Question 1163260: if you have an organic sample of C-14 weighing 220g, how long will it take to be reduced to 55g of C-14?
Found 2 solutions by BriLH22, ikleyn:
Answer by BriLH22(1)   (Show Source):
Answer by ikleyn(52824)  (Show Source):
You can put this solution on YOUR website! .
One half life period for C-14 is 5730 years.
55 grams is exactly one-fourth  =  of the original mass 220 grams of the sample.
Hence, 2 (two, TWO) half-life periods are needed, or 2*5730 = 11460 years for the process. ANSWER
Solved.
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There is a group of lessons in this site, which covers many similar problems on Carbon dating
- Using logarithms to solve real world problems, and
- Carbon dating problems
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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One important post-solution note.
I do not know who is a composer of this problem - you or your professor or the third party,
but I definitely know that this person DOES NOT know the basics of the underlying decay process and the decay dating method.
In the natural organic samples, the initial ratio of the masses of radioactive C-14 to stable C-12 is about  .
It is even less than tiny percent.
Nevertheless, the existing measuring tools allow accurately measure this ratio.
With time, the amount of C-14 decreases exponentially, and the ratio of masses C-14 to C-12 decreases accordingly.
In the dating method, ONLY THIS RATIO is the subject of measuring and consideration.
Therefore, NOBODY and NEVER on the Earth had an organic 220 gram sample of C-14.
So, if you are going to publish this problem and my solution in some web-site, I do not recommend you
to do it: people will laugh on you.
You better learn about the process from these authoritative sources
https://www2.lbl.gov/abc/wallchart/chapters/13/4.html
https://en.wikipedia.org/wiki/Radiocarbon_dating
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