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Question 18 (1 point}sample of corn was found to have 1C to 12C ratio of 8.0 x 10-13 Similar corn samples taken today have 14C to 12C ratio of 1.2 x 10*-12. Use the...

Question

Question 18 (1 point}sample of corn was found to have 1C to 12C ratio of 8.0 x 10-13 Similar corn samples taken today have 14C to 12C ratio of 1.2 x 10*-12. Use these data to estimatc the age of the corn sample?1) 3.300 yrs2) 150 yrs3) 5,200 yrs1,400 yrs500 yrs

Question 18 (1 point} sample of corn was found to have 1C to 12C ratio of 8.0 x 10-13 Similar corn samples taken today have 14C to 12C ratio of 1.2 x 10*-12. Use these data to estimatc the age of the corn sample? 1) 3.300 yrs 2) 150 yrs 3) 5,200 yrs 1,400 yrs 500 yrs



Answers

The first attempt at radiocarbon dating six skeletons discovered in an Italian cave at the beginning of the 20 th century indicated an age of 15,000 years. Redetermination of the age in 2004 indicated an older age for two bones of between 23,300 and 26,400 years. What is the ratio of $^{14} \mathrm{C}$ in a sample 15,000 years old to one 25,000 years old?

For this problem. We want to find the age of a piece of bone. And we're told that the, um carbon 14 to carbon 12 ratio, or the percentage of carbon 12 to carbon 14 is 72% of what it was back when the, um organism was alive, um says and were asked to date how old the piece of bone is now. So the first thing that we have to do is figure out the first order rate constant, and we can calculate that by using the half life, which we know to be 5.73 times 10 to the third years. So our equation for figuring out the rate constant K rate constant equals 0.693 divided by the half life. And we were told that the half life is 5.73 times 10 to the fourth years times 10 to the third years. I'm sorry. 10 to the third. There we go. Okay. And based on that, we have ah, the rate constant equals 1.209 times 10 to the minus fourth. And that's in years to the minus one. So that's the first piece of information that we need to know to solve this problem. Okay, then we can use our activity equation. And we know that the log of the activity now divided by the activity at time zero has to equal negative the first order rate, constant times the amount of time that is passed by. So given the problem statement, it looks like we might not have enough information. Do we know what the current activity is? Um and do we know what the initial activity is? Well, we don't specifically know what each of those values are. However, there's a clue up here. That's where this 72% comes in. What the 72% is telling us is that the activity now is 72% of whatever it was initially. So we can convert 72% into a decimal 720.72 and use that in our fraction, replacing hey over a zero. So 0.72 is are a over 80 and that's going to equal negative times. Ah, they're rate constant, which is 1.209 times 10 to the minus fourth years to the minus one, and that times time the time is actually the age of the piece of bone. And when we solve for T. Um, by figuring out the log of 0.72 and then dividing it by 1.209 times 10 to the minus fourth, we find that the time that is past or the age of the bone is roughly 2700 years. So that's how old the piece of bonus.

First question they tell us that The ruins of a Native American village has a carbon 14 to carbon 12 ratio of .72 times that found in living organisms. And they want us to calculate the age of the bone fragment. Yeah. So Right here we have the ratio of .72. And then the half life of carbon is 5.73 times 10 to the three years. You know the first thing that we can do is calculate kate. Right? So the first equation that we need is half life Is equal 2.693 over K. Since we have half life, this means that we are only missing one variable. And we can software equation when we're only missing one. So let's isolate K. So we multiply both sides by K. Now we divide both sides by half life. And we get K 2.693 over half life. I was plugging our value. Yeah. Three years. Uh put that into the calculator and we get 1.21 times 10 to the -4. Uh huh. For you has that K. Value. Now the next part we need a different equations. So Ln Mhm. Oh yeah, 80. Which is the activity after a short amount of time over eight hunt, which is an interactive physical to negative play times T. Now let's determine what 80 over a nineties. So they tell us that the ratio between carbon 14 and carbon 12 is 120.72 So 80/8 9 is 90.72 We know what K. Is, Right? So 1.21 times 10 to the -4 per year. And we're just trying to turn the T. Is. So we're gonna do is divide both sides by negative K. Or negative 1.21 times 10 to the negative four per year. To isolate T. What you want to extend to the -4, and we get T. Is equal to 2.71 times 10 to T. Three years as our answer.

So in this question, it's given to us that in a fresh sample often born, the ratio of carbon 14 to carbon 12 is 1.3 times came to the power minus 12. Whereas in the ex curated sample, the issue of carbon 14, carbon 12 years 3.25 times to the power negative 13 and were asked to calculate how old the sample of the bone is. Mhm Sure. The time it's given us one over lambda. Love off the ratio of carbon 14 to carbon 12. And ex curated sample divided by the ratio and fresh sample. Now, dickie cost in itself is given as locked to over T half. And this would be logged off 3.25 times 10 to the power negative 13. And you had it by 1.3 times 10 to the power negative tour the T half for carbon 14 is 5730 years. So, plugging all these values, the time of the bone comes out to be 11,500 use. So this bone is 11,500 years. Oh

First calculating the value of initial number of carbon 14 atoms present in the given sample. So I can write and not as equal to 1.2 multiplication. 10 to the power managed to world multiplication N am by I. M. A. So solving it further, I can write the Express and at 1.2 multiplication and 10 to the four minus two World multiplication. Six point you know 23 multiplication 10 to the power 23 multiplication 13.83 by two World. Which is equal to 8.3 2981 multiplication 10 to the power 11. Now going forward and calculating the percent number of carbon 14 nuclear in this temple. So I will use the formula and is equal to and not eat of the power minus 140.693 T. V. I T huh? On further simplification, I can ride the value of N. Is equal to 8.32981 multiplication, 10 to the power 11, multiplication into the power minus 0.693 Multiplication 4814 by 5730 Which one simplification? I get the value and is equal to 4.6 5 35. Multiplication 10 to the power 11. Now going forward and calculating the activity of the temple. So I can write a sequel to and multiplication 0.693 by t ha solving it further. I can write the expression of A. Is equal to 4.6 535 multiplication and 10 to the part 11. Multiplication 110.693 by 5730 year. So changing the unit, I just multiply it by this value 3.156 multiplication, 10 to the past seven second possible implicates. And I get the value of a age 1.783 teddy decade. Poor second. So just changing the unit so I just multiplied by 60 seconds per minute. Which one simplification? I get the value add of A is equal to €1.7 DK, but me not as our final answer.


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