archaeologist digging at the site of an ancient settlement discover the remains of a wooden structure. carbon 14 dating of the wood from the structure finds a decay rate of 180 decays/min. Knowing that the decay rate for living wood is 600 decays/min and the decay constant for 14C decay is 8270 years, determine the age of the structure. Show works!
Thank you!
To determine the age of the wooden structure using carbon-14 dating, we can use the formula:
Age (in years) = -ln(Rn/R0) / λ
Where:
Rn = the ratio of the carbon-14 decay rate in the wooden structure (180 decays/min)
R0 = the ratio of the carbon-14 decay rate in living wood (600 decays/min)
λ = the decay constant for carbon-14 (8270 years)
Let's substitute the values into the formula to find the age of the structure:
Age = - ln(180/600) / 8270
First, let's calculate the ratio of decay rates:
Rn/R0 = 180/600 = 0.3
Now, rearranging the formula:
Age = - ln(0.3) / 8270
Next, take the natural logarithm (ln) of 0.3:
ln(0.3) ≈ -1.204
Now substitute this value into the formula:
Age = - (-1.204) / 8270
Simplifying:
Age ≈ 0.0001456 years
The age of the wooden structure is approximately 0.0001456 years.