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# KCC's Quizzes AQQ245 on Fossil Dating with Carbon14  You probably heard the method of dating fossils by measuring Carbon14 (also note C14 concentration. To refresh, the concentration of C14 in the air and on earth surface is constant (thanks to cosmic radiation) since ever (in fact it is assumed so). C14 is not stable and is changed into Nitrogen and an electron: C14 concentration versus the standard carbon (C12) decades with time. That speed is characterized by Its half-life period which is 5568 years for C14 (quantity of C14 still present in an isolated place decays by half after each 5568 years).

Today, in free air and on the earth surface, the ratio N0 = C14/C12 is 0.8 10-12

A mammoth bone has been just extracted and the concentration of C14/C12 is 0.2 10-12.

Questions:

1. How old is that bone?

2. Since humanity is constantly putting more carbon in the atmosphere. How it affects the Carbon14 dating? For example, if C12 concentration is doubled. How will be the dating of our previous bone?

Good Luck!

P.S. If you think there are colleagues who should try those quizzes, please forward them the link!

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[edited by: StephenV at 3:24 PM (GMT -4) on 18 Oct 2023]
• 3113 yrs old, ratio in old bone would remain the same if c12 doubled and the baseline is known so no problem there but future dating of artefacts from today would need a new baseline if the c14/c12 constant shifts due to more c12 in future years.

• 1/2 life of 5568  implies that after 5568 years, there is only half of the original content left.
Since the content is about one quarter of its original content, that makes exactly 2 half lifes, or that your mammoth failed to meet Homer, in the 800 BC (roughly 3000 years ago) or the construction of the pyramids in Egypt, but died more about like  11136 years ago.

As for the concentration of C12 of today, that does not matter since we compare the ratio of the today residual C14 to C12 from the bone with respect to the initial ratio which was in vigor at the time of the living... died. Since its death, the bone didn't capture any new Carbon and thus, as a photo that we would have taken then, it is unaffected by today ratio.

• 1) From 0.8 to 0.2 it is factor 4. That means C14 isotopes two times halved.
2 times 5536 years makes 11172 Years. This should last ice age, aka Last glacial period LGP 2) Due to more pollution, we will have more CO2 in future. Which produces a lot C12.
The problem by fossil oil is the C14 isotopes in oil are already diminished due to millions of years radioactive decay.
Thus the ratio C14/C12 will be in future less, and similar levels to e.g. 1000 years old material from forensic or archeology.
So we will have more uncertainty in the forensic identification.

Analogy to Electronics, our SNR (Signal to Noise Ratio) will be less.

• 1. The bone will be 11136 yrs old.

• 1. Since the 14C concentration is reduced by a factor of 4, the bone has 2x5568= 11136 years (exponential decay law)

2. If, to calculate the age of a "carbon isolated" bone, we compare the 14C/12C concentration we find in this bone with current atmosphere concentration, then, if the 12C concentration in the atmoshere is doubled, No=14C/12C is halved and the bone age results 5568 years.

• Thanks Simon for your reply! But 3113 years is quite low.... If the half life period is already 5568 years, it means, the concentration of C14 is decreased by 2 after 5568 years and by 4 after 2 x 5568 years = 11136 years. And here, we are well facing to that latter situation: concentration of C14 has been decreased from 0.8 to 0.2 10^-12.

• Thanks for your replay  ! Answer to question 1 is indeed correct (11136 years). I don't know if there as still mammoth alive at the time of Homer or pyramids constrution in Egypt... May be in Siberia?

On question 2, I agree there can be many assumption with unknowns like how fast and where (? only in the upper atmosphere level)  the C12 atoms are transformed in C14? By assuming the C12 generated by the human actvitiies, thus only in the very last 50 years and by assuming those additional C12 have not the time to reach the upper atmoshere layer, we can then extrapolate the C14/C12 ratio appears much less than it should be; thus giving a longer age

Answer to question 1 is right!

On question 2, I agree there can be many assumptions with unknowns like how fast and where (? only in the upper atmosphere level)  the C12 atoms are transformed in C14? By assuming the C12 generated by the human actvities, thus only in the very last 50 years and by assuming those additional C12 have not the time to reach the upper atmosphere layer, we can then extrapolate the C14/C12 ratio appears much less than it should be; thus giving a longer age to our bone...

• Right Gaetano for question 1!

On question 2: I am not sure.... If the concentration of C12 is more than expected, this means the ratio C14/C12 is decreased. And if it decreases, it means we will conclude for a much linger date (and not shorter. Do you agree?

• OK guys, let's publish the "official" answers. Most of you gave the same and right answer of 11136 years old for the bone.

Reasoning is :

The decay of radioactivity obeys the first order partial derivative law:

-dN/dt = k.N            where N is the concentration of the radioelement, k is the decay speed constant and t is the time variable

Solving the equation :

Ln(N/No) = -k.t or N = No. Exp(-kt)         with No the initial concentration at t=0

Let’s call T the half-period live time of the radio element.

Per definition of T, we can write; No/2 = No.Exp(-kT) or k = Ln(2)/T

For C14, T=5568 years and hence k = 1.2449 10-4

Age of the bone is given by: N/No = Exp(-t.Ln2/T)

t = Ln(No/N) * (T/Ln2) = Ln(0.8/0.2) * 5568/Ln2 = 11136 years

On question 2, it is subject to interpretation...  There are many assumptions with unknowns (at least for us, the non-specialist of nuclear science) like how fast and where (? only in the upper atmosphere level ?)  the C12 atoms are transformed in C14?). By assuming the C12 generated by the human actvities (thus only in the very last 50 years) and by assuming those additional C12 have not the time to reach the upper atmosphere layer, we can then extrapolate the C14/C12 ratio appears much less than it should be; thus giving a longer age.

With C12 "artificially" doubled, the concentration C14/C12 is halved. This is in fact an additional haf-life period. Our bone will then be dated at 11136 + 5568 years = 16704 years

Not so easy this one!

Congratulation to all having found at least the first answer! And big applause to our 4 winners:

Barry Kulp,  ,

And now, be ready for the next coming challenge (this time we will be back to our fundamentals that is Electronics...