High School

a team of archeologists recover a plank of wood believed to be from an ancient ship. the plank has a carbon-14 activity of 38.8 bq per gram of carbon. in comparison, a living organism has a c -14 activity of 47.5 bq per gram of carbon. part a if the half-life of carbon-14 is 5730 years, what is the age of the plank?

Answer :

To determine the fraction of C-14 remaining in the plank compared to a living organism: the age of the plank is approximately 1508 years old.

fraction remaining = (activity of sample) / (activity of living organism)

fraction remaining = 38.8 / 47.5

fraction remaining = 0.817

Next, we can use the half-life of C-14 to calculate the number of half-lives that have passed:

number of half-lives = (ln fraction remaining) / (ln 0.5)

number of half-lives = (ln 0.817) / (ln 0.5)

number of half-lives = 0.263

Finally, we can use the half-life and number of half-lives to calculate the age of the plank:

age = (number of half-lives) x (half-life)

age = 0.263 x 5730

age = 1508 years

Therefore, the age of the plank is approximately 1508 years old.

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