Question 1: Radioactive decay is a spontaneous process where an unstable nucleus transforms into a more stable nucleus by emitting radiation. The rate of decay is described by decay equations involving the decay constant or half-life.

Answer: Radioactive decay involves the transformation of an unstable nucleus into a stable one, emitting radiation; decay equations describe this process mathematically.

Question 1: Define the term 'half-life' in the context of radioactive decay.

Answer: Half-life is the time taken for half of the radioactive nuclei in a sample to decay.

Question 2: Explain why some isotopes are more suitable for medical imaging than others based on their decay properties.

Answer: Isotopes suitable for medical imaging have appropriate half-lives to minimise radiation exposure while providing clear images, and emit radiation types that can be detected safely.

Question 1: A sample of a radioactive isotope has a half-life of 10 hours. How much of a 100 g sample remains after 30 hours? (Use the decay formula N = N₀ × (1/2)^{t/T_{1/2}}).

Answer: 12.5 g

Question 2: Calculate the decay constant (λ) for a isotope with a half-life of 5 days. (Use λ = ln(2) / T_{1/2}).

Answer: 0.1386 day^{-1}

Question 1: Describe the key safety precautions that must be taken when handling radioactive materials during an experiment.

Answer: Use shielding to protect from radiation, wear protective clothing and gloves, minimise exposure time, and follow proper disposal procedures.

Question 2: Identify three variables that could affect the rate of decay observed in a controlled experiment.

Answer: Sample purity, environmental temperature, and measurement accuracy.

Question 1: A certain isotope shows a decay pattern where after 15 hours, 25% of the original sample remains. What is its half-life?

Answer: Approximately 10 hours

Question 1: Derive the relationship between the decay constant (λ) and the half-life (T_{1/2}).

Answer: Starting from N = N₀ e^{-λt} and knowing that at t = T_{1/2}, N = N₀ / 2, we set: N₀ / 2 = N₀ e^{-λ T_{1/2}}. Dividing both sides by N₀ gives 1/2 = e^{-λ T_{1/2}}. Taking natural logarithms: ln(1/2) = -λ T_{1/2}, hence λ = ln(2) / T_{1/2}.

Question 1: Describe how decay equations are used in radiocarbon dating to estimate the age of archaeological finds.

Answer: Radioactive carbon-14 decays at a known rate; by measuring remaining C-14 in artefacts, scientists can calculate how long ago they were formed using decay equations.