A research laboratory stores a pure sample of a radioisotope whose half‐life is precisely 5.0 h. Scientists are preparing an experiment that will begin 20 h after the sample is removed from its shielding container. The experiment requires that the researchers understand how the number of undecayed nuclei and the decay rate change over time.
(a) After 10 h have elapsed, what fraction of the original nuclei in the sample remain undecayed? Express your answer as an exact fraction.
(b) Describe qualitatively how the rate at which nuclei decay (the activity) varies as time progresses. In your explanation, make explicit reference to the proportionality between decay rate and the number of undecayed nuclei.
(c) Without drawing a graph, give a detailed verbal description of the expected shape of a plot of the number of undecayed nuclei N versus time t for the entire 20 h interval. Include comments on the concavity, intercepts, and long‐term behaviour of the curve.