This exercise uses the radioactive decay model.
A wooden artifact from an ancient tomb contains 80% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
? yr
I am having trouble with this question as well can anybody help me?
general equation
amount = a (1/2)^(t/5730) , where t is in years
.8 = 1 (1/2)^(t/5730)
.8 = 1 (.5)^(t/5730)
log .8 = (t/5730) log.5
t/5730 = log.8/log.5
t = 5730(log.8/log.5) = appr 1844.6 years
To solve this question, we need to use the concept of radioactive decay and the half-life of carbon-14.
First, let's understand the concept of half-life. The half-life is the time it takes for half of a radioactive substance to decay. In the case of carbon-14, its half-life is 5730 years. This means that after 5730 years, half of the original amount of carbon-14 will remain.
Now, let's break down the problem. We are given that the wooden artifact contains 80% of the carbon-14 present in living trees. This means that only 20% of the carbon-14 has decayed. Since each half-life represents a decay of half the substance, we can calculate the number of half-lives that have occurred.
To find the number of half-lives, we can use the formula: t = (ln(R) / ln(0.5)) * t1/2
Where:
t = the number of half-lives
R = 0.2 (the remaining amount after decay, which is 20%)
t1/2 = 5730 years (the half-life of carbon-14)
Plugging in the values, we get:
t = (ln(0.2) / ln(0.5)) * 5730
Using a calculator, we find t ≈ 2.773.
Since we cannot have fractional half-lives, we need to round this number to the nearest whole number. In this case, it would be 3.
Therefore, the artifact was made approximately 3 half-lives ago, which means it was made around 3 x 5730 = 17190 years ago.
So, the answer to the question is: The artifact was made approximately 17190 years ago.