Answer to Question #121540 in Atomic and Nuclear Physics for Raghuveer

Question

3. Iodine-120 has a half life of 1.35 hours. If you start off with a sample which has an activity of 1.0 Ci, how
long is it before the activity drops to the following values: (a) 0.50 Ci; (b) 9.77×10−4 Ci; (c) 9.31×10−10 Ci.

Kindly explain in detail and give the correct solution.

Answer 1

The activity is

$$A(t)=A_0\text{exp}\bigg(-0.693\frac{t}\tau\bigg).$$

Express time:

$$t=\tau\frac{\text{ln}[A_0/A(t)]}{0.693}.$$

Substitute activity at time $t$ and calculate the corresponding time:

$$(a)\space t=1.35\text{ h},\\ (b)\space t=13.5\text{ h},\\ (c)\space t=40.5\text{ h}.$$