Radioactivity and Nuclear Energy
Radioactivity and Nuclear Energy tests the random nature of radioactive decay, the properties and hazards of radiation, decay equations, half-life, and the energy released in nuclear fission and fusion. HKDSE questions often ask you to use half-life graphically or numerically, balance a nuclear equation, and explain why mass defect appears as energy.
Core rules and concepts
- Radioactive decay is random and spontaneous; we cannot predict which nucleus decays next, only the average behaviour of a large sample.
- Alpha decay emits a helium nucleus (⁴₂He), beta-minus decay converts a neutron into a proton and an electron, and gamma emission is electromagnetic radiation from an excited nucleus.
- In nuclear equations, mass number and atomic number are conserved.
- Half-life is the time for half the undecayed nuclei, or half the activity, to remain. After n half-lives, remaining fraction = (1/2)ⁿ.
- Fission splits a heavy nucleus; fusion joins light nuclei. Both release energy because the total mass decreases; E = mc².
- Radiation safety uses distance, shielding, and time; background radiation must be subtracted in measurements.
Worked example
A sample has an activity of 800 Bq. After 12 days the activity is 50 Bq. Find the half-life.
The activity falls from 800 to 400 to 200 to 100 to 50 Bq. That is four halvings, so 4 half-lives = 12 days. Half-life = 12/4 = 3.0 days. Equivalently, 50/800 = 1/16 = (1/2)⁴, confirming four half-lives. The activity is proportional to the number of undecayed nuclei for a given isotope, so the same factor applies to the count rate after background subtraction.
Traps that cost marks
- Forgetting to subtract background count rate before finding half-life.
- Treating half-life as the time for all activity to disappear; activity never reaches exactly zero in the model.
- Balancing a nuclear equation by atomic number only, or by mass number only.
- Confusing fission with fusion, or alpha with beta charge.
- Using the initial activity instead of the remaining activity in (1/2)ⁿ calculations.