(Comparison of two isotopes in a mixture)
A laboratory preparation contains equal numbers of nuclei of two radioisotopes A and B. The half-life of A is 2 h, while the half-life of B is 6 h.
(i) Show which isotope has the greater decay constant, giving a brief reason.
(ii) Calculate the ratio of their activities AA:AB after 6 h.
(iii) Calculate the ratio of their activities after 12 h.
(iv) Comment on how the relative contributions of the two isotopes to the total activity change with time.