Question 1: Radioactive decay is a spontaneous process where unstable atomic nuclei lose energy by emitting radiation. The decay process can be described mathematically using decay equations that relate the number of remaining radioactive nuclei to time.

Answer: Radioactive decay involves unstable nuclei emitting radiation and decreasing in number over time, described mathematically by decay equations.

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

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

Question 2: Explain why radioactive decay is considered a random process but still follows a predictable decay law.

Answer: Decay is random at the level of individual nuclei, but statistically, the number of nuclei remaining decreases exponentially over time according to decay laws.

Question 1: A sample contains 10,000 radioactive nuclei. The decay constant (λ) for this isotope is 0.001 per day. How many nuclei remain after 100 days?

Answer: Approximately 368 nuclei remain after 100 days.

Question 2: If a sample has 500 radioactive nuclei remaining after 50 days, what is the decay constant λ?

Answer: λ ≈ 0.01386 per day

Question 1: Describe a simple experiment to measure the half-life of a radioactive isotope. Include safety precautions that must be taken.

Answer: The experiment involves measuring the activity of a radioactive sample at regular intervals using a Geiger counter, recording the data, and calculating the half-life from the decay curve. Safety precautions include wearing protective clothing, using shielding to limit radiation exposure, and handling radioactive materials with tongs.

Question 2: Identify the key variables that affect the rate of radioactive decay in a sample.

Answer: The key variable is the decay constant (λ), which depends on the type of isotope, but the decay rate is unaffected by external factors like temperature or pressure.

Question 1: A researcher observes that after 20 days, 25% of a radioactive sample remains. What is the decay constant (λ) for this isotope? Show your calculation process using the decay equation.

Answer: λ ≈ 0.03466 per day

Question 1: Explain how decay equations are used in radiocarbon dating to determine the age of archaeological artifacts.

Answer: Decay equations relate the remaining amount of carbon-14 in a sample to its original amount and the known half-life, allowing scientists to estimate the time elapsed since the organism died.

Question 2: Discuss the importance of understanding decay constants in nuclear medicine, such as in radioisotope treatments.

Answer: Knowing decay constants helps determine the appropriate dosage and timing of radiopharmaceuticals to ensure effective treatment while minimizing radiation exposure.