23.2. Radioactive decay
A subsection of Physics, 9702, through 23. Nuclear physics
Listing 10 of 67 questions
A radiation detector is placed close to a radioactive source. The detector does not surround the source. Radiation is emitted in all directions and, as a result, the activity of the source and the measured count rate are different. Suggest two other reasons why the activity and the measured count rate may be different. 1. 2. The variation with time t of the measured count rate in is shown in . count rate / min–1 t / hours State the feature of that indicates the random nature of radioactive decay. Use to determine the half-life of the radioactive isotope in the source. half-life = hours The readings in were obtained at room temperature. A second sample of this isotope is heated to a temperature of 500 °C. The initial count rate at time t = 0 is the same as that in . The variation with time t of the measured count rate from the heated source is determined. State, with a reason, the difference, if any, in 1. the half-life, 2. the measured count rate for any specific time.
9702_w17_qp_43
THEORY
2017
Paper 4, Variant 3
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Radioactive decay is both random and spontaneous. State what is meant by: random spontaneous. A sample of radioactive material contains atoms of an unstable nuclide X. The activity of the sample due to the atoms of X is A. The variation with time t of ln A is shown in . 35.00 35.4 35.8 36.2 36.6 In (A / Bq) t / min Use to determine the half-life, in minutes, of nuclide X. half-life = min At time t = 0, the mass of the atoms of X in the sample is 5.66 × 10–7 kg. Determine the nucleon number of X. nucleon number =
9702_w21_qp_42
THEORY
2021
Paper 4, Variant 2
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Carbon-15 (15 6 C) is an isotope of carbon that undergoes radioactive decay to nitrogen-15 (15 7 N), which is a stable isotope of nitrogen. Radioactive decay is both a random and a spontaneous process. State what is meant by: random spontaneous. A small sample of carbon-15 decays. The mass M of carbon-15 in the sample decreases with time t. shows the variation with t of the value of ln (M / 10–16 g). – 8 – 7 – 6 – 5 – 4 In (M / 10–16 g) t / s State how demonstrates that radioactive decay is random. On , draw the straight line of best fit. Show that the decay constant λ of carbon-15 is given by the magnitude of the gradient of your line in . Use your line in to determine λ. Give a unit with your answer. λ = unit Use your answer in to calculate the half-life of carbon-15. half-life = s The equation for the decay of carbon-15 can be written as 6C 7N + 0 –1β + 0 0ν. State and explain how the mass of the products of the decay must compare with the mass of the carbon-15 nucleus.
9702_w22_qp_41
THEORY
2022
Paper 4, Variant 1
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Carbon-15 (15 6 C) is an isotope of carbon that undergoes radioactive decay to nitrogen-15 (15 7 N), which is a stable isotope of nitrogen. Radioactive decay is both a random and a spontaneous process. State what is meant by: random spontaneous. A small sample of carbon-15 decays. The mass M of carbon-15 in the sample decreases with time t. shows the variation with t of the value of ln (M / 10–16 g). – 8 – 7 – 6 – 5 – 4 In (M / 10–16 g) t / s State how demonstrates that radioactive decay is random. On , draw the straight line of best fit. Show that the decay constant λ of carbon-15 is given by the magnitude of the gradient of your line in . Use your line in to determine λ. Give a unit with your answer. λ = unit Use your answer in to calculate the half-life of carbon-15. half-life = s The equation for the decay of carbon-15 can be written as 6C 7N + 0 –1β + 0 0ν. State and explain how the mass of the products of the decay must compare with the mass of the carbon-15 nucleus.
9702_w22_qp_43
THEORY
2022
Paper 4, Variant 3
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Define radioactive decay constant. Show that the decay constant λ is related to the half-life t 1 2 of a radioactive isotope by the expression λ t 1 2 = ln2 A small volume of solution containing the radioactive isotope sodium-24 (2 1Na) has an initial activity of 3.8 × 104 Bq. Sodium-24, of half-life 15 hours, decays to form a stable daughter isotope. All of the solution is poured into a container of water. After 36 hours, a sample of water of volume 5.0 cm3, taken from the container, is found to have an activity of 1.2 Bq. Assuming that the solution of the radioactive isotope is distributed uniformly throughout the container of water, calculate the volume of water in the container. volume = cm3
9702_m18_qp_42
THEORY
2018
Paper 4, Variant 2
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Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of 5.9 × 105 Bq. Determine, for this sample of americium-241, the number of nuclei, number = the decay constant, decay constant = s–1 the half-life, in years. half-life = years Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not appropriate for the determination of its half-life.
9702_s10_qp_42
THEORY
2010
Paper 4, Variant 2
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Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of 5.9 × 105 Bq. Determine, for this sample of americium-241, the number of nuclei, number = the decay constant, decay constant = s–1 the half-life, in years. half-life = years Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not appropriate for the determination of its half-life.
9702_s10_qp_43
THEORY
2010
Paper 4, Variant 3
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Questions Discovered
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