2.1 Antiquity of the Earth (continued)
(3) Conventional Techniques of Radiometric Dating. There are seven radiometric techniques used to date rocks. The carbon-14 (C-14) method is used to date specimens that are 40,000 years old or younger. Methods used to date rocks one million years of age and older include: uranium-238/lead-206, uranium-235/lead-207, thorium-232/lead-208, lead-207/lead-206, potassium-40/argon-40, and rubidium-87/strontium-87. Tables 2.1, 2.2, and 2.3 represent the sequences of events and half-lives of the uranium-238/lead-206, uranium-235/lead-207, and thorium-232/lead-208 series with respective half-lives of 4.51 x 109, 7.1 x 108, and 1.39 x 1010  years. Figure 2.3 depicts the decay curves of each of these three series.
Table 2.1. The 238U (Uranium) series. Decay
constant of 238U is 1.54 x 10-10 per year.*
*NOTE: Adapted, with permission, from Hamilton, E. I.
London: Academic Press Inc.; 1965. © 1965 E. I. Hamilton.
Table 2.1 400dpi 120k
Table 2.2. The 235U (actinium) series.
Decay constant of
235U is 9.71 x 10-10 per year.*
*NOTE: Adapted, with permission, from Hamilton, E. I. Applied geochronology.
London Academic Press Inc.; 1965. © 1965 E. I. Hamilton.
Table 2.2 400dpi 100k
Table 2.3. The 232Th (thorium) series. Decay
212Th is 4.99 x 10-10 per year.*
*NOTE: Adapted, with permission, from Hamilton, E. I. Applied geochronology.
Academic Press Inc.; 1965. © 1965 E. I. Hamilton.
Table 2.3 400dpi 80k
(a) Uranium-lead, Thorium-lead, Lead-lead Methods. The uranium-lead and thorium-lead methods are based on the decay of uranium-238, uranium-235, and thorium-232 into lead-206, lead-207, and lead-208 respectively, all of which are stable isotopes. The decay of intermediate radioactive atoms in all three series is much faster than the decay of the parent atoms. Therefore, all the intermediate atoms are disregarded in the age calculation. A fourth naturally occurring isotope of lead, lead-204 (common lead) is not produced by radioactive decay, and it extremely stable. Uranium-238, uranium-235, and thorium-232 frequently occur together, allowing at least three independent age determinations from the same rock.
The lead present with each of the above samples may not have been derived from radioactive parents. The lead (common lead), assumed to have been present when the mineral was formed (Di in equation ), must be taken into consideration when age determination is to be carried out. This can be done by correcting for the amount of common lead in the sample. Geochronologists assume that when the earth was first  formed, the proportion of the three lead isotopes (Pb 206, 207, 208) was fixed with respect to common lead-204 (25).
Figure 2.3. Decay curves for uranium - 235, uranium - 238, thorium - 232.
 Figure 2.4. Graphs showing changes in isotope ratios in common lead in the earth during the past 4.5 billion years. Curves are based on mass spectrometric analysis of many samples. Individual data points are not shown. Reproduced, by permission, from Harbaugh, J. W. Stratigraphy and the geologic time scale. 2nd ed. Dubuque, IA: Wm, C. Brown Co. Publishers; 1974: 168. © Wm. C. Brown Co. Figure 2.5. Graph showing ratio of lead-206/uranium-238 with respect to time. Reproduced by permission, from Harbaugh, J. W. Stratigraphy and the geologic time scale. 2nd ed. Dubuque, IA: Wm. C. Brown Co. Publishers; 1974: 168. © 1974 Wm. C. Brown Co
In making age determinations it is necessary to subtract the common lead from the radiogenic lead. Two things have to be kept in mind in doing this: the approximate age of the mineral and the proportion of lead-204. By referring to Figure 2.4, one can deduce the amount of lead 206, 207, or 208 that is associated with the common lead. Then by subtracting these quantities from the age equation (10), a more precise age can be determined. Figure 2.5 represents the age determination by uranium-238/lead-206 after corrections have been made.
