Technetium-99m, a radioisotope used to image the skeleton and the heart muscle, has a half-life of about 6 hours. Find the decay constant. Use the decay function N(t)=N0e^-kt to determine the amount of a 250 mg dose that remains after 24 hours.
1)
\(N(t)=N_0e^{-kt}\\ \frac{N(t)}{N_0}=e^{-kt}\\ k=-\frac{\ln(\frac{N(t)}{N_0})}{t}\\ k=-\frac{\ln(\frac{0.5N_0}{N_0})}{6hr}=0.116hr^{-1}\\\)
2)
\(N(24)=(250mg)e^{-(0.116hr^{-1})(24hr)}\\ N(24)=15.625mg\)
