Intermediate Topic 107 of 1102 Atomic Structure & Periodicity
Half-life
The time required for half of a radioactive sample to decay.
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In-depth explanation of Half-life
The half-life is the time required for half of the nuclei in a radioactive sample to decay, and it is constant for a given isotope regardless of the sample size. Half-lives range from fractions of a microsecond to billions of years. The number of nuclei remaining follows N = N0 x (1/2) raised to the power t / t1/2. Radioactive decay is first order, and the decay constant is lambda = 0.693 / t1/2. Half-life is the main quantity used to describe and date radioactive isotopes.
Going deeper: Half-life
Key ideas: Half-life t1/2 is the time for half the nuclei to decay and is constant: N = N0 x (1/2)^(t / t1/2) = N0 e^(-lambda t), with lambda = 0.693 / t1/2. After n half-lives the fraction is (1/2)^n. Example: 14C has 5730 years, so after 17190 years 1/8 remains. Values range from microseconds to billions of years (238U, 4.5 x 10^9 years).
Common mistakes and connections: Students believe that after two half-lives everything is gone, or that half-life depends on the starting amount. Neither is true. It is a first-order process, so it matches first-order chemical kinetics (t1/2 = 0.693 / k). It underlies radiocarbon dating and decides the safe storage time for waste.
Visualization of Half-life
Every half-life the remaining radioactive amount halves, so 100 percent falls to 50, 25, 12.5 and so on regardless of the starting amount. The interactive lesson shows this as a live animation or chart.
Worked example and use case
After three half-lives, 12.5 percent of the original radioactive nuclei remain, since (1/2) cubed is 0.125.
Frequently asked questions about Half-life
What is Half-life?
The time required for half of a radioactive sample to decay.
Is Half-life a beginner, intermediate or advanced topic?
Half-life is a intermediate topic in Atomic Structure & Periodicity. It builds on the vocabulary of beginner topics in this area.
What should I learn before Half-life?
Study these earlier topics in Atomic Structure & Periodicity first: Alpha Decay, Beta Decay, Gamma Radiation.
What comes after Half-life?
The next topics in Atomic Structure & Periodicity are Nuclear Fission and Nuclear Fusion.
Can I practise Half-life with quizzes?
Yes. The interactive lesson includes a self-check question on Half-life, and the Atomic Structure & Periodicity quiz draws on every topic in this area.
Where Half-life fits in Atomic Structure & Periodicity
Half-life is topic 107 of 115 in Atomic Structure & Periodicity.