Question #121540
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.
1
Expert's answer
2020-06-12T11:16:50-0400

The activity is


A(t)=A0exp(0.693tτ).A(t)=A_0\text{exp}\bigg(-0.693\frac{t}\tau\bigg).

Express time:


t=τln[A0/A(t)]0.693.t=\tau\frac{\text{ln}[A_0/A(t)]}{0.693}.

Substitute activity at time tt and calculate the corresponding time:


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

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