with nucleon number A of the binding energy per nucleon. Plutonium ( 239 94 Pu ) undergoes nuclear fission according to the reaction given below. 239 9 46 94Pu + 0n 38Sr + 56Ba + x0n Calculate the number x of neutrons produced. Use the graph to estimate the energy released in this reaction. Stable nuclei with a mass number greater than about 20, contain more neutrons than protons. By reference to the properties of the nuclear force and of the electrostatic force, suggest an explanation for this observation................ (4) (Total marks) 3/8
4. This question is about unified atomic mass unit and a nuclear reaction. (a) Define the term unified atomic mass unit....... (b) The mass of a nucleus of rutherfordium-254 is 254.00 u. Calculate the mass in GeV c 2....... In 99, Rutherford produced the first artificial nuclear transmutation by bombarding nitrogen with α-particles. The reaction is represented by the following equation. α + 4 N 7 7 8 O + X Identify X. The following data are available for the reaction. Rest mass of α = 3.7428 GeV c 2 4 Rest mass of N = 3.0942 GeV c 2 7 7 Rest mass of O + X = 6.8383 GeV c 2 8 The initial kinetic energy of the α-particle is 7.68 MeV. Determine the sum of the kinetic energies of the oxygen nucleus and X. (Assume that the nitrogen nucleus is stationary.) (3) (d) The reaction in produces oxygen (O-7). Other isotopes of oxygen include O-9 which is radioactive with a half-life of 30 s. State what is meant by the term isotopes. Define the term radioactive half-life. 4/8
(e) A nucleus of the isotope O-9 decays to a stable nucleus of fluorine. The half-life of O- 9 is 30 s. At time t = 0, a sample of O-9 contains a large number N 0 nuclei of O-9. On the grid below, draw a graph to show the variation with time t of the number N of O- 9 nuclei remaining in the sample. You should consider a time of t = 0 to t = 20 s. Additional Problems (Total 0 marks) 5. A sample contains an amount of radioactive material with a half-life of 3.5 days. After 2 weeks the fraction of the radioactive material remaining is A. 94 %. B. 25 %. C. 6 %. D. 0 %. 6. Which nucleons in a nucleus are involved in the Coulomb interaction and the strong short-range nuclear interaction? Coulomb interaction Strong short-range interaction A. protons protons, neutrons B. protons neutrons C. protons protons D. protons, neutrons neutrons 7. This question is about nuclear processes. 226 (a) A nucleus of radium-9 ( 9Ra ) undergoes alpha particle decay to form a nucleus of radon (Rn). Identify the proton number and nucleon number of the nucleus of Rn. Proton number:... Nucleon number:... 5/8
The half-life of radium-9 is 600 years. Determine the length of time taken for 87.5 % of the radium to disintegrate. (b) Immediately after the decay of a stationary radium nucleus, the alpha particle and the radon nucleus move off in opposite directions and at different speeds. Outline the reasons for these observations....... (3) Outline why a beta particle has a longer range in air than an alpha particle of the same energy....... (3) (Total 0 marks) 8. This question is about α-particle scattering and nuclear processes. α-particle scattering Radium-226 decays with the emission of α-particles to radon (Rn). (a) Complete the nuclear reaction equation. Ra 226 88 Rn + (b) Experimental evidence that supports a nuclear model of the atom was provided by α- particle scattering. The diagram represents the path of an α-particle as it approaches and then recedes from a stationary gold nucleus. On the diagram, draw lines to show the angle of deviation of the α-particle. Label this angle D. 6/8
The gold nucleus is replaced by another gold nucleus that has a larger nucleon number. Suggest and explain the change, if any, in the angle D of an α-particle with the same energy and following the same initial path as in (b). The diagram shows the initial path of an α-particle that approaches the gold nucleus along a line joining their centres. On the diagram draw the subsequent path of the α- particle. Nuclear processes (d) The main nuclear process that gives rise to energy emission from the Sun may be simplified to 4H He + energy. State the name of this nuclear process. The total mass of four hydrogen (H) nuclei is 6.693 0 27 kg and the mass of a helium (He) nucleus is 6.645 0 27 kg. Show that the energy released in this reaction is 4.3 0 2 J. (iii) The Sun has a radius R of 7.0 0 8 m and emits energy at a rate of 3.9 0 26 W. The nuclear reactions take place in the spherical core of the Sun of radius 0.25R. Use these data and the answer in (d) to determine the number of nuclear reactions occurring per cubic metre per second in the core of the Sun. (3) (Total 2 marks) 9. Radioactive decay (a) Carbon-4 is a radioactive isotope with a half-life of 5500 years. It is produced in the atmosphere by neutron bombardment of nitrogen. The equation for this reaction is 4 7 N + 0n 6C + X. 4 Explain what is meant by isotopes.... 7/8
