A laboratory is comparing two radioactive isotopes, U and Z. Separate samples are prepared so that at t=0 the activities of the two samples are equal. Isotope U has a known half-life of 20 min. After 60 min have elapsed, the activity of isotope U has fallen to 12.5 % of its initial value, while the activity of isotope Z has dropped to 50 % of its initial value.
(a) Show that the observed 60 min activity decrease for isotope U is consistent with its stated half-life.
(b) Using the information provided, determine the half-life of isotope Z.
(c) Based on their half-lives, discuss the relative nuclear stability of isotopes U and Z and how that would influence choices for practical applications.