What is the age in years of a bone in which the ratio 14C/ 12C is measured to be 2.3×10^−13?
To determine the age in years of a bone based on the ratio of 14C/12C, we need to use a formula called radiocarbon dating. This method relies on the fact that the ratio of 14C (a radioactive isotope of carbon) to the stable isotope 12C changes predictably over time due to radioactive decay.
The formula for radiocarbon dating is:
Age (in years) = -ln(Ratio of 14C/12C) / (decay constant * 1st order radioactive decay equation)
The decay constant for 14C is 0.693 / half-life of 14C, which is approximately 0.00012 per year.
Now, let's plug in the values we have:
Ratio of 14C/12C = 2.3×10^−13
Decay constant = 0.00012 per year
Age (in years) = -ln(2.3×10^−13) / (0.00012)
Using a scientific calculator, we can calculate the natural logarithm (ln) of the ratio:
ln(2.3×10^−13) ≈ -29.7
Plugging this value into the equation:
Age (in years) = -(-29.7) / (0.00012)
≈ 247,500 years
Therefore, the age of the bone, based on the given ratio of 14C/12C, is approximately 247,500 years.