Radioactive Isotope Dating

The evolution of radioacive isotope dating began with, physist Lord
Rutherfords', work on the structure of the atom, 1905.  Radiochemist B.B
Boltwood built from this idea a geologic time chart measuring in units of
hundreds to thousands of millions of years based on radioactivity. The
discovery of nuclear fission and fusion from atomic research performed with
respect to the behavior of atoms led to the development of techniques used in
age dating the Earth's material constituents.

The process of radioactive age dating stems from the atomic nature of some of
the 94 natural occuring elments.  These particular elements are made up of
atoms containing a specific number of protons in there nucleus but having
different atomic masses due to varing numbers of neutrons.  An isotope is an
atom with the same atomic number but with a different atomic weight.  These
isotopes are subject to spontaneous decay.  Where the isotope, a parent, loses
atomic particles from its nuclei to form an isotope of a new element, the
daughter.  This rate of atomic decay is known as the radioactive half-life. 
Particular isotopes with slow rates of decay can be used as geologic clocks.

One of these geologic clocks is based on the radioactive decay of the
carbon-14 isotope.  The carbon-14 isotope si formed in the upper atomoshere by
a collision between a neutron and the nucleus of a nitrogen-14 isotope.  This
radioactive form of carbon is subject to spontaneous beta decay.  This process
occurs very slow, where the the half-life is 5730 years for C-14 to change
back to N-14.  This form of radioactive dating is very useful in formulating
an age for samples ranging in age from 50,000 years to the present.  Which is
an extremely useful tool in dating the history of man and other recent
pre-historical events because all material that was once living contains this
carbon isotope.

A more prevallent method of radioactive dating, with reguards to geology, is
the potassium-argon method.  This technique is based on the detected ratio of
Ar-40 to K-40.  Roughly 89% of K-40 converts to Ar-40 through electron
capture.  Resulting in a half-life of 1.25 billion years.  However, this form
of dating can only be applied to rocks which were solidified from a molten
state, ie: igneous.  This is do to the slow solidification of molten material,
where dissolved gasses are displaced from a crystalline solid which forms
because the gas molecules are released from there positions in the crystalline
lattice structure.  It is this tightly bonded lattice that which the decaying
K-40 daughter product Ar-40 gas, is trapped in the newly formed crystalline
matrix.

The process for geologically dating igneous rocks, by way of the
potassium-argon method is explained as follows. Potassium is found in almost
all rock forming minerals.  For example, igneous rock makes up roughly 80% by
volume of earth's crust and we know that the earth's interior material gets
progressively more molten with increasing depth to the core.  And feldspars
make up roughly 60% by volume of the continents.  And furthermore feldspars
are almost always present in igneous rocks.  There are two categories of
feldspars; plagioclase feldspars (Na rich) and alkali feldspars (K rich).     
With this obvious abundance of rock material containing potassium it is
apparent that this form of age dating is imparitive in geologically dating the
Earth and the material of which it is made up of. Material canidates for
potassium-argon dating are pulverized in an evacuated container where a
machine called a mass spectrometer compares the ratio of Ar-40 to K-40.  The
resultant amounts are then calculated using the formula, Pt= Po ^-lambda(to-t)
where Pt is the quanity of parent isotope at t=0, Po is the quanity of the
parent isotope at some earilier time to, when the isotopic system was closed
to any additional isotopic changes, lambda is the decay constant for the
system.  The decay constant of each parent isotope is related to its half-life
by the expression  t^1/2= ln2/lambda.

Radioactive isotope commonly used in determining the age of rocks. 
isotope               half-life(years)              daughter product

K-40                  1.3 billion                   Ar-40
U-238                 4.5 billion                   Pb-206
U-235                 713 million                   Pb-207
Th-232                14.1 billion                  Pb-208
Rb-87                 49 billion                    Sr-87
C-14                  5730 thousand                 N-14

PROBLEM:
The Nyquist et.al. (1979) obtained the following isotopic data for a (WR)
sample from Apollo 12 lunar basalt 12014,

              ^87 Rb/^86Sr        ^87Sr/^86Sr
WR            0.02960             0.70096

Calculate the age of this rock.  What is the (^87Sr/^86Sr)o value.  If present
day bulk earth value is 0.7044 and the pristine mantle is thought to be
0.6988, what can be concluded about the origin of the moon and its
relationship to Earth.