Question

A wooden artifact from an ancient tomb contains 60% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your decay rate, r, to 6 decimal places. Then round your answer to the nearest whole number.)

Answer 1

Answer:

The age of the sample is 4224 years.

Explanation:

Let the age of the sample be t years old.

Initial mass percentage of carbon-14 in an artifact = 100%

Initial mass of carbon-14 in an artifact = $[A_o]$

Final mass percentage of carbon-14 in an artifact t years = 60%

Final mass of carbon-14 in an artifact = $[A]=0.06[A_o]$

Half life of the carbon-14 = $t_{1/2}=5730 years$

$k=\frac{0.693}{t_{1/2}}$

$[A]=[A_o]\times e^{-kt}$

$[A]=[A_o]\times e^{-\frac{0.693}{t_{1/2}}\times t}$

$0.60[A_o]=[A_o]\times e^{-\frac{0.693}{5730 year}\times t}$

Solving for t:

t = 4223.71 years ≈ 4224 years

The age of the sample is 4224 years.