SECTION A. Define the activity of a radioactive sample. ...

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1 3 N00/430/H(2) SECTION A Candidates must answer all questions in the spaces provided. A1. Radioactive decay measurement A medical physicist wishes to investigate the decay of a radioactive isotope and determine its decay constant and half-life. A Geiger-Muller counter is used to detect radiation from a sample of the isotope, as shown. Radioactive source source Geiger-Muller tube Voltage supply and counter (a) Define the activity of a radioactive sample [1] Theory predicts that the activity A of the isotope in the sample should decrease exponentially with time t according to the equation A = A e "! t 0, where A0 is the activity at t = 0 and! is the decay constant for the isotope. (b) Manipulate this equation into a form which will give a straight line if a semi-log graph is plotted with appropriate variables on the axes. State what variables should be plotted Turn over

2 4 N00/430/H(2) (Question A1 continued) The Geiger-counter detects a proportion of the particles emitted by the source. The physicist records the count-rate R of particles detected as a function of time t and plots the data as a graph of ln R versus t, as shown below. 2 1 ln ( R / s " ) 1 (c) (d) t / hr Does the plot show that the experimental data are consistent with an exponential law? Explain The Geiger-counter does not measure the total activity A of the sample, but rather the count-rate R of those particles that enter the Geiger tube. Explain why this will not matter in determining the decay constant of the sample [1] [1] (e) From the graph, determine a value for the decay constant!

3 5 N00/430/H(2) (Question A1 continued) The physicist now wishes to calculate the half-life. (f) Define the half-life of a radioactive substance [1] (g) Derive a relationship between the decay constant! and the half-life #. (h) Hence calculate the half-life of this radioactive isotope [1] Turn over

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11 15 N04/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B1 continued) Part 2 Radioactivity and nuclear energy levels (a) Define the following terms. (i) Radioactive half-life (T 12 ) [1] (ii) Decay constant (!) [1] (b) Deduce that the relationship between T 12 and! is! T 12 1n Turn over

12 16 N04/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B1, part 2 continued) Thorium-227 (Th-227) undergoes!-decay with a half-life of 18 days to form radium-223 (Ra-223). A sample of Th-227 has an initial activity of Bq. (c) Determine, the activity of the remaining thorium after 50 days In the decay of a Th-227 nucleus, a "-ray photon is also emitted. (d) (i) Use the following data to deduce that the energy of the "-ray photon is MeV. (ii) mass of Th-227 nucleus = u mass of Ra-223 nucleus = u mass of helium nucleus = u energy of!-particle emitted = MeV unified atomic mass unit (u) = MeV c You may assume that the Th-227 nucleus is stationary before decay and that the Ra-223 nucleus has negligible kinetic energy. Calculate the frequency of the "-ray photon

13 17 N04/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B1, part 2 continued) Although in the decay of a Th-227 nucleus, an!-particle and a "-ray photon are emitted, they may have different energies to those in (d) (i). However, all the!-particles emitted in the decay of Th-227 have discrete energies as do the associated "-ray photons. This provides evidence for the existence of nuclear energy levels. The diagram below represents some of the energy levels of a nucleus of Ra-223 relative to Th-227. Th-227 energy energy levels of Ra-223 (e) On the diagram above label (i) the arrows associated with!-particles (with the letter A). [1] (ii) the arrows associated with "-ray photons (with the letter G). [1] (iii) the ground state energy level of Ra-223 (with the letter R). [1] (f) Use data from (d), to suggest a value for the energy difference between the ground states of a nucleus of Th-227 and the ground state of a nucleus of Ra [1] Turn over

14 14 M05/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B1 continued) Part 2 Radioactive decay A nucleus of the isotope xenon, Xe 131, is produced when a nucleus of the radioactive isotope iodine I-13 decays. (a) Explain the term isotopes (b) Fill in the boxes below in order to complete the nuclear reaction equation for this decay I Xe! 54 The activity A of a freshly prepared sample of the iodine isotope is Bq and its half-life is 8.0 days. (c) Using the axes, draw a graph to illustrate the decay of this sample. A / Bq time / days

15 15 M05/4/PHYSI/HP2/ENG/TZ1/XX+ Question B1, part 2 continued) (d) Determine the decay constant of the isotope I The sample is to be used to treat a growth in the thyroid of a patient. The isotope should not be used until its activity is equal to Bq. (e) Calculate the time it takes for the activity of a freshly prepared sample to be reduced to an activity of Bq Turn over

16 10 M05/4/PHYSI/HP2/ENG/TZ2/XX+ SECTION B This section consists of four questions: B1, B2, B3 and B4. Answer two questions. B1. This question is about collisions and radioactive decay. (a) (i) Define linear momentum and impulse. Linear momentum: (ii) Impulse: State the law of conservation of momentum. (iii) Using your definitions in (a) (i), deduce that linear momentum is constant for an object in equilibrium

