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

1. (a)(i)the average activity of the sample during the time ∆T[1]
2. (a)(ii)the probability of decay of a nucleus in the time ∆T[1]
3. (a)(iii)the decay constant λ of the isotope.[1]
4. (b)(i) 1.The isotope polonium-208 (^208_84Po) is radioactive and decays to form lead-204 (^204_82Pb). The nuclear equation for this decay is ^208_84Po → ^204_82Pb + ^4_2He. Data for nuclear masses are given in Fig. 12.1. [Figure 12.1] Determine, for the decay of one nucleus of polonium-208: the change, in u, of the mass[1]
5. (b)(i) 2.the total energy, in pJ, released.[3]
6. (b)(ii)The polonium-208 nucleus is initially stationary. The initial kinetic energy of the ^4_2He 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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