Carbon-14 Dating

Question

The C-14 content of an ancient piece of wood was found to have three tenths of that in living trees (indicating 70% of the C-14 had decayed). How old is that piece of wood?

Answer 1

Hi John,

 

The half-life for Carbon-14 is 5,730 years. This means that every 5,730 years, we halve the amount of C14 we have.

 

At time=0, our C14 level is 100%. At time = 5,730 years, we have 50% of the C14 left. At time = 2x5,730 we have 25% of our C14 left.

 

So the piece of wood is between 5,730 and 11,460 years old.

 

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To get a more specific answer, you can use the half-life formula.

 

Amount Remaining = Initial Amount x (1/2)^(age of specimen/half life)

 

In our case, Amount Remaining/Initial Amount = 30% = 0.3. Therefore:

 

0.3 = 0.5 ^ (age/5730)

 

We can take the logarithm of both sides, then simplify and solve for the age of the wood specimen:

 

ln(0.3) = (age/5730) x ln(0.5)

 

ln(0.3)/ln(0.5) = age/5730

 

1.73 = age/5730

 

age of wood = 1.73*5730

 

age of wood = 9,952 years.

 

I hope that helps, and please let me know if I can help clarify anything! Best of luck.