Answer to Question #120119 in Atomic and Nuclear Physics for Higgins

Question

A radioactive tracer used in a medical test has a half-life of 2.6 h. What proportion of this tracer
will remain after 24 h?

Answer 1

The number of atoms $N$ remaining at time $t$ is given by the law od radioactive decay:

$$N = N_02^{-\frac{t}{T}}$$

where $N_0$ is number of atoms at the initial moment of time, $T$ is the half-life. Thus, the proportion of this tracer after 24 h will be:

$$p = \dfrac{N}{N_0} = 2^{-\frac{t}{T}} = 2^{-\frac{24h}{2.6h}} = 2^{-9.23} = 0.0017$$

Answer. p = 0.0017.