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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]
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• 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...

• 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...

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