# Carbon-14 has a half life of 5714 years. How many years old is an artifact that contains 50% of its original carbon-14?

Jan 21, 2016

$5714$ years or so, depending on how accurate the 50% and $5714$ figures are.

#### Explanation:

Half life is the time required for half of the original $\text{^14"C}$ in the sample to decay into $\text{^14"N}$ through beta decay.

The way that $\text{^14"C}$ dating works is as follows: $\text{^14"C}$ is naturally present in a certain tiny ratio to $\text{^12"C}$ in the atmosphere, due to the effect of cosmic rays on nitrogen in the atmosphere. So during the lifetime of a plant such as a tree, the ${\text{CO}}_{2}$ that it incorporates in its tissue (wood) has approximately that ratio of ""^14C to ""^12C. When the plant dies, it stops absorbing $\text{C}$ including $\text{^14"C}$ from the atmosphere. Thereafter, the proportion of $\text{^14"C}$ in the wood reduces by beta decay, halving every $5700$ years or so.

Actually the proportion of $\text{^14"C}$ in the atmosphere is not constant, so $\text{^14"C}$ dating needs to be adjusted (calibrated) slightly in order to give accurate ages.

Internet sources seem to give the half life of $\text{^14"C}$ as $5730$ years rather than $5714$. This estimate may be subject to adjustment based on better estimates of the variation of $\text{^14"C}$/$\text{^12"C}$ ratio.