The age of a piece of wood from an archeological site is to be determined using the Carbon-14 method. The activity of the sample is measured to be 0.767 times the Carbon-14 activity of living plants. What is the age of the sample in years? (The half-life of the Carbon-14 isotope is 5730 years.)
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[A]/[Aº] = e^-kt
k = 0.693 / 1/2life
k = 0.693 / 5730 = 1.2x10^-4
0.767 / 1 = e^-(1.2x10^-4 x t)
ln0.767 = -1.2x10^-4 x t
-0.265 / -1.2x10^-4 = t
t = 2210.5years.....we know that if 5730 years had passed, we would have 0.5 the activity, here we have > 0.5 so we have < time than 1 half-life
k = 0.693 / 1/2life
k = 0.693 / 5730 = 1.2x10^-4
0.767 / 1 = e^-(1.2x10^-4 x t)
ln0.767 = -1.2x10^-4 x t
-0.265 / -1.2x10^-4 = t
t = 2210.5years.....we know that if 5730 years had passed, we would have 0.5 the activity, here we have > 0.5 so we have < time than 1 half-life