Question

The remnants of an ancient fire in a cave in Peru showed a decay rate of 8.0 counts per minute per gram of carbon. Assuming that the decay rate in freshly cut wood is 12.7 counts per minute per gram of carbon, calculate the age of the remnants. The half life of 614C is 5730 years.

Answer 1

The age of the remnants is calculated as 3807 years.

What is the half life?

The half life is the time taken for only half of the number of the radioactive atoms to remain.

Half life of carbon - 14 = 5730 years.

Initial count rate = 8.0 counts per minute per gram

Count rate at time t =  12.7 counts per minute per gram of carbon

Since;

0.693/t1/2 =2.303/t log (N/No)

0.693/5730 = 2.303/t log (12.7/8)

1.21 * 10^-4 = 2.303/t * 0.2

t = 2.303 * 0.2/1.21 * 10^-4

t = 0.4606/1.21 * 10^-4

t = 3807 years

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