A laboratory has two radioisotopes R and S, each prepared so that their initial activities are equal.
When lnA is plotted against time on the same set of axes, the straight line for isotope R has a slope of −0.015min−1, while that for isotope S has a slope of −0.005min−1.
(i) Write an expression for the activity of each isotope as a function of time, taking the common initial activity as A0.
(ii) Calculate the decay constant and half-life of each isotope.
(iii) Find the ratio of the activities AR/AS after 30 min.
(iv) Which isotope is more suitable for a diagnostic medical scan that requires the activity to drop to less than 1 % of its initial value within 4 h? Justify quantitatively.