Suppose you are working in a carbon dating laboratory and are examining a piece of wood found in an archaeological site in Arizona. You find that a carbon sample of mass 1.00 g from the piece of wood undergoes 7.90 * 10³ carbon-14 disintegrations in a period of 20.0 h. In the same period, 1.00 g of carbon from a modern source you are using as a standard undergoes 1.84 * 10⁴ disintegrations. Calculate the age of the sample, given that the half-life of ¹⁴C is 5.73 ka.

ANTICIPATE Because the half-life of ¹⁴C is 5.73 ka and the activity of the sample has fallen to less than half that of the modern sample, you should expect that it is more than 5730 years old.

PLAN First, rearrange Eq. 3 to give an expression for the time and then express k in terms of t_1/2 by using Eq. 4. The carbon-14 activity of the modern sample can be used to represent the original activity in the ancient sample. Therefore, N/N₀ is equal to the ratio of the number of disintegrations in the ancient and modern samples.