Radioactive decay — common mistakes

Remember to always check your units! The decay constant (\lambda) and time (t) in exponential decay equations ($e^{-\lambda t}$) must always be in consistent units (e.g., s^{-1} and s, or year^{-1} and years). Mixing them up is a common error in exams.

It's spontaneous because external conditions like temperature or pressure don't affect when a nucleus decays. It's random because we cannot predict when a specific nucleus will decay, only the probability over time for a large sample.

Half-life is crucial for applications such as carbon dating (determining the age of ancient artefacts), medical diagnostics (using isotopes with short half-lives that quickly decay), and nuclear waste management (planning for safe storage of long-lived radioactive materials).

No, radioactive decay is an intrinsic property of the unstable nucleus. It is not influenced by external physical or chemical conditions, meaning its rate cannot be altered by heating, cooling, pressurising, or chemical reactions. The decay constant and half-life are fixed for each isotope.