Themes > Science > Chemistry > Nuclear Chemistry > Nuclear Chemistry Index > Radioactive Dating


Radioactive dating is a method of determining the age of a material by the ratios of various radioactive isotopes in the sample. (It has nothing to do with that blind date your "friends" arranged for you.) Depending on the isotope involved, this technique can be used to date sample ranging from a few years to billions of years.

The best known example is radiocarbon dating. 14C is a radioactive isotope of carbon. It is a beta emitter with a half life of about 5720 years. It is produced in the atmosphere by high energy cosmic rays and has a concentration of about 1 14C atom for every 1012 12C atoms in the atmosphere. So long as something is living, it is taking in CO2 from the atmosphere or from eating plants that took in the 14C. Thus, the amount of 14C in the plant or animal stays the same as the amount in the air, even though the 14C in the plant or animal is constantly disappearing due to radioactive decay . When the plant or animal dies, the exchange stops and the amount of 14C in the plant or animal becomes fixed. The remaining 14C in the plant or animal then decays as normal to 14N, but is no longer replaced. By looking at the amount of 14C in the sample, we can determine the time at which the exchange of 14C stopped: i.e., the time that the plant or animal died.

A normal 1.0 gram sample of carbon has an activity of 13.6 atoms/sec due to 14C. Since activity is proportional to the amount of a substance, we can use the first order kinetics law expressed in terms of activity to determine the age:

ln(A0/A) = k*t
where A is the activity of a 1 gram sample of the material to be dated, A0 is the activity of a 1 gram sample of the material with the initial radioactivity (13.6 atoms/sec, in the case of carbon) and k is the rate constant.

(In reality, the concentration of 14C has varied over the years and careful dating must correct for this, but this is outside the scope of this discussion.)

Other decay patterns can be used to date things older than 14C allows. For example, the decay of 238U to 206Pb is a 14 step process that takes 4.5 billion years. Comparing the ratio of uranium to lead in a rock will give a date that the rock was formed.

Example: 146C is a radioactive isotope of carbon with a half life of 5720 years. If you have a sample of linen (made from flax plants) that has an activity of 9.65 atoms/sec for a sample containing 1 gram of carbon, when were the flax plants harvested?

Solution: We need to get the rate constant before we get the age: we use the relationship between half life and the rate constant k:

k = 0.693/t1/2
k = 0.693 / 5720 yr
k = 1.21*10-4 1/yr
Next, simply use the above equation and solve for the time:
ln(A0/A) = k*t
ln(13.6/9.65) = 1.21*10-4 1/yr * t
0.343 = 1.21*10-4 1/yr * t
t = 2.84*103 years
The flax was harvested close to 3000 years ago.


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