(a)Number of half-lives elapsed = time ÷ half-life. Activity after n half-lives = A0 × (1/2)ⁿ.

(a)Corrected count rate = gross count rate − background count rate.

(b)Background radiation from cosmic rays and naturally occurring radioactive materials is always present and would otherwise be wrongly counted as coming from the source, giving an inflated reading.

(a)An alpha particle has mass number 4 and atomic number 2. Mass and atomic numbers must balance on both sides of the equation.

(a)Alpha radiation is the least penetrating — stopped by a sheet of paper or a few cm of air. Beta radiation is stopped by a few mm of aluminium. Gamma radiation is the most penetrating and is only significantly reduced by several cm of lead or thick concrete.

(a)After each half-life, activity halves: A0 × (1/2)³.

(a)Find n such that (1/2)ⁿ = 62.5/500 = 1/8.

(a)Corrected rate = gross rate − background rate.

(a)A beta particle has negligible mass number and charge −1 (equivalent to atomic number −1 on the other side), so mass number stays the same and atomic number increases by 1.

(a)Medical: radiotherapy to treat cancer (or tracers for medical imaging). Industrial: checking for flaws in metal welds, or measuring material thickness.

(a)Alpha particles are large and heavily charged (+2), so they interact strongly with and ionise many atoms over a short distance, losing energy quickly (hence low penetration). Gamma rays have no charge and interact far less often with matter, so they ionise weakly but travel much further before losing their energy.