Nuclear Physics 5. Name: Date: 8 (1)

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1 Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly with time. B. increases linearly with time. C. decreases exponentially with time. D. increases exponentially with time. 2. A sample of a radioactive isotope of half-life T initially contains N atoms. Which one of the 2 following gives the number of atoms of this isotope that have decayed after a time 3T? A. N 8 B. N 3 2 C. N D. N 8 3. An isotope of radium has a half-life of 4 days. A freshly prepared sample of this isotope 7N contains N atoms. The time taken for 8 of the atoms of this isotope to decay is A. 32 days. B. 6 days. C. 2 days. D. 8 days.

2 4. This question is about radioactivity. (a) A sample of radioactive material is found by chemical analysis to contain atoms of uranium-235. The activity of the sample is Bq. Calculate, for the uranium-235 the decay constant; the half-life in years. (b) An isotope has a half-life of approximately four hours. Suggest why measurement of the number of atoms and the activity of a sample of this isotope cannot be used to determine its half-life (Total 5 marks) 5. Nuclear decay (a) State the nature of an α-particle.... 2

3 (b) In the Rutherford-Geiger-Marsden experiment to investigate the structure of the atom, α-particles were directed towards a gold foil. Explain why α-particles, rather than electrons, were used in this experiment (c) Uranium-238 ( U) U is years. 92 undergoes α-decay to form thorium (Th). The half-life of uranium Define half-life. Write down the nuclear equation for the α-decay of uranium to thorium. (d) Thorium is radioactive and further decays occur, eventually giving lead which is stable. These further decays all occur within a time that is short compared to the half-life of U. In a sample of rocks the ratio of the number of uranium atoms to the number of lead atoms is. 7 Estimate the age of the rocks assuming that no lead was initially present in the rocks. 3

4 State one further assumption that is made in this estimate. (Total 0 marks) 6. This question is about radioactive decay. A nucleus of the isotope xenon, Xe-3, is produced when a nucleus of the radioactive isotope iodine I-3 decays. (a) Explain the term isotopes (b) Fill in the boxes below in order to complete the nuclear reaction equation for this decay. 3 3 I Xe 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 4

5 (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 (Total marks) 7. Radioactive decay (a) Carbon-4 is a radioactive isotope and is produced in the atmosphere by neutron bombardment of nitrogen. The equation for this reaction is 4 7 N + 0n 6C + X. 4 Identify the particle X.... (b) Living trees contain atoms of carbon-4. 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. disintegrations per minute. 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. 5

6 The half-life of carbon-4 is 5500 years. Calculate the decay constant for carbon-4 and use this value to estimate the age of the carbon found at the campsite. (5) (iii) Suggest one reason why radioactive dating of carbon samples that are more than years old is unreliable. (Total 0 marks) 8. 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. State what is meant by a nucleon. Outline the structure of nucleons in terms of quarks. (iii) Explain, in terms of the number of nucleons and the forces between them, why argon-36 is stable and argon-39 is radioactive. 6

7 (4) (b) Argon-39 undergoes β decay to an isotope of potassium (K). The nuclear reaction equation for this decay is 39 Ar 8 K + β + 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 β energy spectra, for postulating its existence. (iii) Use the following data to determine the maximum energy, in J, of the β particle in the decay of a sample of argon-39. Mass of argon-39 nucleus Mass of K nucleus = u = u 7

8 (c) The half-life of argon-39 is 270 years. 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. (Total 2 marks) 8