In addition to the uranium-thorium-lead ratios, the ratio of lead-207 to lead-206 is useful in age determination. Since the half-life of uranium-235 (0.7 billion years) is much less than that of uranium-238 (4.5 billion years), the amount of lead-207 produced by decay of uranium-235 increases much more rapidly than that of lead-206 produced from uranium-238. Consequently, the ratio of lead-207/lead-206 is a good indication of the age of rock and is useful for dating specimens half a billion years old or older. Moreover, the lead-207/lead-206 ratio is less likely to be affected by partial loss of lead due to erosion, for both lead-207 and lead-206 have essentially the same chemical properties; therefore, any loss of lead will probably be the same. A graph of lead-207/lead-206 ratio versus time is shown in Figure 2.6
(b) Potassium-argon Method. The potassium-argon method of age dating has certain advantages over the uranium-thorium-lead methods because potassium is more widely found among rocks in different areas. The element potassium consists of three isotopes, namely, potassium-39, potassium-40, and potassium-41, and only potassium-40 is radioactive. Potassium-40 decays via two alternate routes, but 88% of the time it decays into calcium-40 by emitting a beta particle while 12% of the time it decays by electron capture yielding argon-40. The half-life of either of these decay routes is 1.3 x 109 years. Therefore, age determination can be carried out either by potassium-40/calcium-40 ratio or by potassium-40/argon-40 ratio. But since nonradiogenic calcium-40 is ubiquitous, it tends to complicate the dating procedure. Therefore, the potassium-40/argon-40 ratio is used exclusively for dating purposes.
Argon-40 is a gas and is assumed to be absent from rocks during their formation because of their high heat. Extreme care is taken by geochronologists to insure the preservation of this gas in the rock. In order to insure against loss of argon gas, a new technique involving the conversion of potassium-39 to argon-39 is used. Neutron activation is followed by heating the sample in stages to release argon-39 together with the argon-40. In  a sample that has preserved the argon gas generated both radiogenically and artificially, the two isotopes are expected to reside in fixed proportion in equivalent crystal sites since they have both been produced from potassium. Therefore, the ratio of argon-39/argon-40 can be related to potassium-40/argon-40 in a simple way (26, 27). Care is also taken to detect the contamination of argon-40 by the argon in the air. The argon-36 isotope present in the air is used for the detection and subtraction of the amount of argon-40 absorbed by the sample from the air. However, since the leakage of argon-40 sometimes poses a problem in rocks that are known not to behave as a closed system, potassium-40/argon-40 dating is usually taken as the minimum age limit.
Figure 2.6. Graph of radiogenic lead-207/lead-206 ratio versus time. Reproduced, by permission, from Harbaugh, J. W. Stratigraphy and the geologic time scale. 2nd ed. Dubuque, IA: Wm. C. Brown Co. Publishers; 1974: 168. © Wm, C. Brown Co.
(c) Rubidium-strontium. The rubidium-strontium method is based on the decay of rubidium-87 to strontium-87 by the emission of a beta particle with a half-life of 4.7 x 1010 years. Rubidium-87 is much more abundant than potassium and tends to occur in minerals that are rich in potassium. Therefore, two independent dating methods can be applied to the same sample containing potassium and rubidium.
(d) Carbon-14. The carbon-14 decay clock is widely used for more recent samples (less than 40,000 years old). It is produced when a nitrogen-14 atom absorbs a neutron in its nucleus and in turn emits a proton. Carbon-14 decays by emitting a beta particle with a half-life of 5,730 years, reverting back to nitrogen-14. Carbon-14 is produced in the atmosphere above 3,000 feet where nitrogen-14 is subjected to bombardment by neutrons produced by cosmic rays, consisting of a large number of high-speed protons that collide with the atmospheric gases. Newly created carbon-14 atoms continually enter the world, and some of them  change into radioactive carbon dioxide. Some of the radioactive carbon dioxide is taken up by photosynthetic plants and enters the food chain of the living world. Thus, carbon-14 is present in all living materials and forms a major internal radioactive source inside the bodies of the organisms.
