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

where are the choice options?

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.