Question

A patient is given 0.045 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 8.0×10⁻⁴ mg ? (Assume no excretion of the nuclide from the body.)

Answer 1

half life = 6 hours

rate constant = 0.693 / half -life

                      = 0.693 / 6

                      = 0.1155 hour-1

Ao = initial = 0.045 mg

At = 8.0 x 10^-4 mg

t = 1/k * ln (Ao /At)

t = 1 / 0.1155 * ln (0.045 / 8.0×10⁻⁴ )

t = 34.89 hours

time taken = 34.89 hours