Identify the particle X.... (b) Each gram of a living tree contains approximately 4 0 0 atoms of carbon-4. On the axes below, draw a graph to show the variation with time of the number of carbon-4 atoms in one gram of wood from a tree. Your graph should indicate the number of atoms for a period of.8 0 4 years after the tree has died. (Half-life of carbon-4 = 5500 years) (3) The activity of a radioactive sample is proportional to the number of atoms in the sample. The activity per gram of carbon from a living tree is 9.6 disintegrations per minute. The activity per gram of carbon in burnt wood found at an ancient campsite is.9 disintegrations per minute. Estimate the number of atoms of carbon-4 in the burnt wood.... From the graph you have drawn in (b), estimate the age of the burnt wood.... (Total 7 marks) 8/8
Mark Scheme. A 3. D 5. C 7. C 9. C. D 2. B 4. A 6. A 8. C 0. A 3. (a) the (minimum) energy required to completely separate the nucleons of a nucleus / the energy released when a nucleus is assembled; 2. C mass defect is 94.007276+ 45.008665 238.990396 =.95u; binding energy is.95 93.5 = 86 MeV; 86 binding energy per nucleon is MeV; 239 = 7.6 MeV 3 (b) x = 3; binding energy of plutonium is 7.6 239 = 86 800MeV (known in ) binding energy of products is 8.6 9 + 8.2 46 = 980 2000 MeV; energy released is (2000 800) = 200MeV; 2 the electric force is repulsive/tends to split the nucleus; the electric force acts on protons, the strong nuclear force acts on nucleons; the nuclear force is attractive/binds the nucleons; but the electric force is long range whereas the nuclear force is short range; so adding more neutrons (compared to protons) contributes to binding and does not add to tendency to split the nucleus / a proton repels every other proton (in the nucleus) so extra neutrons are needed for binding; 4 max [] 4. (a) th mass of an atom of carbon 2/ 2 C; 2 (b) (254.00 93.5 =) 236.7(GeV c 2 ); (only accept answer in GeV c 2 ) proton / hydrogen nucleus / H + / H/ p ; m = (6.8383 [3.7428 + 3.0942] =) 0.003(GeV c 2 ); energy required for reaction =.3 (MeV); 7 KE of 8 O + X = (7.68.3 =) 6.4 (6.38) MeV; (allow correct answer in any valid energy unit) 3 (d) (nuclei of same element with) same proton number, different number of neutrons / OWTTE; the time for the activity of a sample to reduce by half / time for the number of the radioactive nuclei to halve from original value; 9/8
(e) scale drawn on t axis; (allow 0 grid squares = 30 s or 40 s) smooth curve passes through at 30 s, at 60 s, 2 4 N 0 N 0 N 0 at 90 s, at 20 s (to within square); (points not necessary) 2 6 N 0 8 [0] 5. C 6. A 7. (a) proton number: 89; nucleon number: 222; 2 [] [] 2.5% remains; 3 half lives 4800 years; 2 (b) momentum conserved; so different speeds as different masses; opposite directions because momentum zero initially; 3 beta have smaller mass / smaller / have greater speed than alpha; beta have smaller charge than alpha; therefore less likely to interact with air molecules; 3 [0] 0/7
222 8. (a) Rn ; 4 86 α 2 ; 2 (b) angle shown correctly; Horizontal line must be present, angle can be marked to straight portion of deviated path. same number of protons / additional number of neutrons / nuclei are isotopes; no charge change so deviation unchanged; 2 Award [0] for bald answer or answer with incorrect explanation. shows alpha-particle returning along original path and path must not touch gold nucleus; (d) fusion; m = 0.048 0 27 kg; E = 0.048 0 27 (3.0 0 8 ) 2 shown clearly; to give 4.3 0 2 J 2 26 3.9 0 (iii) number of reactions = 2 4.3 0 = 9. 0 37 s ; 4 volume of core = π[0.25 7.0 0 8 ] 3 3 (= 2.2 0 25 m 3 ) number = 4.0 0 2 m 3 s or = 4. 0 2 m 3 s 3 Award [3] for bald correct answer. [2] 9. (a) isotopes of elements are chemically identical but have different atomic masses / OWTTE / same number of protons in the nucleus but different number of neutrons / OWTTE; proton / H / p + ; /7
(b) 0 The data points at 4 0 and four data points covering 3 half - lives; 0 0.5 0 must be shown. correct plotting of data points; line of best-fit to.8 0 4 years; 3 0.9 4 0 0 number of atoms = 0.8 0 ; 9.6 from the graph age =.3 0 4 years; Allow ECF from (b) and from. [7] 2/7