Physics · Modern physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A nucleus holds Z protons and N neutrons bound by the strong force. Its mass is less than the mass of its separate nucleons; this mass defect, times c2, is the binding energy. Binding energy per nucleon is greatest near iron, so energy is released when heavy nuclei split (fission) and when light nuclei join (fusion).
Unstable nuclei decay at random by alpha, beta or gamma emission. The number left falls exponentially, with a fixed half-life for each nuclide.
In the Standard Model, matter is made of quarks and leptons. Four forces act: strong, electromagnetic, weak and gravitational. Each of the first three is carried by exchange particles, and beta decay is a weak-interaction process.
Treating decay as a straight-line fall. Each half-life halves what is left, so after three half-lives one eighth remains, not zero.
Answer: 400 Bq; λ = 3.85 × 10−5 s−1.
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