The 14C content of a wooden harpoon handle found in the remains of an Inuit encampment in western Alaska is 61.9% of the 14C content of the same type of wood from a recently cut tree. How old is the harpoon?

3055 years

Explanation:

¹⁴C decays following first-order kinetics. We can find the concentration of ¹⁴C at a certain time using the following expression.

ln [¹⁴C] / [¹⁴C]₀ = - k × t

where,

Given the half-life of ¹⁴C (t1/2 = 5730 years), we can calculate k using the following expression.

k = ln2 / t1/2 = 1.210 × 10⁻⁴ y⁻¹

Then,

ln [¹⁴C] / [¹⁴C]₀ = - k × t

ln 0.691 [¹⁴C]₀ / [¹⁴C]₀ = - 1.210 × 10⁻⁴ y⁻¹ × t

t = 3055 y

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