THE AGE OF THE EARTH
Clarence L. Dulaney and Patrick L. Dulaney
e-mail cldtx1@sbcglobal.net e-mail dulaneyp@comcast.com
ABSTRACT: Finding the age of the earth and of historical artifacts such as fossils, and of archaeological specimens has long been of interest. Because some radioactive elements have very long lived species, attempts to use the decay of these elements to measure age has been accepted as the “benchmark”. This paper discusses why such methods, except for “radiocarbon” dating, have questionable accuracy for measuring the age of the earth.
ORIGIN
OF THE EARTH
Note: references are given as [a.xxx],
where a is the reference number and xxx is the page
number.
Probably the most cogent theory of the origin of the
earth is that it was formed, along with the rest of the solar system by
aggregation of particles of a “cosmic dust cloud”. [1.12-37].
It is here proposed that the “cosmic dust cloud” was
a result of the disintegration of a large star, which became a supernova. It would be hard to otherwise explain the
local concentration of enough total elements to make up the solar system. It is further postulated that all of the
elements present on earth are resultant from and were formed in the precursor
star.
The chemical composition of the large precursor star
varied from Hydrogen to Uranium, with all the “stable” isotopes in between,
with stable indicating those that have half lives greater than 108 years. This includes K40 and U238. All these isotopes had to have been built up
by fusion of various isotopes with hydrogen [2.251]. In the buildup of elements in a star, the
fusion to form isotopes is exothermic up to 26Fe [2.254].
Once a core of iron builds up, the star becomes hotter, and the
endothermic production of the higher elements proceeds. Elements higher than U have very short half
lives. Roughly equal numbers of atoms of
the stable elements with higher atomic numbers than iron are produced, with
those of even atomic number generally being of larger concentration than those
of odd atomic numbers [1.19,22].
Note that, in the solar system, only the sun has
ever been hot enough to support fusion reactions, so that all the elements in
the planets came from the precursor star, (including those from meteorites)..
As the solid earth formed, it almost undoubtedly was
molten, with temperatures of 1500-3000K being proposed [1.54]. There was not enough Oxygen to oxidize all
the metals present, particularly the Fe, Co, and Ni. These metals, being molten,
and heavier than the oxides sank to the center of the mass, and became the core
of the earth. Those elements with higher
heats of formation of oxides than that of FeO were
oxidized and became “lithophiles”, which later became
the earth’s crust when sufficient cooling
occurred.
All the alkali metals,
alkaline earths, rare earths, silicon, Al, Sc and particularly U and Th (among others)are lithophiles [1.51].
When the “original”, molten earth
cooled enough, the composition of the lithosphere was “frozen”. There was almost undoubtedly some inclusion
of atmospheric gasses in the very viscous magma. Estimates of the time the primordial earth
was entirely molten until the crust was formed vary from a minimum of several
thousand of years up to hundreds of thousands of years [1.56].
Once the crust was “frozen”,
the composition of various radioactive systems were fixed,
as far as a basis for radioactive dating of the earth was concerned.
This paper is particularly
interested in two decay cycles, that of K40-Ar40, and U238-Pb206. The latter
cycle goes through several steps, with an overall half-life of 4.5 x 109 years. Note that one of the
intermediates is the gas Rn [3.285]. That of the K40 system has a half-life of
1.25 x 109 years.
Particularly in the case of
the K40 system, for “dating”
purposes, it is assumed that there was no Ar40 in the rock initially, and that any that is found
came from decay of the K40. It is also assumed that the system was ‘closed”
throughout, that there is no loss or gain of K or Ar
throughout the history of the rock. (Note that virtually all K compounds are
water soluble.) If there was no loss or
gain, the general formula for the age of the rock A is: A = (t½/ln2) (ln(1+(D/P))) where ln indicates logarithm to the base e. A is in the same units as t½. D is the number of atoms of the daughter
element (Ar40) and P is the number of
atoms of the parent isotope (K40) at the time of analysis. Thus, in a closed system not subjected to any
outside forces, where there is absolutely no loss of any of the “daughter
elements” age can be relatively accurately estimated.
