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When a radioactive element decays, the number of radioactive nuclei decreases with time. The time it takes for the number of radioactive nuclei to decrease to half its original amount is called its half-life. The fraction of radioactive nuclei remaining after a number of half-lives is shown in the Table below:

Number of half-lives Fraction remaining
1 1/2
2 1/4
3 1/8
... ...
n 1/(2n)

The half-lives of different radioactive materials can vary greatly. For example, Uranium-238 has a half-life of 4.5 billion years, whereas Radon-222, a radioactive gas we encounter in our daily life, has a half-life of 3.8 days. Hence, their radioactive nuclei will reduce to 25 percent in 9 billion years and 7.6 days respectively.

The knowledge of half-life has many applications. Carbon-14, commonly known as radiocarbon, is an isotope of carbon and has a half-life of about 5730 years. During photosynthesis, radiocarbon is 'taken' up by plants. The radiocarbon in plants then gets into other organisms on Earth (including humans) after they die or when they are consumed. From the radiocarbon content that remains, archeologist can estimate the age of their samples. Another application is in forensic science. For example, Polonium-210, with a half-life of 138 days, was found to be related with the murder of Alexander Litvinenko, a former officer of the Russian Federal Security service. By measuring the proportion of Polonium-210, detectives could establish the production date of the substance during their investigation.


  1. Why Is Radiocarbon Dating Important To Archaeology? (
  2. Poisoning of Alexander Litvinenko (