Like say my question was a sample has 80% of its original carbon-14 present. How do I determine the age of the sample?
Like I don't get how to get the answer, this concept is very difficult for me
You know the half life for carbon 14 is 5,730 years. If you aren't told that in the problem you can look it up. You can calculate the rate constant (which you will need later) this way.
k = 0.693/t1/2
k = 0.693/5730 = 1.21E-4
Substitute this k into the equation below.
ln(No/N) = kt.
No = what you started with.
N = what yu end up with
k = from above
t = years it took to go from No to N.
They don't give you a number for No so you choose a convenient one to use. It makes no difference what number you choose but I suggest 100.
No = 100
N = the problem says it has 80% of it's original. So since we picked 100, then 100 x 0.80 = 80 (now you know why I picked 100). If you chose any other number then it's the number you chose x 0.80. So
N = 80
k = from above. solve for t
ln(100/80) = 1.21E-4*t and solve for t. I won't go through the steps here (this is where a blackboard would come in handy) but when I do the math I get 1844 years if I did the math right. Post any follow up questions here.
Ok, I kinda understand it now. Thank u so much :)
Determining the age of a sample based on the amount of carbon-14 present can be done using a technique called radiocarbon dating. Here's a step-by-step explanation of how to calculate the age of the sample:
1. Understand the concept: Carbon-14 (C-14) is an isotope of carbon that is present in the atmosphere and absorbed by living organisms through respiration or consumption of plants. When an organism dies, it stops replenishing its carbon-14 supply, and the existing C-14 begins to decay. By measuring the amount of C-14 remaining in a sample, scientists can estimate its age.
2. Determine the half-life of carbon-14: The half-life of carbon-14 is the time it takes for half of the radioactive isotope to decay. It is approximately 5,730 years. This means that after 5,730 years, half of the original C-14 will remain, and after another 5,730 years, half of that remaining C-14 will be left, and so on.
3. Estimate the number of half-lives: Calculate the number of half-lives that have passed based on the given information. In this case, you mentioned that 80% of the original carbon-14 is present. Since each half-life reduces the amount of C-14 by half, we can divide 80% by 50% to find the number of half-lives. In this case, 80% ÷ 50% = 1.6 half-lives.
4. Calculate the age: Multiply the number of half-lives by the length of one half-life (approximately 5,730 years). In this case, since 1.6 half-lives have passed, the age of the sample would be 1.6 x 5,730 years ≈ 9,168 years.
Therefore, based on the given information, the approximate age of the sample would be around 9,168 years using the concept of carbon-14 dating. It's important to note that this method is most accurate for samples that are less than 50,000 years old, as the amount of carbon-14 remaining becomes too small to measure accurately beyond that timeframe.