Two identical masses of a certain β-emitting isotope, each of atomic mass M g mol⁻¹ and half-life T, are prepared on different days. Sample A is sealed at noon on day 1. Exactly three half-lives later, at noon on day 4, a fresh Sample B of the same mass is prepared.
(i) Obtain the ratio of the number of undecayed nuclei in Sample A to that in Sample B immediately after Sample B is prepared.
(ii) Hence find the ratio of their activities at that instant.
(iii) After a further time interval T, what will be the ratio of the activities of A and B?