PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Nuclear Physics · Radioactivity and decay modes
Mathematical Methods for Physics, Ch First-order differential equations and physical modelling
Problem
The radioisotope technetium-99m, used in medical imaging, decays with a half-life t1/2=6.01hours, so its activity A(t) obeys A˙=−λA for some decay constant λ. A patient is injected with activity A0 at t=0.
((a)) Find the time constant τ=1/λ of the decay, in hours.
((b)) The patient returns for a scan 18.0hours after injection. What percentage of the injected activity remains at that time?
((c)) Hospital procedure allows a further diagnostic injection once the residual activity has fallen below 2.0% of A0. How long after the first injection must the staff wait, in hours?
((d)) Express the waiting time found in part (c) as a multiple of τ, and say whether it is more or less than 5τ, given that an exponential decay has completed 99.3% of its fall after 5τ.