17 11 M05/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B1 continued) A stationary radon-220 ( Rn) nucleus undergoes!-decay to form a nucleus of polonium (Po). The!-particle has kinetic energy of 6.29 MeV. (b) (i) Complete the nuclear equation for this decay Rn Po (ii) Calculate the kinetic energy, in joules, of the!-particle. (iii) Deduce that the speed of the!-particle is ms 1. [1] Turn over

18 12 M05/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B1 continued) The diagram below shows the!-particle and the polonium nucleus immediately after the decay. The direction of the velocity of the!-particle is indicated. polonium nucleus!-particle (c) (i) On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay. [1] (ii) Determine the speed of the polonium nucleus immediately after the decay. (iii) In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c) (i)

19 13 M05/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B1 continued) The half-life of the decay of radon-222 is 3.8 days and radon-220 has a half-life of 55 s. (d) (i) Suggest three ways in which nuclei of radon-222 differ from those of radon-220. (ii) Define half-life. (iii) State the expression that relates the activity A t at time t of a sample of a radioactive material to its initial activity A 0 at time t = 0 and to the decay constant!. Use this expression to derive the relationship between the decay constant! and the half-life T 12. (iv) Radon-222 emits "-particles. The activity of radon gas in a sample of 1.0 m 3 of air is 4.6 Bq. Given that 1.0 m 3 of the air contains molecules, determine the ratio 3 number of radon-222 atoms in 1.0 m of air number of molecules in 1.0 m of air 3. [4] Turn over

20 14 M05/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B1 continued) (e) Suggest whether radon-222 or radon-220 presents the greater hazard to people over a long period of time [1]

21 27 M06/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B3 continued) Part 2 Radioactive decay (a) Carbon-14 is a radioactive isotope and is produced in the atmosphere by neutron bombardment of nitrogen. The equation for this reaction is 14 7 N n C X Identify the particle X. [1]..... (b) Living trees contain atoms of carbon-14. 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 (charcoal) found at an ancient campsite is 2.1 disintegrations per minute. (i) (ii) A living tree continuously takes in carbon dioxide from the atmosphere. Suggest why the activity of the carbon from the charcoal is less than that of the living wood. The half-life of carbon-14 is 5500 years. Calculate the decay constant for carbon-14 and use this value to estimate the age of the carbon found at the campsite. [5] Turn over

22 28 M06/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B3, part 2 continued) (iii) Suggest one reason why radioactive dating of carbon samples that are more than years old is unreliable. [1]

23 29 N06/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B4 continued) Part 2 Radioactivity (a) State what is meant by the term (i) (ii) isotopes. decay constant. [1] (b) Complete the nuclear reaction equation for the decay process indicated below K 20 Ca Turn over

24 30 N06/4/PHYSI/HP2/ENG/TZ0/XX+ (Question B4, part 2 continued) (c) One isotope of potassium is potassium K. Nuclei of this isotope undergo radioactive decay with a decay constant hour 1 to form nuclei of calcium. At time t 0, a sample of potassium-42 contains N 0 nuclei. (i) On the graph below, label the x-axis with values to show the variation with time t / hours of the number N of potassium nuclei in the sample. N 0 N 0 0 t / hours (ii) The isotope of calcium formed in this decay is stable. On the graph above, draw a line to show the variation with time t of the number of calcium nuclei in the sample. [1] (d) Use the graph, or otherwise, to determine the time at which the ratio number of calcium nuclei in sample number of potassium-42 nuclei in sample is equal to

25 33 M07/4/PHYSI/HP2/ENG/TZ1/XX+ B4. This question is in two parts. Part 1 is about using plutonium as a power source. Part 2 is about the orbital motion of a satellite. Part 1 Plutonium as a power source The alpha decay of plutonium-238 is to be used as a power source. Plutonium decays by emission of an!-particle to form an isotope of uranium (U). 238 Pu (a) (b) Write down the nuclear equation for this decay The nuclear masses of the isotopes and the!-particle in this decay are Plutonium u Uranium u!-particle u. (i) Deduce that the energy released in this reaction is J. (ii) The plutonium nucleus is at rest before the decay. Explain why most of the energy in (b)(i) is kinetic energy of the!-particle Turn over

26 34 M07/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B4, part 1 continued) (c) The half-life of plutonium is 88 years. (i) (ii) Explain why over a period of six months the activity of a sample of plutonium-238 may be considered to be constant. The activity of the sample of plutonium-238 is Bq. Calculate the rate at which energy is released. (iii) The mass of the sample of plutonium-238 in (c)(ii) is 65 g. Using your answer to (c)(ii) calculate the rate at which the temperature of the plutonium sample is increasing. Assume that no energy is lost from the sample. (The specific heat capacity of plutonium is 150 J kg 1 K 1.)

