Example 1
A sample initially contains 800 undecayed nuclei and has a 5−hour half-life. How many are expected after 10 hours?
510=2 half-lives. Halve twice: 800→400→200 undecayed nuclei.
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Year 9
Radioactive decay and half-life
Describe nuclear instability, radiation and the statistical pattern of half-life.
Method and worked examples
Unstable nuclei can change spontaneously, emitting radiation. Alpha decay emits two protons and two neutrons. In beta-minus decay a neutron changes into a proton, with an electron and antineutrino emitted. Gamma emission releases nuclear energy without changing proton or neutron counts. Several decays may be needed before a stable nucleus is reached.
Half-life is the time in which half the unstable nuclei in a large sample are expected to decay. Individual decay times are unpredictable, but large populations follow a statistical pattern. After two half-lives, one-quarter of the original undecayed nuclei remain. The atoms have changed rather than vanished. Count elapsed half-lives first, then halve the remaining undecayed population once per interval.
Example 1
Example 2
An alpha-emitting nucleus has mass number 238 and atomic number 92. What are the daughter numbers?
Alpha emission removes two protons and two neutrons. Mass number becomes 234 and atomic number becomes 90; the daughter is a different element.
Watch out: Individual nuclei either have decayed or have not. Half-life describes the expected fraction remaining in a population.