To determine the age of the ancient charcoal, we can use the concept of exponential decay and the measurement of remaining C-14.
Since the ancient charcoal only contains 15% of the radioactive carbon C-14 compared to a modern charcoal, it means that 85% has decayed. The decay of radioactive isotopes follows an exponential decay formula:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the number of radioactive atoms remaining at time t
N₀ is the initial number of radioactive atoms
t is the time that has passed
h is the half-life of the radioactive isotope
We can rearrange this equation to solve for t:
t = (h * log(N(t) / N₀)) / log(1/2)
Substituting the given values:
t = (5730 * log(0.15 / 1)) / log(1/2)
Simplifying the equation:
t = (5730 * log(0.15)) / log(2)
Calculating this equation will give us the time passed since the burning of the ancient charcoal:
t ≈ 17894 years
Therefore, the ancient charcoal was burned approximately 17,894 years ago.
