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Half-life

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The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to decay.[1][2] After one half-life, a sample of N radioactive nuclei falls to N/2; after two half-lives it falls to N/4, then N/8, and so on.[3] Half-lives are used to measure the ages of rocks and of the remains of living things.

Radioactive decay is random

Radioactive decay is purely statistical.[3][4] There is no way to predict whether a particular nucleus will decay during any given second.[4] A more exact way of describing half-life is that each nucleus has a 50 per cent chance of surviving for one half-life. This is like flipping a coin: a nucleus that has already survived hundreds of half-lives still has the same 50 per cent chance of surviving one more.[3][3]

The decay law

The number of nuclei that decay in a short time is proportional to the number of radioactive nuclei present.[1][5] This leads to an exponential decay law, N = N0e−λt, where λ is called the decay constant. The half-life is linked to the decay constant by t½ = ln 2/λ, or about 0.693/λ.[6][2] After ten half-lives, only about 1/1024 of the original nuclei remain.[6]

The total rate of decay of a sample is called its activity.[2] Ordinary objects such as light bulbs do not follow this kind of decay law.[2]

Range of half-lives

Half-lives vary enormously, from about 10−23 seconds to more than 1016 years.[6] Uranium-238 has a half-life of 4.5 billion years.[7][8] Potassium-40 has a half-life of 1.25 billion years.[9] Bananas contain radioactive potassium, but eating one adds less than 1 per cent to the radiation a person's body receives each day from radioactive potassium.[10]

Radioactive dating

If the half-life of a radioactive substance is known, its decay can be used as a clock to measure time.[9]

Carbon-14 dating

Carbon-14 is a radioactive isotope of carbon with a half-life of 5,730 years. It is produced at a steady rate in the upper atmosphere as nitrogen is struck by cosmic rays.[9][11] Living things take in carbon-14 along with ordinary carbon. When an organism dies, it stops taking in carbon, and the carbon-14 in its remains slowly decays.[6][9] By measuring how much carbon-14 is left in a gram of material, scientists can work out how long ago the organism died.[9] The method works for remains up to about 50,000–60,000 years old and has been checked against other evidence, such as tree rings. Willard Libby won the 1960 Nobel Prize in Chemistry for developing it.[6]

Carbon-14 has also been used to study the atmosphere. In 1955 Hans Suess used it to show that ancient carbon from fossil fuels, which has lost its radioactivity, had been added to the modern air.[12]

Dating rocks

Longer-lived isotopes are used to date rocks. Uranium-238 decays to lead-206, and potassium-40 decays to argon-40.[7][9] Measurements like these on the Earth, the Moon and meteorites give a maximum age of about 4.5 billion years.[9]

See also

References

  1. ↑ 1.0 1.1 Boeker, Egbert; van Grondelle, Rienk (2011). Environmental Physics: Sustainable Energy and Climate Change (3rd ed.). Chichester: John Wiley & Sons. section 6.1.1.1: Radioactive Decay. ISBN 978-0-470-66676-0. Retrieved 2026-10-23.
  2. ↑ 2.0 2.1 2.2 2.3 Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 1051. ISBN 9780730382898. {{cite book}}: |access-date= requires |url= (help)
  3. ↑ 3.0 3.1 3.2 3.3 Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 1254. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
  4. ↑ 4.0 4.1 Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 1050. ISBN 9780730382898. {{cite book}}: |access-date= requires |url= (help)
  5. ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 1049. ISBN 9780730382898. {{cite book}}: |access-date= requires |url= (help)
  6. ↑ 6.0 6.1 6.2 6.3 6.4 Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 1255. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
  7. ↑ 7.0 7.1 Urone, Paul Peter; Hinrichs, Roger (2017) [2012]. College Physics. Houston: OpenStax. p. 1257. ISBN 978-1-938168-00-0. Retrieved 2026-10-23.
  8. ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 1054. ISBN 9780730382898. {{cite book}}: |access-date= requires |url= (help)
  9. ↑ 9.0 9.1 9.2 9.3 9.4 9.5 9.6 Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 1060. ISBN 9780730382898. {{cite book}}: |access-date= requires |url= (help)
  10. ↑ Halliday, David; Resnick, Robert; Walker, Jearl (2021). Fundamentals of Physics. Adapted by Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius O. Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons and Dipesh Bhattarai (1st Australian & New Zealand ed.). Milton, Qld: John Wiley & Sons Australia. p. 1053. ISBN 9780730382898. {{cite book}}: |access-date= requires |url= (help)
  11. ↑ Weart, Spencer R. (2008). The Discovery of Global Warming. New Histories of Science, Technology, and Medicine (Revised and expanded ed.). Cambridge, MA: Harvard University Press. p. 24. ISBN 978-0-674-03189-0. {{cite book}}: |access-date= requires |url= (help)
  12. ↑ Weart, Spencer R. (2008). The Discovery of Global Warming. New Histories of Science, Technology, and Medicine (Revised and expanded ed.). Cambridge, MA: Harvard University Press. pp. 24–25. ISBN 978-0-674-03189-0. {{cite book}}: |access-date= requires |url= (help)
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