An archaeologist finds the ¹⁴C in a sample of 3.10 g of material to be decaying at 107 counts per second. A modern 1.00-g sample of the same material decays at 151 counts per second. The half-life of ¹⁴C is 5730 y. How old is the sample?

Question

Quizplus · Accepted Answer

The decay rate is proportional to the amount of radioactive material present. The ratio of the decay rates is equal to the ratio of the amounts of material present.$$\frac{107}{151} = \frac{3.10}{1.00}$$Solving for t, we get:$$t = 5730 y 	imes \ln(2) 	imes \frac{151}{107} 	imes \frac{3.10}{1.00} = 12,200 y$$

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