Given that the half life of c 14 is 5,700 ,use the method c 14 dating to determine the age of a fossil if it has 25% of c 14 compared to living specimen.
k = 0.693/t1/2
Calculate k and substitute into the following:
ln(No/N) = kt.
Use No = 100
N = 25
k from above.
Solve for t. I estimated about 11,000 years but you need to calculate it more accurately and remember the number of significant figures.
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To determine the age of a fossil using carbon-14 dating, we need to understand the concept of half-life. The half-life of carbon-14 (C-14) is the time it takes for half of the radioactive isotope C-14 to decay into stable nitrogen-14 (N-14). In this case, the half-life of C-14 is 5,700 years.
Now, let's use this information to calculate the age of the fossil given that it has only 25% of C-14 compared to a living specimen.
1. Start by determining how many half-lives have occurred since the organism died and became a fossil. Since the fossil has 25% of the C-14 compared to a living specimen, it means that 75% of the C-14 has already decayed. This corresponds to three half-lives, as each half-life reduces the amount of C-14 by half (50%, 25%, and 12.5%).
2. Knowing that each half-life is 5,700 years, multiply this value by the number of half-lives (3 in this case). This gives us the elapsed time since the organism's death, which is 3 x 5,700 = 17,100 years.
Therefore, if a fossil has only 25% of C-14 compared to a living specimen, its age can be estimated to be approximately 17,100 years.