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 different radioactive isotopes have different half-lives.

Answer: Different isotopes have different nuclear structures, which affect the stability and decay rates, resulting in varying half-lives.

Question 3: What is meant by the 'decay constant' in radioactive decay?

Answer: The decay constant is a probability rate that a single nucleus will decay per unit time, related to the half-life by a specific formula.

Question 4: Describe the mechanism by which a radioactive isotope undergoes decay.

Answer: Radioactive decay occurs when an unstable nucleus spontaneously transforms into a more stable nucleus by emitting radiation such as alpha, beta, or gamma rays, thereby reducing the number of undecayed nuclei over time.

Question 1: A sample of a radioactive isotope has a half-life of 8 hours. How much of a 100 g sample remains after 24 hours?

Answer: 12.5 g

Question 2: If 75% of a radioactive sample decays in 12 hours, what is the half-life of that isotope?

Answer: Approximately 16 hours

Question 3: Calculate the decay constant (λ) for a radioactive isotope with a half-life of 10 hours.

Answer: 0.0693 per hour

Question 1: Describe a simple experimental method to measure the half-life of a radioactive isotope in a laboratory setting.

Answer: Measure the activity of the sample at regular time intervals using a Geiger counter, record the counts, and determine the time it takes for the activity to halve, which indicates the half-life.

Question 2: A sample's activity drops from 200 counts per minute to 100 counts per minute in 6 hours. What is the half-life of the isotope?

Answer: 6 hours

Question 3: Interpret the following scenario: A rock containing uranium-238 has a half-life of about 4.5 billion years. Explain how this information is used in radiometric dating.

Answer: By measuring the ratio of uranium-238 to its decay products in the rock, scientists can estimate how many half-lives have passed, thus determining the age of the rock based on its original uranium content and the decay rate.

Question 1: Explain how half-life is important in medical applications such as radiotherapy.

Answer: Understanding the half-life helps in selecting appropriate radioactive isotopes to deliver effective radiation doses while minimising exposure time and ensuring patient safety.

Question 2: Discuss why a shorter half-life isotope might be preferred for medical imaging procedures.

Answer: Shorter half-life isotopes decay quickly, reducing radiation exposure to the patient after the imaging procedure while still providing sufficient signal for imaging.

Question 3: Identify two industries that utilise half-life data and explain their applications.

Answer: The nuclear power industry uses half-life data to manage waste disposal and reactor fuel; archaeological dating relies on half-life measurements of isotopes like carbon-14 to estimate the age of artefacts and fossils.