Question 1: Define radioactive decay and explain what is meant by a decay equation.

Answer: Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. A decay equation shows the relationship between the original isotope and the resulting products as it undergoes decay.

Question 2: Describe the role of the decay constant in the decay equation and its units.

Answer: The decay constant (λ) determines the probability of decay per unit time for a nucleus. Its units are reciprocal seconds (s⁻¹).

Question 3: Multiple Choice: Which of the following correctly represents a decay equation for a radioactive isotope? A) N → N + energy B) ^{A}_{Z}X → ^{A-1}_{Z}Y + beta particle C) N + N → N₂ D) X + Y → Z + energy

Answer: B) ^{A}_{Z}X → ^{A-1}_{Z}Y + beta particle

Question 4: Fill in the blank: The general decay equation for a radioactive isotope can be written as \( _{Z}^{A}X \) → \( _{Z}^{A-1}Y \) + ________.

Answer: beta particle

Question 5: Explain why decay equations are important in nuclear medicine and radiocarbon dating.

Answer: Decay equations are crucial in nuclear medicine for determining the correct dosage and timing of radioactive tracers, ensuring safety and effectiveness. In radiocarbon dating, decay equations allow scientists to estimate the age of archaeological samples by measuring the remaining carbon-14 in organic materials.

Question 6: Calculate the remaining quantity of a radioactive substance that initially had 100 grams after 3 half-lives. (Use the half-life formula and show your working.)

Answer: Remaining amount = 100 × (1/2)^{3} = 100 × 1/8 = 12.5 grams

Question 7: A sample of uranium-238 has a half-life of approximately 4.5 billion years. How much of a 50-gram sample remains after 13.5 billion years? Show your calculations.

Answer: Number of half-lives = 13.5 / 4.5 = 3 Remaining amount = 50 × (1/2)^3 = 50 × 1/8 = 6.25 grams

Question 8: Identify three safety precautions that must be taken when handling radioactive materials in a laboratory setting.

Answer: Use of protective clothing and gloves, working behind shielding barriers, and limiting exposure time.

Question 9: Describe an experiment to measure the activity of a radioactive sample and mention the variables that need to be controlled.

Answer: An experiment involves placing a Geiger-Müller counter near the radioactive sample and recording the count rate over a fixed period. Variables to control include distance between the detector and the sample, background radiation levels, and the duration of measurement to ensure accurate and consistent readings.

Question 10: In a nuclear power plant, decay equations are used to predict the remaining fuel activity over time. Explain how this impacts safety procedures and waste management.

Answer: Decay equations allow operators to estimate the activity level of spent fuel, ensuring appropriate handling, storage, and disposal. Understanding decay rates helps in planning safety measures, such as shielding and containment, to protect workers and the environment from harmful radiation over time.