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?

Question

Chemistry

Aleena Sampson

27 June, 22:58

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?

+5

Answers (1)

Know the Answer?

Kiera Huynh · Answer 1

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,

[¹⁴C]: concentration of ¹⁴C [¹⁴C]₀: initial concentration of ¹⁴C k: rate constant t: time elapsed

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