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By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. I've spent over an hour researching Carbon decay for a Calculus problem, but I have one main problem when solving them: how do you solve for the k value decay constant? The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon, denoted 12C a stable isotope , and carbon, denoted 14C a radioactive isotope.

It is nigh impossible to measure exactly zero. It doesn't take much contamination to spoil a sample with near-zero quantity of C Creationists pounce on this explanation as meaning all carbon 14 readings are suspect.

While that same level of contamination if this is the explanation will add some error to the dating of some reasonably aged sample, the error will be small - so long as the sample is not too old.

(1.) C14 dating is very accurate for wood used up to about 4, years ago. This is only because it is well calibrated with objects of known age. Example: wood found in a grave of known age by historically reliable documents is the standard for that time for the C14 content. This standard content of C14 can then be used for wood not associated. We can use a formula for carbon 14 dating to find the answer. Where t 1/2 is the half-life of the isotope carbon 14, t is the age of the fossil (or the date of death) and ln is the natural logarithm function. If the fossil has 35of its carbon 14 still, then we can substitute values into our equation. Carbon dating is the standard method used by scientists to determine the age of certain fossilized remains. As scientists will often claim something to be millions or billions of years old (ages that do not conform to the Biblical account of the age of the earth), Christians are often left wondering about the accuracy of the carbon method.

The contamination is additive, not proportional. Alternate source of C14 production. Natural diamonds are not pure carbon.

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The most common contaminant is nitrogen, 0. Nearby radioactive material could trigger exactly the same C14 production process from nitrogen as occurs in the upper atmosphere, albeit at a much reduced rate.

Another possible avenue is C13, which has a small but non-zero neutron absorption cross section. By either mechanism, this is essentially internal contamination.

All this means is that measured dates older than some oldest reliable date are just that - to old to date reliably. I might be able to see if I can come up with some references.

Carbon dating is based upon the decay of 14 C, a radioactive isotope of carbon with a relatively long half-life ( years). While 12 C is the most abundant carbon isotope, there is a close to constant ratio of 12 C to 14 C in the environment, and hence in the molecules, cells, and tissues of living organisms. Problem #1: A chemist determines that a sample of petrified wood has a carbon decay rate of counts per minute per gram. What is the age of the piece of wood in years? The decay rate of carbon in fresh wood today is counts per minute per gram, and the half life of carbon is years.

I won't be able to do so in the near term - my wife and kids want me to stop dorking with the internet and go out to eat. The article you were looking for is hereand yeah, it looks like you're right.

The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon, denoted 12C (a stable isotope), and carbon, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,). Name Date Class 1 of 4 MATH SKILLS Half-Life If g of carbon decays until only g of carbon is left after 11 y, what is the half-life of carbon? Feb 17,   Ive been poking about on the internet again (as you do) and found a whole load of stuff by creationists about the problems with carbon 14 radiometric dating. Specifically they report (with some glee) that coal has been found to contain measurable amounts of carbon14 which it .

Note: I think that should be I know I visited talkorigins. What is more alarming is that the Google searches for "carbon 14 RATE", "carbon 14 diamond", and "carbon 14 coal" yield hits predominantly in woowoo fundamentalist sites, and no hits on the first 15 pages 10 links per page to anything at talkorigins.

I eventually managed to find an excellent article see the top of this post using pandasthumb.

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That led me to this non-technical article. I think the news item on their front page refers to a much older event. What happened, from what I recall, is that someone hacked TalkOrigins and managed to get the site to display hidden spam links at the bottom of pages, making Google think it was a spam site and thus getting it removed from Google.

Carbon Dating - Example of exponential decay

They fixed that issue a while ago. PZ Myers says they've had some technical issues.

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I am working my way through Kirk Bertsche's 9 page essay on the subject. Thanks DH for this link.

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This article does a good job at explaining the technical complexities of measuring the very small amounts of C14 present in these ancient samples and why non-zero amounts are measured. I'm a complete non-expert in this field of radiometric dating, but it strikes me reading this how contamination by modern carbon introduced during sample preparation seems to be a severe issue. I'm wonder whether they've extracted samples under an inert atmosphere and then used laser ablation to ionize samples in their mass spectrometers?

I'm probably teaching grandmother to suck eggs, as the old saying goes.

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Getting back to my OP - I feel that some definitive work needs to be done in this area. It's easy to see that the sceptical creationist is simply going to see the scientific response as making excuses for the data instead of holding up some hard data that either explains or explodes the anomaly.

Another thing I've heard from creationists is that fossils made by soaking samples in tar pits appear to be extremely old. Of course, the problem is that this process results in contamination with old carbon, making the sample appear older.

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In the case of old samples with almost no C, even the tiniest bit of contamination would make the sample appear far younger. Always remember that C dating is not a magical process; it is a measure of C and the age interpretation depends on a few assumptions. It's also worth noting that C is only useful for a bit more thanyears. The vast majority of fossils aren't dated using C at all, but other radioisotopes.

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What is the approximate age of the fossil? And I find many websites that insert. Can someone please help me with understanding how to calculate this k value that some places have as.

We don't know this value, but we don't need it. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Exponential Decay Problem Ask Question. Asked 7 years, 5 months ago. Active 7 years, 5 months ago.

Carbon dating problems math

Viewed 5k times. Here is the problem The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon, denoted 12C a stable isotopeand carbon, denoted 14C a radioactive isotope. So, I'm not completely lost.

David David 2 2 silver badges 7 7 bronze badges.

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Active Oldest Votes. Austin Mohr Austin Mohr Radioactive isotopes, such as 14 C, decay exponentially.

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The half-life of an isotope is defined as the amount of time it takes for there to be half the initial amount of the radioactive isotope present. We can use our our general model for exponential decay to calculate the amount of carbon at any given time using the equation. Returning to our example of carbon, knowing that the half-life of 14 C is years, we can use this to find the constant, k. Thus, we can write:.

Simplifying this expression by canceling the N 0 on both sides of the equation gives. Solving for the unknown, kwe take the natural logarithm of both sides.

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Other radioactive isotopes are also used to date fossils. The half-life for 14 C is approximately years, therefore the 14 C isotope is only useful for dating fossils up to about 50, years old. Fossils older than 50, years may have an undetectable amount of 14 C.

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