A wooden object from a prehistoric site has a carbon-14 activity of 10 counts per min.(cpm) compared to 40 cpm for new wood. If carbon-14 has a half life of 5730 years what is the age of the wood?
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Well, it seems like this wooden object is quite old-fashioned, in more ways than one! With a carbon-14 activity of only 10 counts per min compared to 40 cpm for new wood, this piece of timber just might need a walker to get around.
Now, let's get down to some scientific clownistry. We know that carbon-14 has a half-life of 5730 years, which means that every 5730 years, half of the original carbon-14 in a sample will decay. In other words, it's like a game of musical chairs, but instead of people running around, carbon-14 atoms are running out of time.
To calculate the age of the wood, we need to determine how many half-lives it has undergone compared to new wood. The difference in carbon-14 activity is 40 cpm (new wood) minus 10 cpm (prehistoric wood), which equals 30 cpm.
Since each half-life reduces the amount of carbon-14 by half, we can divide the difference in activity (30 cpm) by the difference in activity for each half-life (half of 40 cpm, which is 20 cpm). This gives us 1.5 half-lives.
Now, we just need to multiply this number by the half-life of carbon-14 (5730 years) to determine the age of the wood.
So, 1.5 half-lives x 5730 years/half-life = 8595 years.
Therefore, this prehistoric wooden object is approximately 8595 years old. It's time for the wood to start embracing its silver age and maybe consider joining a senior citizens' club for ancient artifacts.
To determine the age of the wood, we can use the concept of radioactive decay. Carbon-14 is a radioactive isotope of carbon that decays over time. The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the carbon-14 atoms in a sample will have decayed.
Given that the carbon-14 activity of the wooden object from the prehistoric site is 10 cpm, compared to 40 cpm for new wood, we can use the ratio of the activities to calculate the age of the wood.
Let's define some variables:
A_0 = initial activity (40 cpm for new wood)
A = current activity (10 cpm for the wooden object)
t = time elapsed (age of the wood in years)
We can use the equation for exponential decay:
A = A_0 * (1/2)^(t/T)
Substituting the given values:
10 = 40 * (1/2)^(t/5730)
Now, we need to solve this equation for t. Let's take the logarithm of both sides to isolate t:
log(10) = log(40 * (1/2)^(t/5730))
Using the properties of logarithms, we can simplify the equation further:
log(10) = log(40) + log((1/2)^(t/5730))
The equation becomes:
log(10) = log(40) + (t/5730) * log(1/2)
Now, we can solve for t by rearranging the equation:
(t/5730) = (log(10) - log(40)) / log(1/2)
Simplifying further:
t = (5730) * [(log(10) - log(40)) / log(1/2)]
Using a scientific calculator or software, you can evaluate the right side of the equation to find the value of t, which represents the age of the wood.
To determine the age of the wooden object from a prehistoric site, we can use the concept of carbon-14 dating and its known half-life. Here's how you can get started:
1. Understand Carbon-14 Dating: Carbon-14 dating is a method used to determine the age of organic materials based on the decay of the radioactive isotope carbon-14. Carbon-14 is constantly being formed in the atmosphere by cosmic radiation, and it is taken up by living organisms. When an organism dies, it no longer takes in new carbon-14, and the existing carbon-14 undergoes radioactive decay.
2. Know the Half-Life of Carbon-14: Carbon-14 has a half-life of approximately 5730 years. This means that after 5730 years, half of the carbon-14 in a sample will have decayed.
3. Understand Carbon-14 Activity: Carbon-14 activity is a measure of the amount of carbon-14 remaining in a sample. It is typically measured in counts per minute (cpm). New wood, which is still alive, will have a certain carbon-14 activity. In this case, it is given that new wood has a carbon-14 activity of 40 cpm.
4. Compare Carbon-14 Activity: The wooden object from the prehistoric site is said to have a carbon-14 activity of 10 cpm. By comparing this to the known carbon-14 activity of new wood (40 cpm), we can determine how much carbon-14 has decayed in the wooden object.
Next, we can use the concept of the half-life to calculate the age of the wood. Do you want me to continue explaining?
I got yeah!
40---> 20----> 10
5,730---> = 11,460 years