Question

The half life of radium is 1600 years. If a sample of radium-226 has an original activity of 200 bq, what will it’s activity be after 4800 years

Answer 1

After time $t$ the number of radium atoms will be $2^{-t/T}$ times its original number, where $T$ is the half-life time. In our case, $t/T = 4800/1600 = 3$, and $2^{-3} = 1/8$. Since the radioactivity is proportional to the number of radioactive atoms, it will decrease 8 times and, therefore, will constitute 200/8 = 25 bq. The answer is: 25 bq.