A chemist determines that a sample of petrified wood has a carbon-14 decay rate of 6.00 counts per minute per gram. The decay rate of carbon-14 in fresh wood today is 13.6 counts per minute per gram, and the half life of carbon-14 is 5730 years. What is the age of the piece of wood in years?

6,765 years

Explanation:

Calculation to determine the age of the piece of wood in years

First step is to calculate decimal fraction of Carbon-14 that was remaining

Decimal fraction of Carbon-14= 6.00 counts per minute per gram/ 13.6 counts per minute per gram

Decimal fraction of Carbon-14 remaining= 0.4411765

Second step is to calculate the numbers of half-lives that have elapsed

(1/2)^n= 0.4411765

Hence,

n log 0.5 = log 0.4411765

n = 1.18057

Last step is to calculate the length of time that has elapsed

Using this formula

Elapsed length of time=Half life of carbon-14 *n

Let plug in the formula

Elapsed length of time=5,730 years * 1.18057

Elapsed length of time= 6,765 years

Therefore the age of the piece of wood in years will be 6,765 years

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