1.1. State what is meant by radioactive decay.

1.2. A radioactive sample consists of an isotope with a half-life T that decays to form a stable product. Only the isotope and the stable product are present in the sample. 

At time t = 0, the sample has an activity of A₀ and contains N₀ nuclei of the isotope. 

(i) On Fig. 1.1, sketch the variation with t of the number N of nuclei of the isotope present in the sample from time t = 0 to time t = 3T.

Fig. 1.1

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(ii) State the name of the quantity represented by the gradient of the graph in Fig. 1.1.

[1]

1.3. (i) On Fig. 1.2, sketch the variation with N of the activity A of the sample for values of N between N = 0 and N = N₀.

Fig. 1.2

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(ii) State the name of the quantity represented by the gradient in Fig. 1.2.

[1]

1.4. Calculate the fraction of undecayed nuclei N remaining relative to N₀ at time t = 1.25T.