i dont understand this question:(
Study Figure 10-3. How much nitrogen-14 will be produced from a 200-g sample of carbon-14 after 17,190 years?
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To understand the question, we need to look at Figure 10-3, which represents the decay of carbon-14 into nitrogen-14 over time. The question is asking about the amount of nitrogen-14 that will be produced from a 200-g sample of carbon-14 after 17,190 years.
Before we can determine how much nitrogen-14 will be produced, we need to understand the concept of radioactive decay. Carbon-14 is a radioactive isotope that undergoes decay, meaning it spontaneously transforms into a different element over time. In this case, carbon-14 decays into nitrogen-14.
To solve the question, we need to use the concept of half-life. The half-life of carbon-14 is the time it takes for half of a sample to decay. The half-life of carbon-14 is approximately 5,730 years.
Now, we can use the half-life concept to determine the number of half-lives that have passed in 17,190 years. We divide the total time (17,190 years) by the half-life of carbon-14 (5730 years):
Number of half-lives = 17,190 years / 5,730 years = 3
This tells us that three half-lives have passed during the 17,190 years.
Since each half-life means that half of the original sample has decayed, we need to determine the amount of carbon-14 remaining after three half-lives.
After the first half-life, half of the carbon-14 has decayed, leaving us with 100 g.
After the second half-life, half of the remaining carbon-14 has decayed, leaving us with 50 g.
After the third half-life, half of the remaining carbon-14 has decayed, leaving us with 25 g.
So, after 17,190 years, only 25 g of the original 200 g sample of carbon-14 will remain. This means that 175 g of carbon-14 have decayed into nitrogen-14.
Therefore, the amount of nitrogen-14 produced from a 200-g sample of carbon-14 after 17,190 years is 175 grams.
Solve for k as in the earlier problems.
I think figure 10-3 just gives you the disintegration process. it is a beta emitter so 6C^14 ==> -1e^o + 7N14
Apply ln (No/N) = kt
You know No is 200 g C-14
You want to solve for N
You know k
You know t is 17,190 years
N will tell you how much C-14 is left at the end of 17,190 years.
200 g C-14 initially - C-14 left = grams C-14 that was converted to N.
The only thing left is to convert the mass of C to mass N,
mass C-14 converted to N14 x (atomic mass N-14/atomic mass C-14) = ? g N-14. Post your work if you get stuck.