A wooden artifact is found in an ancient tomb. Its carbon-14 activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of carbon-14 was initially present in the wood from which the artifact was made, determine the age of the artifact.
Calculate how long it take for the decay rate to decrease to 60% of the initial value, when the half life is that of C-14, which is 5568 years. They expect you to look that up, or know it.
Let t = the age in years
2^(-t/5568) = 0.6
Solve for t.
(-t/5568)*log 2 = log 0.6
-t/5568 = log .6/log2 = -.737
t = 4100 years
9200 years
Half life of C-14 is 5730 yrs. Which would give you 4.22x10^3 yrs as your answer.
To determine the age of the artifact, we can set up an equation using the formula for radioactive decay:
2^(-t/5568) = 0.6
Where t represents the age of the artifact in years, and 5568 is the half-life of Carbon-14.
To solve for t, we can take the logarithm of both sides of the equation:
(-t/5568)*log2 = log0.6
Using a calculator, we can evaluate the right side of the equation:
log0.6 ≈ -0.2218
Then, we can isolate t by dividing both sides of the equation by (-log2/5568):
-t/5568 = -0.2218 / (log2)
Using the base-10 logarithm for simplicity, we can substitute the value of log2 ≈ 0.30103:
-t/5568 = -0.2218 / (0.30103)
Simplifying the equation:
-t/5568 ≈ -0.7368
Finally, we can solve for t:
t ≈ (-0.7368)(5568)
t ≈ 4100 years
Therefore, the age of the artifact is approximately 4100 years.
To determine the age of the artifact, we need to calculate how long it took for the carbon-14 activity to decrease to 60% of the initial value.
The decay of carbon-14 follows an exponential decay equation, where the amount of carbon-14 remaining is given by the equation N(t) = N0 * 2^(-t/t_half), where N(t) is the current amount of carbon-14, N0 is the initial amount, t is the time passed, and t_half is the half-life of carbon-14.
Given that the carbon-14 activity in the artifact is 60% (or 0.6) of the carbon-14 activity in a fresh sample of wood from the same region, we can rewrite the equation as 0.6 = 2^(-t/5568).
Now, let's solve for t. Taking the logarithm of both sides of the equation to eliminate the exponential, we have (-t/5568) * log2 = log(0.6).
We can calculate the right side of the equation as log(0.6)/log(2) ≈ -0.737.
Now, we can solve for t by multiplying both sides of the equation by -1 and dividing by 5568: t ≈ (-0.737) * (-1) * 5568 ≈ 4100 years.
Therefore, the age of the artifact is approximately 4100 years.