Question 1: Define radioactive decay and explain the role of decay equations in describing this process.

Answer: Radioactive decay is the spontaneous process by which unstable atomic nuclei lose energy by emitting radiation. Decay equations mathematically represent how the quantity of a radioactive substance decreases over time.

Question 2: What is the decay constant, and how does it relate to the half-life of a radioactive isotope?

Answer: The decay constant (λ) is a probability rate at which a nucleus decays per unit time. It is related to the half-life (T½) by the formula T½ = ln(2)/λ.

Question 1: A sample contains 100 grams of a radioactive isotope with a decay constant of 0.0012 per day. Calculate how much remains after 30 days.

Answer: Approximately 65 grams remain after 30 days.

Question 2: If a sample originally had 200 grams of a substance with a half-life of 10 days, how much will remain after 30 days?

Answer: Approximately 25 grams remain after 30 days.

Question 1: Describe a simple experimental setup to measure the half-life of a radioactive isotope in a school laboratory. Include safety precautions.

Answer: The experiment involves measuring the activity of a radioactive source at regular intervals using a Geiger counter, recording the counts, and plotting decay over time. Safety precautions include handling sources with tongs, wearing protective gear, and working in a well-ventilated area or behind shielding.

Question 2: Identify at least three variables that could affect the accuracy of decay measurements in an experiment.

Answer: Variables include detector sensitivity, background radiation levels, and environmental conditions such as temperature and electromagnetic interference.

Question 1: A scientist records the activity of a radioactive sample over a period of 50 days. The activity decreases from 1000 counts per minute to 125 counts per minute. Explain what this data indicates about the decay process and estimate the half-life of the isotope.

Answer: The data shows exponential decay, with activity decreasing by a factor of 8 over 50 days. Since each half-life halves the activity, the number of half-lives is log₂(8) = 3. Therefore, the estimated half-life is approximately 50 days divided by 3, which is about 16.7 days.

Question 1: Explain how understanding radioactive decay and decay equations is important in medical imaging, such as PET scans, and in nuclear power generation.

Answer: In medical imaging, decay equations help determine the timing and dosage of radioactive tracers to produce clear images while minimising radiation exposure. In nuclear power, decay equations are essential for managing fuel lifecycles, waste disposal, and safety protocols.