Question 1176270: A bone is measured for its age and it is found that it contains 87.5 grams of Nitrogen-‐14 for every 12.5 grams of Carbon-‐14; how old is the bone?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! to solve this question, you need to know the rate of decay in the carbon 14.
when it decays, it turns into nitrogen.
best i can think of with this information is that the total grams is 87.5 + 12.5 = 100 grams.
the carbon is only 12.5/100 = .125 of its original mass.
the half life of carbon is 5730 years.
the formula to use is f = p * .5 ^ n
n is equal to 1 for every 5730 years.
f is the ratio of carbon to mass in the future.
p is the ratio of carbon to mass in the present.
when n = 1, the formula becomes f = 1 * .5 ^ 1 = .5
to find the number of years, multiply n by 5730 to get 5730 years.
to solve for when f = .125, the formula becomes .125 = 1 * .5 ^ n
simplify to get .125 = .5 ^ n
take the log of both side of the equation to get:
log(.125) = log(.5 ^ n)
by the law of logs that says log(x^n) = n * log(x), the formula becomes:
log(.125) = n * log(.5)
solve for n to get:
n = log(.125) / log(.5) = 3
since n represents 5730 years, then the age of the bone is estimated to be 3 * 5730 = 17190 years.
i tried to get a reference that specifically addresses the raltionship between carbon 14 and nitrogen 14 but was unsuccessful.
any answer more sophisticated than this required much further study in how bones are dated.
my assumptions are basic.
when the bone was alive, the mass was all carbon 14.
as the bone dies, it loses carbon 14 which gets transformed to nitrogen.
not being a chemist, this is the best i can do.
from an algebraic standpoint it makes sense, but not knowing the ratio of carbon to nitrogen in a living organism, it's only a guess.
here's a reference that talks about the issue, but discusses carbon 12 as well.
https://www.nde-ed.org/Physics/X-Ray/carbon14dating.xhtml
an excerpt from that article is shown below.
How do scientist use Carbon-14 to determine the age of an artifact?
To measure the amount of radiocarbon left in a artifact, scientists burn a small piece to convert it into carbon dioxide gas. Radiation counters are used to detect the electrons given off by decaying Carbon-14 as it turns into nitrogen. In order to date the artifact, the amount of Carbon-14 is compared to the amount of Carbon-12 (the stable form of carbon) to determine how much radiocarbon has decayed. The ratio of carbon-12 to carbon-14 is the same in all living things. However, at the moment of death, the amount of carbon-14 begins to decrease because it is unstable, while the amount of carbon-12 remains constant in the sample. Half of the carbon-14 degrades every 5,730 years as indicated by its half-life. By measuring the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of the artifact.
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