Radioactive nuclei are unstable and break down over time, giving out radiation. We cannot predict when any single nucleus will decay, but for a large sample a steady pattern appears. The half-life is the time taken for half of the nuclei present to decay.
After one half-life, half the original nuclei remain; after two half-lives, a quarter remain; after three, an eighth, and so on. The count keeps halving over equal periods. Importantly, the half-life does not depend on how much you begin with, nor on temperature or pressure; it is a fixed property of that isotope.
Half-lives range enormously, from fractions of a second to thousands of years. This is what lets carbon dating estimate the age of old wood, and it guides how radioactive waste and medical sources are handled.
In SPM you should use half-life to find the fraction of a sample remaining after a given time.
Common misconceptions
- Half-life is the time for the sample to fully decay -> It is the time for half to decay; a portion always remains after each half-life.
- Heating or compressing a sample changes its half-life -> Half-life is fixed for an isotope and is not affected by temperature or pressure.
- After two half-lives nothing is left -> After two half-lives one quarter remains, not zero.
The physics behind it
Radioactive nuclei are unstable and decay at random, giving out radiation. You cannot predict when one nucleus will decay, but for a large sample the numbers follow a steady pattern.
The half-life is the time taken for half of the radioactive nuclei present to decay.
After each half-life the number remaining halves: from the original amount to one half, then one quarter, then one eighth, and so on. The fraction remaining after a whole number of half-lives is one half raised to that number.
If a sample starts with 800 undecayed nuclei and the isotope has a half-life of 6 hours, then after 18 hours, which is 3 half-lives, the number remaining = 800 × (1/2)³ = 800 × 1/8 = 100 nuclei.
The half-life does not depend on how much you start with, nor on temperature or pressure; it is a fixed property of that isotope. Activity, the number of decays per second measured in becquerel (Bq), falls in exactly the same way.
See it in daily life
Half-life is what makes radioactive dating possible. Living things take in carbon that includes a small, steady share of radioactive carbon-14.
When the organism dies it stops taking in fresh carbon, and the carbon-14 already inside slowly decays with a known half-life. By comparing how much is left, scientists can estimate the age of old wood, cloth or bone.
Half-life also decides how radioactive sources are chosen and handled. A medical tracer used to scan the body is picked to have a short half-life, so it does its job and then quickly fades, limiting the dose to the patient.
By contrast, some waste from nuclear power has a very long half-life and must be stored safely for a long time.
The smoke detector in many buildings uses a tiny source with a long half-life, so it keeps working steadily for years without needing replacement.
How this comes up in SPM
In Paper 2 you are commonly asked to define half-life and to determine the fraction or amount of a sample remaining after a given time. Recall the halving pattern yourself, as there is no formula sheet.
A frequent task is to read a half-life from a decay graph of count rate or number of nuclei against time, or to calculate the number of half-lives that have passed and work back to the starting amount. You may also be asked to explain why half-life is constant for a given isotope.
This concept sits within nuclear physics, alongside the types of radiation and radioactive decay, so be ready to link half-life to how a source is chosen for a use and to the idea that decay is a random, fixed-chance process for each nucleus.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)