The amount of carbon-14 (_6^14text (C)) in a wooden artifact is measured to be 12.5 percent the amount in a fresh sample of wood from the same region. The half-life of carbon-14 is 5715 years. Assuming the same amount of carbon-14 was initially present in the artifact, determine the age of the artifact.

Question

Frida Lam

Mathematics

1 June, 13:23

The amount of carbon-14 (_6^14text (C)) in a wooden artifact is measured to be 12.5 percent the amount in a fresh sample of wood from the same region. The half-life of carbon-14 is 5715 years. Assuming the same amount of carbon-14 was initially present in the artifact, determine the age of the artifact.

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Ishaan Tanner · Answer 1

17145 years

Step-by-step explanation:

Let n be the quantity of carbon-14 in the wooden artifact and n₀ be the quantity in the fresh sample of wood. The percentage of carbon - 14 in the wooden artifact = 12.5%. This implies that n/n₀ = 12.5/100 = 0.125

For the carbon-14 to decay to 12.5% of its original value, it takes

(1/2) ⁿ have lives which equals 0.125

(1/2) ⁿ = 0.125 = 125/1000 = 1/8 = 1/2³

So, n = 3. It becomes 12.5% after three half lives.

So the original age of the artifact = 3 * half - life = 3 * 5715 = 17145 years