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Problem 35 Medium Difficulty

A wooden artifact is found in an ancient tomb. Its carbon - 14 $\left(\begin{array}{c}{14} \\ {6}\end{array}\right)$ activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of $^{14} \mathrm{C}$ was initially present in the artifact as is
now contained in the fresh sample, determine the age of the artifact.

Answer

4.22 \times 10^{3} y r

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Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Jared E.

University of Winnipeg

Meghan M.

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Video Transcript

for number 35. There is a piece of wood, old wood that has Ah, carbon 14 is measured toe have 60% of the activity that a fresh piece of wood would have. So this is activity. But if you remember, get to 10. If you remember that the activity is proportional to the number of nuclei I can you just use this equation where the number of nuclear present Now there's the original number nuclei. It sounds 1/2 raised to the number of half lives. And I can look up in appendix B in the back and see that the half life for carbon 14 is 5730 years. So now when I pull you over here, um, I don't know what the original Waas By now, you know it's 60% of the original, so this is 600.6 times the original when this is the original. Well, when this is times 1/2 raised the number of half lives. Well, I'm looking for the time trying to find is how old this piece of wood is. Um so it's, however old the wood is divided by half life, which is 57 30. This would be you know how many half lifes I have them on will be in years. So if I just solve this equation for X, I'm good. So I'm gonna divide both sides by the original end. I'm gonna take the log of both science. So here I have the log. A 0.6 ever. Here I have the log 4.5. Remember, when you take the log off something this exponents can come out in front instead. So this would be over here squeezes him. X times 57. 30. I'm sorry. That's getting sloppy. So now if I want to solve for this ex, it's going to be the log of 6.6. Bring that over. Divided by the log 1.5 and I'm gonna multiply times 57. 30. And that will have x way itself. And I get 4222 years

University of Virginia
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Jared E.

University of Winnipeg

Meghan M.

McMaster University