Half-life

Formula: Number of half-lives = Total time / Half-life; Remaining atoms = Initial atoms / 2^(number of half-lives)

Working: Number of half-lives = 6.0 hours / 2.0 hours = 3
Remaining atoms = 8000 / 2³ = 8000 / 8 = 1000

Answer: 1000 atoms

Explanation: After each half-life, the number of radioactive atoms halves. After 3 half-lives, the initial number of atoms is halved three times.

The activity halves twice in 6 hours (800 -> 400 -> 200). Therefore, two half-lives is 6 hours.

Half-life = Total time / Number of half-lives = 6 hours / 2 = 3 hours

Answer: 3 hours. This calculation uses the decrease in activity to determine how many half lives have passed, and then relates that to the total time elapsed.

Knowing the half-life of a radioactive isotope in waste is essential because it allows scientists to predict how long the waste will remain hazardous. Isotopes with longer half-lives remain dangerous for a longer period, thus requiring longer-term storage solutions, such as deep geological repositories, to prevent environmental contamination and harm to living organisms. Short half life isotopes decay away quickly, becoming inert.

Activity after two half-lives = Initial Activity / (2^(number of half-lives))
Number of half-lives = Total time / Half-life = 864 years / 432 years = 2
Activity = 8.0 Bq / (2^2) = 8.0 Bq / 4 = 2.0 Bq

Answer: 2.0 Bq. Smoke detectors require long half-lives so they don't need frequent replacement of the radioactive source.

Gamma radiation has a high penetration power, allowing it to pass through packaging and effectively kill bacteria and viruses throughout the equipment. Alpha radiation has very low penetration power; it is easily stopped by even a thin layer of material like paper. Therefore, it cannot reach the bacteria inside wrapped equipment effectively.