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Wize University Physics Textbook (Master) > Modern Physics

Carbon Dating

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Carbon Dating




The Carbon-14 isotope  614C_{ \ 6}^{14}C is being used for radioactive dating.

It is produced in the upper atmosphere. The abundance ratio of Carbon-14 to Carbon-12 is constant, and its value is 1.3×10−121.3\times10^{-12} in living organisms.

As soon as the body dies, this ratio changes due to the fact that no more Carbon-14 is absorbed by a living body.

Since Carbon-14 decays, if you know the initial and final ratios of  614C_{\ 6}^{14}C in the tissues you can find the age.


Wize Concept
Carbon-14 undergoes beta negative decay.










Exam Tip
The half-life of  614C_{\ 6}^{14}C is about 57305730 years.


Watch Out!
You can only use carbon dating when the age of the object is comparable to the half-life. For example, you cannot use it for things that are not very old (e.g. a few years), or things that are too old (e.g. millions of years).

Example: Dating Charcoal


A piece of charcoal found in an archaeological site contains 64%64\% as much Carbon-14 as a modern day piece of charcoal. How old is the sample? (Use a half-life of 57305730 years)


We have a final value equal to 64%64\% of the initial, which means that N=0.65 N0N=0.65 \ N_0.

  • Let's put this in the half-life equation:

N=N0(12)tthalfN=N_0\bigg(\dfrac{1}{2}\bigg)^{\frac{t}{t_{half}}}

0.64 N0=N0 (12)t57300.64 \ \cancel{N_0}=\cancel{N_0} \ \bigg(\dfrac{1}{2}\bigg)^{\frac{t}{5730}}


  • Take the ln⁡\ln of both sides:

ln⁡0.64=ln⁡(12)t5730\ln 0.64=\ln \bigg(\dfrac{1}{2}\bigg)^{\frac{t}{5730}}

ln⁡0.64=t5730×ln⁡0.5\ln 0.64={\dfrac{t}{5730}}\times\ln 0.5


  • Isolate the time:

t=5730×ln⁡0.64ln⁡0.5t=\dfrac{5730\times\ln 0.64}{\ln 0.5}

=3689=3689 (yrs)

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Practice: Find the Half-Life


The radioactive decay of carbon-14 is given by the equation: N=N0 e−ln⁡25370 tN=N_0\ e^{-\frac{\ln2}{5370}\ t}. Algebraically find its half-life.