Question

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 0.596 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.)

Answer 1

Answer:

4276.98 years

Explanation:

t = age of the sample in numbers of years

T = half life of the carbon-14 isotope = 5730 yrs

λ = decay constant of carbon-14

decay constant is given as

$\lambda =\frac{0.693}{T}$

$\lambda =\frac{0.693}{5730}$

$\lambda = 0.000121$

A₀ = activity of Carbon-14 in living plants

A  = activity of Carbon-14 after time "t" = (0.596) A₀

Using the equation

$A = A_{o} e^{-\lambda t}$

$(0.596) A₀  = A_{o} e^{-0.000121 t}$

$0.596 = e^{-0.000121 t}$

t = 4276.98 years