A sample of a radioactive isotope contains N nuclei of the isotope at time T. At time (T + AT), the sample contains (N – AN) nuclei of the isotope. The time interval AT is short. Use the symbols N, AN, T and AT to give expressions for:

1. (a)(i)the average activity of the sample during the time AT[1]
2. (a)(ii)the probability of decay of a nucleus in the time AT[1]
3. (a)(iii)the decay constant λ of the isotope.[1]
4. (b)The isotope polonium-208 (208 84 Po) is radioactive and decays to form lead-204 (204 82 Pb). The nuclear equation for this decay is 208 84 Po→204 82 Pb + 4 2 He. Data for nuclear masses are given in Fig. 12.1. [Figure 12.1]
5. (b)(i)Determine, for the decay of one nucleus of polonium-208: 1. the change, in u, of the mass[1]
6. (b)(i)2. the total energy, in pJ, released.[3]
7. (b)(ii)The polonium-208 nucleus is initially stationary. The initial kinetic energy of the 4 2 He nucleus (α-particle) is found to be less than the energy calculated in (i) part 2. Suggest two possible reasons for this difference.[2]

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