ANOMALOUS K40-Ar40 DATES
Lava samples obtained from
Mount Nguruhoe in New Zealand from known eruptions
dating back to 1949 were sent to a commercial dating laboratory, Geochron Laboratories in Cambridge, MA, with the notation
that they were “probably young, with little Ar in
them” [4]. The measured ages were
reported to be from 0.27 to 3.5 million years.
This indicated that there must have been some Ar
in the hot lava, and it must have remained there after the lava solidified.
These results cast serious
doubts on dates obtained on older, unknown history, samples. Either the Ar was
present in the lava and not evolved while it was molten, or was included from
atmospheric contamination with the 0.9% Ar of the
air.
It is here proposed that
some Ar could have been included in the primordial
magma, and that there may have been “reaction” between the very electropositive
alkali metals and the “inert” Ar in the high
temperature melt. There may have also
been the same sort of inclusion in the molten lava.
THE U238-Pb206 SYSTEM
In this system there would
definitely be some Pb206
present in the primordial system. To
determine the age of this system, it would be necessary to know the amount of
Pb206 initially present. One method of determining this amount would
be to use the concentration of the stable, non-radiogenic isotope Pb204 in the present sample,
along with an estimate of the Pb206/Pb204 initially present.
This ratio has been determined on an ancient sample of galena, PbS, and was found to be 16.25
[3.290]. (This is fairly close to the
ratio in current Pb, with a Pb204 content of 1.48% and a Pb206 content of 23.6%, for an
atomic ratio of 16.10 [5.B481].)
Thus, the age A of a U238-Pb206 sample would be:
[3.287ff] A = (1/1.55125 x 10-10) x (ln(1+((Pb206/Pb204) – (16.25))/(U238/Pb204))). The 16.25 is the initial lead isotope ratio,
and all the other concentrations are the number of atoms in the current sample
There are several doubtful
assumptions tacitly made in this analysis.
As Faure himself pointed out, (We give a paraphrased
quote applying only to this system), “For the formula to hold, 1. The
mineral has remained closed to U, and Pb, and to the
intermediate daughters throughout history.
2. Correct values are used for the Pb isotope
ratios. 3. The decay constant for U238 is known accurately. , and 4. All
analytical results are accurate and free from systematic error”.
In regard to closed systems,
it is known that the U in the lithosphere is close enough to the surface that
it is impossible to date samples by amount of He in the rocks, because of loss
of He by evaporation [3.283]. (Note also
that the gas Rn is a daughter product, and might also
be lost in the same manner.)
Secondly, in most cases, at
least some of the U is oxidized to the uranyl ion (UO22+), for which most salts are
water soluble. This could lead to loss
(or gain) of U in samples,
Concerning the Pb isotope ratio, it would seem that the initial
concentration of Pb204
would at least be equal to that of the Pb206, at least in the star where both were made only by
fusion. If the star were old enough that
a considerable amount of U238
had decayed, then the Pb206
would be higher.
The reason that the Pb206/Pb204 ratio is 16.25 may be that
all the daughter elements of U238 have fairly short half lives, with the longest
being 2.5 x 105
years, and many having half lives less than a year. In the large stars, fusion builds up these
daughters, which in turn rapidly, (compared to the life of the life of the
star), decay to Pb206,
while the number of atoms of Pb204 remains virtually the same. Of course, the fusion goes on to U238, which builds up at
slightly less rate than the Pb204. (There are 18 daughters, as shown by Figure 18.1 by Faure [3.285]).
This again indicates that the radiometric agers
are measuring something pertaining to the age of the large precursor star.
Other samples that are used in dating are U235-Pb207, t½ = 7.04 x 106 years, Th238-Pb238, t½ = 14 x 109 years, Rb87- Sr87, t½ = 48.8 x 109 years, and Sm147-Nd143, t½ = 106 x 109 years. In any of these systems, the analytical problems
are formidable, and there are the same sort of questions about “closed systems”
and initial daughter concentrations.
