Radioactive carbon-14 dating has determined that a fossil is 5:7 (103) years old. What is the total amount of the original (C14) still present in the fossil?
C14 has a half-life of 5730 years. the fraction of C14 remaining is
(1/2)^(5700/5730) = 0.5018
I expect they just wanted 1/2 as the answer.
Well, you've really given me a math challenge with that ratio! I'm just a Clown Bot, not a math wizard. But I'll try my best to make you laugh while we figure this out!
Okay, let's break it down. If the fossil is 5:7 (103) years old, we can say that there are 5 parts of time that have passed since the organism died, and 7 parts of time that should've passed according to the carbon-14 half-life.
Now, assuming that the carbon-14 is decaying at a constant rate, we can say that in the same amount of time it takes for half of the carbon-14 to decay (half-life), only 5 parts of time have passed. So, we can deduce that the original carbon-14 remaining in the fossil is less than half.
As for the exact amount? I'm afraid I can't calculate that for you. But I can assure you that there's definitely less carbon-14 in there than what it originally had!
To determine the total amount of original carbon-14 (C14) still present in the fossil, we need to use the concept of half-life.
The half-life of carbon-14 is approximately 5730 years. This means that after 5730 years, half of the original carbon-14 in a sample will have decayed.
Let's assume the original amount of carbon-14 in the fossil was X.
Since the fossil is determined to be 5/7 (103) years old, we need to calculate how many half-lives have passed.
Number of half-lives = (age of the fossil) / (half-life of carbon-14)
Number of half-lives = (5/7 * 10^3 years) / (5730 years)
Number of half-lives ≈ 0.8705 half-lives (rounded to four decimal places)
Now, we can calculate the remaining amount of carbon-14 in the fossil using the formula:
Remaining amount of carbon-14 = Original amount of carbon-14 * (1/2)^(number of half-lives)
Remaining amount of carbon-14 = X * (1/2)^(0.8705)
Therefore, the total amount of the original carbon-14 still present in the fossil is given by X * (1/2)^(0.8705).
To determine the total amount of the original carbon-14 (C14) still present in the fossil, we need to understand the concept of radioactive decay and the half-life of carbon-14.
Carbon-14 is a radioactive isotope of carbon that is present in the atmosphere. When an organism is alive, it takes in carbon from the atmosphere through processes like photosynthesis or consuming other organisms. The carbon-14 in the organism's body remains at a constant ratio with carbon-12 until the organism dies.
Once the organism dies, it no longer takes in carbon-14, and the existing carbon-14 begins to undergo radioactive decay. Carbon-14 has a half-life of about 5730 years, which means that after this amount of time, half of the carbon-14 will have decayed into nitrogen-14.
In this case, we know that the fossil is 5/7 (or 5:7) of its original age, which is 1.03 million years. Now, we can calculate the amount of carbon-14 still present in the fossil.
First, we need to determine the number of half-lives that have occurred. We can do this by dividing the fossil's age by the half-life of carbon-14:
Number of half-lives = (1.03 million years) / (5730 years per half-life)
Calculating this gives us approximately 179.82 half-lives.
Now, we can calculate the remaining fraction of carbon-14 in the fossil. Because each half-life halves the amount of carbon-14, the remaining fraction after 179.82 half-lives is given by:
Remaining fraction = (1/2)^(number of half-lives)
Calculating this gives us a remaining fraction of approximately 1.16 x 10^-54.
Finally, we can calculate the total amount of the original carbon-14 still present in the fossil by multiplying the remaining fraction by the initial amount of carbon-14:
Total amount of original C14 in the fossil = (remaining fraction) x (initial amount of C14)
However, to accurately determine the initial amount of carbon-14 in the fossil, additional information is needed, such as the carbon-14 to carbon-12 ratio at the time the organism died. Without this information, it is not possible to provide a specific value for the total amount of original carbon-14 still present in the fossil.