Carbon 14 Dating
~Regular carbon or Carbon 12, as researchers call it, is an
element which is found in all living things. But elements can come
in unstable forms, called isotopes. Isotopes have extra neutons in their nuclei, and are often
radioactive.
Carbon14 is an isotope of the regular stable element Carbon
12. This
is due to the interaction of cosmic rays in the upper
atmosphere. The earth consists of approximately 99% of regular Carbon
12 and trace amounts of carbon 14. Carbon 12 has 6 neutrons & 6
protons while carbon 14 has 8 neutrons & 6 protons. This makes
carbon 14 unstable and radioactive. Organic life absorbs Carbon 14
and Carbon 12 (stable form of carbon) through the atmosphere as
long as it is living. Once it dies, both forms of carbon are no
longer absorbed. The level of Carbon 12 in the dead matter remains
constant while the level of Carbon 14 decreases due to its unstable
nature (it decays). Therefore, the percentage of Carbon 14 found
decreases and the constant ratio of C14 to C12 decreases from
this natural constant amount. By measuring this decrease, the age of
the organic sample can be estimated.
~This is the method of Carbon 14 dating (technically
called Radiocarbon Dating). How this is
done mathematically will be shown in a simple example at the end of
this discussion.
~The "half-life" of a radioactive substance is the amount of time it
takes for half of the amount present (at any given time) to
dissapear. For Carbon 14, it
takes quite a long time, some 5,600 years. Many other radioactive
materials have very long half-lives as well. This is a major problem
facing our
present civilization today (what to do & how to store this
material). It turns out, only a vast amount time will eventually
eliminate this radioactive material...much too long to wait. For carbon
14, it will take roughly 60,000 years to eliminate all
significant amounts. That means, life-forms existing at that time or
before are not subject to Carbon 14 dating. There are similar dating methods using isotopes of other elements
that have longer half-lives to date artifacts older than the limits of the Carbon 14 method.
~Knowing the constant ratio of Carbon 14 to regular Carbon 12 during the
life of the item and by measuring the lower ratio of Carbon14 to
regular Carbon 12 when an artifact is found, lab techniques can be used to
determine how long the Carbon 14 has been decaying, consequently, how
much time has passed since it's death.
~For example, bones and other organic material from an ancient
civilization could be dated to
determine their ages. Researchers, particularly archaeologists, often
use
this technique for dating, usually within 50,000 years. Beyond that
time, other radioactive elements are used that have a longer half-life
since the amount of C14 left is insignificant.
~Some historians believe The Shroud of Turin
(claimed to be the burial cloth of Christ), is a fake. Carbon14 testing
has dated it to the middle 13th century-14th century. That's the same
time it was claimed to be found, suggesting that it was a forgery. This
controversy still remains today.
UPDATE: The latest scientific experiments using carbon dating and additional blood spatter patterns have confirmed that the Shroud is a fake.
Not all, including religious sectors, agree with these results and continue to believe in its authenticity.
~The mathematics behind simple growth/decay is not
that involved. From the rate of change (derivative of the amount of
Carbon 14 present with respect to time) we can find an exponential
equation relating the quantities. Knowing the half-life of the
substance, we can estimate the unknown constant in the equation.
Consequently, relating the variables directly. Hence, time can be
estimatied. All of this is programed in the lab techniques used for
this method.
~Simple example: A bone
is found during an excavation to contain 54% of the carbon 14 normally existing naturally (i.e., 54%
of the original amount of Carbon 14 is remaining). Using
the half-life of 5600 years for Carbon 14, estimate the age of this
bone.
Since the time rate of change of the amount of Carbon 14 is
proportional to the amount present at any given time t, we have this
simple differential equation:
dN/dt = kN, where N=amount of carbon 14 present at any time t.
Separating the variables and integrating, we get: ln(N)=kt +C
At t=0, let No represent the amount of carbon 14 present, so we
can represent the constant C as ln(No). Replacing this constant and
solving for N, we get: (I'm calling this equation A)
(A) N = No e(kt) (this is the basic form for simple growth/decay)
or N/No = e(kt). Since the ratio N/No = .54, we
substitute this value into the above equation and solve for t in terms
of k. We get:
(I'm calling this equation B)
(B) t= (ln.54)/k or approximately, t= -0.616186/k. Now, for the half-life.
Substituting (1/2)No for N and 5600 for t in equation (A),
we get k = -0.0001238 (this is called the decay constant for C14)
Note: Decay constants are determined by the half-life of the radioactive substance used in the procedure.
Therefore, Using this value in equation (B), we get, t = 4977 years approximately.