Question

When radioactive tracers are used for medical scans, the tracers both decay in the body via radiation, as well as being excreted from the body. The effective half-life of the radioactive tracer is due to the combination of both effects. Medical experiments show that a stable (nonradioactive) isotope of a particular element have an excretion half-life of 6 days. A radioactive isotope of the same element has a half-life of 9 days. What is the effective half-life of the radioactive tracer due to both effects?

(Hint: Write out an expression for N excreted (t), the amount of tracers left in the body due only to being excreted, in terms of the initial number of tracers N0. Then use this to write an expression for N total (t), the amount of tracers left in the body due to both excretion and decay; and solve this for the effective half-life.)

Answer 1