Problem 2- Calculate the age of a fossil

Approximately how old is a fossil with 12 g of ¹⁴C if it initially possessed 32 g of ¹⁴C?

Tutorial

Using our model with N₀ = 32,

N(t) = 32 e ^{− 0.0001216 t}.

We would like to know how long it takes for the initial 32 g of ¹⁴C to decay to 12 g. Let’s call the time it takes for this decay to occur, τ. Then we write,

N(τ) = 12 = 32 e ^{− 0.0001216τ} .

Solving for τ,

Thus, it takes approximately 8066 years for 32 g of ¹⁴C to decay to 12 g.

Again, this makes sense in light of the half-life. That is, 16 g of ¹⁴C would remain after 5700 years and 8 g would remain after 11,400 years.