Carbon-14
serves as an atomic clock capable of determining the age of archeological
artifacts up to about 50,000 years old. It is used to date objects such
as bone, cloth, wood and plant fibers.
Innovator
As a member of the Manhattan Project (1941-45), Willard
Frank Libby (1908-1980) helped develop
method for separating uranium isotopes--an essential step in the creation
of the atomic bomb. In 1946 he showed that tritium, the heaviest isotope
of hydrogen, was produced by cosmic radiation. The following year he developed
the carbon-14 dating technique. This technique is used to date material
derived from former living organisms as old as 50,000 years. It measures
small amounts of radioactivity from the carbon-14 in organic or carbon-containing
materials and is able to identify older objects as those having less radioactivity.
Awarded the 1960 Nobel Prize in Chemistry for radiocarbon dating, the nominating
committee offered the following in praise of Libby:
"Seldom
has a single discovery in chemistry had such an impact on the thinking
of so many fields of human endeavor. Seldom has a single discovery generated
such wide public interest."
Producing Carbon-14
Cosmic rays collide with atoms in
the upper atmosphere producing energetic neutrons. When these neutrons
collide with nitrogen (7 protons/7 neutrons), carbon-14 (6 protons/8 neutrons)
is produced:
Being radioactive, carbon-14 eventually
decays to form nitrogen-14 and a beta particle (high speed electron).
While one can’t predict exactly when a particular C-14 atom will emit
an electron and turn into N-14, the statistics are very
predictable. Given a large number of C-14 atoms, we can say with a
high degree of confidence that half of them will turn into
N-14 in 5,730 years. This is called the “half-life” because half of
the C-14 will turn into N-14. Half of the remaining C-14 turns into N-14
in another 5,730 years. The half-life is a convenient concept for getting
a general feel for how fast radioactive elements decay, but it isn't very
convenient for calculating the amount left after an arbitrary period of
time. For example, how much will be left in 2,000 years? An equation
is needed to predict how much is left at any particular time, not just
multiples of the half-life.
Equation
Carbon-14 atoms combine with oxygen
to form carbon dioxide; the ratio of normal carbon (C-12) to C-14 in the
air and in all living things at any given time is nearly constant (about
one in a trillion carbon atoms are C-14). Although C-14 atoms are always
decaying, they are replaced by new C-14 atoms at a constant rate. At this
moment, your body has the same percentage of C-14 as all living plants
and animals. However, when a
living organism dies, it stops taking in new carbon and the ratio of C-14
to C-12 decreases (C-14 decays with a half-life of 5,730 years while stable
C12 remains constant). By measuring the ratio of C-12 to C-14, it is possible
to determine the age of a formerly living object.
Decay of C-14 follows
first-order kinetics:
ln
(A0/At) = kt
k = 0.693/t1/2
(t1/2 =
5,730 yr)
where A0/At
is ratio of C-14 in currently living objects compared to C-14 in sample
Substituting 0.693/t1/2
for k gives:
ln
(A0/At) = (0.693)t/t1/2
or t
= (t1/2)[ln(A0/At)]/0.0693
For example, an object with
1/10 C-14 content compared to a living sample would be about 19,000 years
old:
t = [5,730 yr][
ln (10)/(0.693)] = 19,000 yr
To determine how much C-14 is left
in an object and therefore how old it is, we count the number of beta radiations
given off per minute per gram of carbon. Modern C-14 emits about 15 beta
radiations per minute per gram while objects 5730 years old emit half that
amount per minute. So if a sample taken from an object emits 7.5 radiations
per minute per gram, the organism must be 5730 years old. The accuracy
of radiocarbon dating was tested on objects with dates that were already
known through historical records such as parts of the dead sea scrolls
and some wood from an Egyptian tomb. Analysis showed that C-14 agreed very
closely with the historical information.
Dead Sea Scrolls
Between 1947 and 1956 thousands of fragments of biblical and early
Jewish documents
were discovered in eleven caves near the site of Khirbet Qumran on
the shores of the Dead Sea. Carbon-14 dating of samples taken from ragged
edges of manuscript margins determined the ages of the scrolls to range
from the third century B.C. to 68 A.D. These dates support earlier paleographic
research, which estimated the ages of the scrolls by analyzing the handwriting
styles, materials, and formatting of the manuscripts.
Limitations
Martian Meteorite
The principle of carbon-14 dating
applies to other isotopes including: