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Radio Carbon Dating
Early tests using Carbon 14 were on the linen. The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample. By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely.
Improved results by AMS(Accelerator Mass Spectrometry)in the 1990's on scrolls.