How is radioactive dating performed?
For example, the carbon-14 decay rate of a sample obtained from a young tree is 0.260 disintegrations per second per gram of the sample. Another wood sample prepared from an object recovered at an excavation site gives a decay rate of 0.186 disintegrations per second per gram of the sample.
If we know that carbon-14 has a half-life of 5730 years, How can we determine the age of the object?
T1/2 = 0.693/λ = 5730
λ = 0.693 / 5730 = 1.21 x 10-4
Rt = λN
Rt (Young tree) = (1.21 x 10-4)(NY) = 0.260 ; NY = 2150 atoms / gram
Rt (Old tree) = (1.21 x 10-4)(NO) = 0.186; NO = 1540 atoms / gram
T(O-Y) = 5730(log0.5(1540/2150)) = 2760 years