Carbon dating calculation
However, radioisotope dating may not work so well in the future.Anything that dies after the 1940s, when Nuclear bombs, nuclear reactors and open-air nuclear tests started changing things, will be harder to date precisely.A secondary standard, Oxalic Acid SRM 4990C, also referred to as HOx II, 1,000 lb of which was prepared by NIST in 1977 from French beet harvests, is now in wide use.where the δ13C value remaining in the equation is the value for the sample itself.Other useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years).The use of various radioisotopes allows the dating of biological and geological samples with a high degree of accuracy.
The fossil fuel effect was eliminated from the standard value by measuring wood from 1890, and using the radioactive decay equations to determine what the activity would have been at the year of growth.
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. So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.
Different labs use this data in different ways; some simply average the values, while others consider the measurements made on the standard target as a series, and interpolate the readings that would have been measured during the sample run, if the standard had been measured at that time instead.
The fraction modern is then converted to an age in "radiocarbon years", meaning that the calculation uses Libby's half-life of 5,568 years, not the more accurate modern value of 5,730 years, and that no calibration has been done: There are several possible sources of error in both the beta counting and AMS methods, although laboratories vary in how they report errors.