27 35 M07/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B4, part 1 continued) (d) As the temperature of the sample in (c) rises the plutonium will eventually melt. Describe and explain, in terms of atomic behaviour, the processes of (i) (ii) the temperature rise of plutonium. the phase change of plutonium Turn over

28 31 M07/4/PHYSI/HP2/ENG/TZ2/XX+ B4. This question is in two parts. Part 1 is about radioactive decay. Part 2 is about friction. Part 1 Radioactive decay (a) The nucleon number (mass number) of a stable isotope of argon is 36 and of a radioactive isotope of argon is 39. (i) (ii) State what is meant by a nucleon. Outline the structure of nucleons in terms of quarks. [1] (iii) Explain, in terms of the number of nucleons and the forces between them, why argon-36 is stable and argon-39 is radioactive. [4] Turn over

29 32 M07/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B4, part 1 continued) (b) Argon-39 undergoes decay to an isotope of potassium (K). The nuclear reaction equation for this decay is (i) (ii) 39 18Ar K x. State the proton (atomic) number and the nucleon (mass) number of the potassium nucleus and identify the particle x. Proton number: Nucleon number: Particle x: The existence of the particle x was postulated some years before it was actually detected. Explain the reason, based on the nature of energy spectra, for postulating its existence. (iii) Use the following data to determine the maximum energy, in J, of the in the decay of a sample of argon-39. Mass of argon-39 nucleus = u Mass of K nucleus = u particle

30 33 M07/4/PHYSI/HP2/ENG/TZ2/XX+ (Question B4, part 1 continued) (c) The half-life of argon-39 is 270 years. (i) (ii) State what quantities you would measure to determine the half-life of argon-39. Explain how you would calculate the half-life using the quantities you have stated in (i) Turn over

31 5 M08/4/PHYSI/HP2/ENG/TZ2/XX+ A2. This question is about radioactivity. (a) Outline a method for the measurement of the half-life of a radioactive isotope having a half-life of approximately 10 9 years. (b) A radioactive isotope has a half-life T 12. Determine the fraction of this isotope that remains in a particular sample of the isotope after a time of 1.6 T Turn over

32 26 M09/4/PHYSI/HP2/ENG/TZ1/XX+ B4. This question is in two parts. Part 1 is about the decay of radium-226 and Part 2 is about diffraction and resolution. Part 1 Decay of radium-226 (a) The nuclear reaction equation for the decay of radium-226 (Ra) may be written as 226 Ra Rn 88 (i) State the value of the proton number and neutron number of the isotope of radon (Rn). Proton number:... Neutron number:.... [1] (ii) Compare, with reference to the nuclear reaction in (a), the binding energy of Ra with that of Rn. (b) The following data are available. mass of Ra mass of Rn mass of α = u = u = u Show that the energy released in the decay of a Ra nucleus is 4.94 Me V

33 27 M09/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B4, part 1 continued) (c) An α-particle of energy 4.94 MeV emitted in the decay of a Ra nucleus, travels a distance d in air before coming to rest. (i) Show that the initial speed of the α-particle is m s (ii) State the relationship between the magnitude of the average force F acting on the α-particle, the change in kinetic energy E K and the distance d. [1] (iii) Use your answer to (c)(ii) to calculate F given that d 10 m. (iv) Estimate the time that it takes the α-particle to come to rest. [4] Turn over

34 22 M10/4/PHYSI/HP2/ENG/TZ1/XX+ B3. This question is in two parts. Part 1 is about nuclear decay and ionization. Part 2 is about radio waves. Part 1 Nuclear decay and ionization (a) A nucleus of radium radon (Rn). 226 Ra undergoes alpha particle decay to form a nucleus of Identify the proton number and nucleon number of the nucleus of Rn. Proton number:... Nucleon number:... (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. α radon (i) (ii) Outline the reasons for these observations. Show that the ratio is about 56. initial kinetic energy of alpha particle initial kinetic energy of radon atom

35 23 M10/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B3, part 1 continued) (c) The initial kinetic energy of the alpha particle is 4.9 MeV. As the alpha particle passes through air, it loses all its kinetic energy by causing the ionization of air molecules. (i) (ii) State what is meant by ionization. Estimate, in joules, the average energy needed to ionize an air molecule. [1] (d) Outline why a beta particle has a longer range in air than an alpha particle of the same energy Turn over

36 A2. This question is about radioactive decay and binding energy. 4 M10/4/PHYSI/HP2/ENG/TZ2/XX+ (a) (b) Describe what is meant by radioactive decay. A nucleus of potassium-40 (K-40) undergoes radioactive decay to a nucleus of argon-40 (Ar-40). In the reaction equation below, identify the proton number Z of argon and the particle x. K Ar β x Z (c) (d) Z : x : The mass of a K-40 nucleus is MeV c 2. Determine the binding energy per nucleon of K-40. State why the binding energy of Ar-40 is greater than that of K-40. [4] [1]

37 14 M09/4/PHYSI/HP2/ENG/TZ1/XX+ (Question B1, part 2 continued) Nuclear spectra (c) A nucleus of the isotope bismuth-212 undergoes α-decay into a nucleus of an isotope of thallium. A γ-ray photon is also emitted. Draw a labelled nuclear energy level diagram for this decay. (d) The activity of a freshly prepared sample of bismuth-212 is Bq. After 80.0 minutes the activity is Bq. Determine the half-life of bismuth-212. [4]

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