(a) Define the following terms related to radioactivity:
(i) decay constant, (ii) half-life, (iii) mean life.
(b) Explain, without performing any numerical calculation, why an isotope with a shorter half-life must have a larger decay constant than one with a longer half-life.
(c) Two radioactive nuclides, P and Q, have half-lives of 15 s and 75 s respectively. For equal initial numbers of nuclei, which nuclide will show the greater activity after 45 s? Justify your answer qualitatively.