Answer to Question #174080 in Physics for Sam

Question

8. The activity of a radioactive sample fell from 2400Bq to 75 Bq over period of 24 hours. How long is the isotope’s half life?

Answer 1

We know that change in activity depends on the half-life and time:

$$A=\frac{A_0}{2^{t/T}},\\\space\\ \frac{A_0}{A}=2^{t/T},\\\space\\ T=\frac{t\ln2}{\ln(A_0/A)}=4.8\text{ h}.$$