The age of an artifact can be determined using the carbon-14 dating method, which measures the amount of carbon-14, a radioactive isotope of carbon, in the artifact. The carbon-14 dating method is based on the fact that carbon-14 is continuously being produced in the Earth's atmosphere by cosmic rays, and that it decays over time.
In order to determine the age of an artifact using carbon-14 dating, it is necessary to know the initial 14C activity of the artifact and the rate at which 14C decays. The initial 14C activity of modern-day wood can be assumed to be 100%. The half-life of 14C, which is the time it takes for half of the 14C atoms to decay, is approximately 5730 years.
Using these values, it is possible to calculate the age of the artifact based on the percentage of 14C activity it has. To do this, we can use the formula: age = -(half-life)/ln(percentage of 14C activity/100%), where ln is the natural logarithm.
Substituting the values given in the problem, we get: age = -(5730 years)/ln(59.3%/100%) = -(5730 years)/ln(0.593) = -(5730 years)/(-0.4568) = 12,490 years.
Therefore, the artifact is approximately 12,490 years old.
The artifact is 4,320 years old. Option A is correct.
Here, we are given that Rick finds a wooden artifact with 59.3% of the 14C activity of modern-day wood.
We know that-
Decay constant k = ln 2/ t₀.₅
= 0.693/ 5730
= 1.209 × 10⁻⁴
Now, the rate of counts will be proportional to the number of C14 atoms in the sample.
⇒ N₀ = 100, N = 59.3
The age of the sample t will be-
t = 2.303/ k × log(N₀/ N)
t = 2.303/ (1.209 × 10⁻⁴) log(100/ 59.3)
t = 1.9048/ 10⁻⁴ × 0.2269
t = 4,320 years
Thus, the artifact is 4,320 years old. Option A is correct.
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