A hospital receives a shipment containing 6.00\,mCi of the medical radioisotope 128I. Nine hours after receipt, a measurement shows that the activity has fallen to 1.50\,mCi.
Answer the following questions about the decay of 128I.
(a) Determine the decay constant of 128I based on the activity measurements. Show all steps in your calculation.
(b) Calculate the half-life of 128I in hours.
(c) A diagnostic procedure scheduled 12.0\,h after the shipment arrives requires a minimum activity of 0.800\,mCi. Will the sample still meet this requirement? Support your answer with calculations.
(d) How many half-lives will have elapsed 48.0\,h after the shipment arrives, and what fraction of the original nuclei will remain at that time? Express the remaining amount both as a decimal and as a percentage.