A hospital orders a sealed γ-ray source for internal radiotherapy. The manufacturer prepares the source so that its activity is 1.80×108Bq at the moment it leaves the facility. Transport to the hospital takes 36h, during which the source is not used.
Upon arrival, the hospital physicist measures the activity and finds it to be 1.12×108Bq.
(a) Using the shipment data, determine the decay constant of the radionuclide in s−1. Show all algebraic and numerical steps.
(b) From the value obtained in part (a), calculate the half-life of the radionuclide in hours.
(c) A single treatment session requires the source to maintain an activity of at least 9.0×107Bq for 10h. Evaluate whether the ordered source can be used for an entire treatment session beginning immediately upon arrival. Support your conclusion with quantitative reasoning.