While exploring a coal mine, scientists found plant fossils which had been preserved by an earthquake in the ceiling of the mine. Samples taken from one of the fossils had carbon‑14 activities of 20.0 counts/min.20.0 counts/min. A reference sample of the same size from a plant alive today has a carbon-14 activity of 160.0 counts/min.160.0 counts/min. If carbon‑14 has a half-life of 5730 years, what is the age of the plant fossil in years?
While exploring a coal mine, scientists found plant fossils which had been preserved by an earthquake in the ceiling of the mine. Samples taken from one of the fossils had carbon‑14 activities of 20.0 counts/min.20.0 counts/min. A reference sample of the same size from a plant alive today has a carbon-14 activity of 160.0 counts/min.160.0 counts/min. If carbon‑14 has a half-life of 5730 years, what is the age of the plant fossil in years?
Given:
Amount of carbon-14 in fossil = 20 counts/min = Nf
Amount of carbon-14 in living tissue = 160 Counts/ min = N0
By carbon dating formula,
age of fossil T = [In(Nf /N0) / (-0.693)] / t1/2
where,
Nf / N0 = ratio of carbon-14 in fossil to carbon-14
in living tissue (20/160) = 0.125
t1/2 half life of carbon-14 = 5730 years
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