Half life is the time required for half of the original #""^14"C"# in the sample to decay into #""^14"N"# through beta decay.
The way that #""^14"C"# dating works is as follows: #""^14"C"# is naturally present in a certain tiny ratio to #""^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 #"CO"_2# that it incorporates in its tissue (wood) has approximately that ratio of #""^14C# to #""^12C#. When the plant dies, it stops absorbing #"C"# including #""^14"C"# from the atmosphere. Thereafter, the proportion of #""^14"C"# in the wood reduces by beta decay, halving every #5700# years or so.
Actually the proportion of #""^14"C"# in the atmosphere is not constant, so #""^14"C"# dating needs to be adjusted (calibrated) slightly in order to give accurate ages.
Internet sources seem to give the half life of #""^14"C"# as #5730# years rather than #5714#. This estimate may be subject to adjustment based on better estimates of the variation of #""^14"C"#/#""^12"C"# ratio.
