Fossil Dating for the anthropology department

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TL;DR Summary: I was curious for any help or advice on this project I was told I could do if I can come up with a good plan to successfully radioactively date this fossil.

I am a community college student. At my college, the anthropology department found some Colombian mammoth bones and have not officially dated them yet. They said that if I could write up a proposal which could work for the radio-dating, they could provide some funding such that it is not super expensive.

I was wondering, upon looking up how radiocarbon dating works, and researching the chemicals and processes used it actually seems possible. The set up I have in mind is this:

1. Get a small piece of the bone and grid it up into a powder.
2. Use HCl to dissolve any remaining bones parts
3. Heat up the now aqueous solution and allow it to gelatinize
4. Filter solution
5. Freeze dry, removed any excess water that isn’t needed

6. This is where I was wondering for advice. Now that I have freeze dried and removed the excess material, I can focus on testing the remaining substances for C-14. I have seen a couple different ways to do it. The most community college friendly/cheapest one I was able to find was converting it all into liquid benzene and then using that combined with butyl-PBD so that a liquid scintillator spectrometer could pick up and make a C-14 curve and determine the date of mammoth bone. Is this a practical way of going about things or is there a better method that I could not find in my research that can be done with the resources a typical community college would have?

Also is this idea even feasible, I know it sounds feasible but I also know benzene is a chemical best avoided and I am not sure how hard to get a scintillator would be to find? Would that be possible to make by chance if it is to costly?

My apologies for the long description and many questions, and thank you so much for taking the time to read this and provide and thoughts!
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If possible, talk to a local lab that is already doing the tests you are interested in.
If you can find them they may have a stash of equipment and reagents, as well as expertise, that you might be able to avail yourself of.
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And PLEASE keep us updated on your progress and results!

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"The succession of steps undergone by the sample in the benzene synthesis line for radiocarbon dating from its original state to benzene through the intermediate formation of carbon dioxide in the Vycor tube, lithium carbide with molten lithium metal heated to at least 700C and in absence of air, acetylene by its hydrolysis and its conversion to benzene on the catalyst, is schematically described. The optimum conditions for these operations are defined and secondary reactions. responsible for reduced yields in the various steps, are described."

I am not sure whether you realized how ambitious this project is.
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I remember a detailed article in scientific american from the 50ies of a high school student doing c14 dating at home. He used photomultipliers and the fridge of his parents to cool the device. Can't find even a hint of this article online.
PS: I found a paper copy in my bookshelf: The Amateur Scientist: How a youg amateur mastered the carbon-14 method of dating ancient organic materials. I don't know the year of the article.
He uses reaction of carbon dioxide with methyl magnesium iodide to form acetic acid which can be measured in a scintillation counter.
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I really love these graphics!
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