Question

1. A patient is given 0.050 mg of technetium-99 m, a radioactive isotope with a half-life of about 6.0 hours.

How long does it take for the radioactive isotope to decay to 5.9×10⁻³ mg ? (Assume no excretion of the nuclide from the body.)

Express your answer using two significant figures.

Answer 1

half-life (t1/2) = 6 hours

decay constant () = 0.693 / t1/2 = 0.693 / 6

                               = 0.1155 hour-1

A= initial weight of Tc = 0.050 mg

At = remaining weight = 5.9×10⁻³ mg

time (t) = ?

radioactive decay follows first order kinetics

t = (2.303 / ) log (A/At)

   = ( 2.303 / 0.1155 ) log (0.050 /5.9×10⁻³)

    = 18.51 hours

18 hours will take ---------------------(answer)