Answer the following questions about radioactive dating:
(i) Define half-life of a radioactive nuclide and derive its relation with the decay constant.
(ii) Explain why radioisotopes whose half-life is much shorter than the expected age of an archaeological sample or much longer than it are unsuitable for dating that sample.
(iii) Describe qualitatively how measurement of the present parent-to-daughter ratio in a closed system permits the determination of the sample’s age.