The age of the original star may actually be what is measured rather
than that of any system on earth. It is interesting that many
of the estimates of the age of the oldest earth rocks by different methods all
give around 4 x 109
years, which is believed by us to be that of the precursor star..
CARBON14 DATING
In measuring ages less than
50,000 years, the decay of isotope C14 is usually measured, following the work of
W. F. Libby in 1949 [6].
There is roughly a constant
amount of C14 in the atmosphere in the
form of C14O2. 1 x 10-10 % of the
total atmospheric CO2. The generally accepted mechanism for
generation of C14
is high altitude absorption of a neutron by N14 which then becomes C14 by emission of a
proton. Then the C14 is oxidized to CO2. It is here proposed that a more plausible
scenario is that the isotope is made at any altitude by striking of a C13O2 molecule by a high speed H atom (from “cosmic rays”). C13 amounts to about 1.1% of ordinary Carbon and is a
stable isotope.
At any rate, C14O2 is present in the
atmosphere and is metabolized by plants in a proportional amount with the
normal CO2. Animals eat the plants and thus also acquire
an amount of the radioactive isotope.
When the plants and animals
die, the C14 begins to decay with a
half-life of 5730 years. By measuring
the amount of isotope remaining in the sample, the time since the sample was
alive can be estimated.
Not all organic samples give
meaningful results, particularly samples that came from, or have been covered
by water, because the carbon dioxide makeup in seawater is significantly
different from that of the atmosphere.
For example, it would be impossible to correctly determine the date of
coral beds.
Also, after about 10
half-life periods, the radioactive isotope content falls so low as to be
essentially non-measurable. Thus C14 dating does not work at all
for samples over about 50,000 years old.
Several methods are used to
measure the C14 content of a sample. The sample is generally burnt to produce CO2, and the CO2 recovered by
absorption. Then the radioactivity can be
counted directly. Other methods include
converting the carbon dioxide to acetylene, and measuring the amount of C14 directly by mass
spectrometry. Since the C14
content of even recent samples is very low, analytical techniques must be very
sophisticated.
Carbon dating has been
compared with known historical dates with some success. In particular, the carbon age of acacia wood
from Pharaoh Djoser’s tomb gave results within 10% of
the historical date[7].
Dates obtained by C14 measurements are probably
good up to 40,000 to 50,000 years, but this assumes the atmospheric content of
C14O2 has been constant over this
period of time.
Basically the only thing
that can be said about the age of the earth is that it is between 40,000 and
about 4 billion years.
Since the age of the
precursor star is probably about 4 billion years, the universe must be at least this old.
CONCLUSIONS
Measurement of the age of
ancient rocks by radiometry is questionable, because it is not known how large
a concentration of “daughter” atoms was present in the primordial rock, and because
it cannot be guaranteed that the rock has remained a “closed system” throughout
its entire history. The oldest ages
being measured are likely that of the precursor star.
It is possible to estimate the age of organic matter
that is less than about 40,000 years old by means of C14 analysis.
The age of the earth cannot be estimated more accurately than between 40,000 and about 4 billion years.
REFERENCES
1. B. Mason, “Principles of Geochemistry”, John
2. E. Novotny, “Introduction to Stellar Atmospheres and Interiors”,
Oxford U. Press,
3. G. Faure, “Principles of Isotope Geology”,
2nd Ed., John Wiley & Sons, NY, (1986)
4. A. Snelling, Creation Ex
Nihilo. 22, (1), 18, December 1999, February 2000
5. “Handbook of Chemistry and Physics”, 35th Ed., R. Weast, Ed., Chemical Rubber Co., Cleveland, (1972)
6.W. Libby,
7. W. Libby, “Radiocarbon Dating”,
© 1/26/03
Clarence L. Dulaney
Patrick L. Dulaney