Talha's Physics Academy
Half-Life of Radioactive Elements and Radioactive Dating
Half-Life of Radioactive Elements
The radioactive decay process is completely random, and the rate of radioactive decay is directly proportional to the number of unstable nuclei present. During decay, a constant fraction of unstable radioactive nuclei disintegrates over a specific time interval. Because the lifespan of individual unstable nuclei is indefinite, it is challenging to measure directly, making half-life a statistical measure of stability.
Example: Iodine-131
Iodine-131 ($_{53}^{131}\text{I}$) is a radioactive isotope of iodine with an eight-day half-life. This means that half of an original iodine-131 sample converts into other stable elements within $8$ days. In the next $8$ days, half of the remaining sample decays, leaving only one-fourth ($\frac{1}{4}$) of the original amount, and so on.
The fraction of the sample remaining after a certain number of half-lives ($n$) is given by the relation:
Radioactive Dating
Principle of Carbon-14 Dating
The radioisotope carbon-14 ($_6^{14}\text{C}$) is produced in small amounts in the atmosphere by cosmic ray interactions and is widely used to measure the age of organic materials. Living plants and animals absorb carbon dioxide and maintain a balanced, slightly radioactive state. While an organism is alive, its carbon-14 content remains relatively constant because fresh carbon-14 enters whenever the organism consumes nutrients or breathes.
When an organism dies, it stops absorbing new carbon, and the carbon-14 trapped inside starts decaying into nitrogen-14 ($\gamma^-$ decay). Given that the half-life of carbon-14 is $5730$ years, archaeologists can estimate the age of ancient organic remains by computing the remaining activity and ratio of carbon-14 in live versus dead specimens.
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