Question

What is the age of mummified primate skin that contains 8.25% of the original quantity of 14C?

Answer 1

Answer:

20619.4793 years

Explanation:

The half life of carbon-14 = 5730 years

The formula for the half life for a first order kinetic reaction is:

$t_{1/2}=\frac {ln\ 2}{k}$

Where,  

$t_{1/2}$ is the half life

k is the rate constant.

Thus rate constant is:

5730 years=ln(2)/k

k = 1.21×10⁻⁴ years ⁻¹

Using integrated rate law as:

$ln\ \frac {A_t}{A_0}=-k\times t$

Where,

$A_t$ is the concentration at time t

$A_0$ is the initial concentration

Given that the final concentration contains 8.25 % of the original quantity which means that:

$\frac {A_t}{A_0}=0.0825$

So,

ln(.0825)= -1.21×10⁻⁴×t

t = 20619.4793 years