Question

The normal activity of a living matter containing carbon is found to be 15 decays per minute per gram of carbon. An archaeological specimen gives 6 decays per minute per gram of carbon. If the half -life of carbon is 5730 years, estimate the approximate age of the specimen.

Answer 1

Using the half-life of carbon-14, which is 5730 years, we can calculate the approximate age of the specimen.

Step-by-step explanation:

To estimate the age of the archaeological specimen, we can use the concept of radioactive decay. The decay rate of carbon-14 is given as 15 decays per minute per gram of carbon in living matter, while the archaeological specimen has a decay rate of 6 decays per minute per gram of carbon. Using the half-life of carbon-14, which is 5730 years, we can calculate the approximate age of the specimen.

First, we need to find the fraction of carbon-14 remaining in the archaeological specimen compared to the living matter. We can do this by dividing the decay rate of the specimen (6 dpm/g) by the decay rate of living matter (15 dpm/g). The result is 0.4.

Next, we use the formula for exponential decay to find the number of half-lives that have passed since the specimen was alive. We take the natural logarithm of the fraction remaining (ln(0.4)) and divide it by the natural logarithm of 0.5 (ln(0.5)), which is the decay constant for exponential decay. The result is approximately 0.693.

Finally, we multiply the number of half-lives by the half-life of carbon-14 (5730 years) to estimate the age of the specimen. The age of the archaeological specimen is approximately 3954 years.