The carbon-14 dating method is based on the removal of the material containing carbon-14 from the world exchange reservoir of carbon. As soon as an organism dies and becomes fossilized, it will stop participating in the food chain of the living world. Therefore, the amount of carbon-14 trapped in the dead organism is limited and will diminish with time. The major assumption made in carbon-14 dating is that the carbon-14 in the world remains at a steady level, i.e., the rate of formation of carbon-14 in the atmosphere by cosmic rays is equal to the rate of the decay of carbon-14 that already exists. This assumption was used to calculate the number of disintegrations per minute (17.2 dpm) for the carbon-14 exchange reservoir in the earth, and it agrees closely with the observed rate of 16.1 + 0.5 dpm (28). Therefore, the assumption is a reasonable one. It is further assumed that the time required for exchange of carbon-14 in the organism with the environment is relatively short compared with the subsequent time that is to be measured after the organism has died. Thus, if a tree grew 200 years and yielded wood specimens that are 10,000 years old at present, the 200 years that the carbon-14 in the tree was exchanged with the environment is relatively short compared with the present age and will not enter into the calculation of age.
(4) Reliability of Age Determination and the Geological Column of
the Earth. The reliability of the age determination by radioactive
dating has been challenged (17, 23,
Arguments used to refute the validity of the radioactive dating methods
include: the lack of assurance of the absence of environmental interchange
in the uranium/lead and thorium/lead dated rocks; the inaccurate estimate
of the contamination of the potassium-40/argon-40 clock by the argon-40
in the atmosphere; the unwarranted assumption of the time index in common
lead; and discrepancy in the carbon-14 exchange equilibrium hypothesis.
While many of these criticisms may be justified, the close agreement of
the results of the various radioactive methods when used to date rocks
from different parts of the world impress many because of their reproducibility.
Table 2.4 lists a comparison of the ages of the rocks taken from different parts of the world as determined by five different radioactive dating methods. The agreement, except in the first case, was well within Å l0%, a degree of error commonly encountered in many scientific experiments. These ages are termed concordant ages because of their close agreement. There are well-documented cases of discordant ages, ages showing large  discrepancy as determined by different methods, but they are usually within a three- or fourfold difference (Table 2.5). Moreover the discordant ages seem to follow a regular pattern, and in some cases they can be explained by the contamination or loss of the parent intermediate, final products in the sample, or by the continuous diffusion of lead from the rock into the environment.
Table 2.4. Degree of concordance between age estimates determined by different methods.*The quantitative analytical techniques utilized by geochronologists have produced reliable information. The decay constants of most of the radioactive elements used in the dating methods can be known to within at least 5%, and in the case of uranium-238, uranium-235, and rubidium-87, the error is probably less than 3%. The ratio of isotopes can also be accurately measured to within 1-3% error. For example, five laboratories in the United States analyzed a sample from the Department of Geophysics of Massachusetts Institute of Technology. The reported values of argon-40 in the sample were all within 1% of the mean. In a critical sample, several duplicate analyses are routinely made, and intercalibrations on at least one sample were made by all laboratories involved in the dating process to avoid systematic errors (40). Therefore, gross experimental errors are eliminated.
*NOTE: Reprinted, by permission, from Harbaugh, J. W. Stratigraphy and the geologic time scale. 2nd ed. Dubuque, IA: Wm. C. Brown Company Publishers: 1974: 168. ©1974 Wm. C. Brown Co. Table 2.4 400dpi 132k
Recently six different methods of radioactive dating on the moon rocks,  namely, uranium-238/lead-207; uranium-235/lead-208; thorium-232/ lead-208; rubidium-87/strontium-87; argon-39/argon-40; and lead-207/lead-206, yielded dates of 4.70; 4.67; 4.60; 3.4-4.5; 3.7; and 4.75 billion years, respectively (41, 42, 43). These are in close agreement with each other and with the age of the earth that is estimated to be 4.5 billion years using the same methods.
Table 2.5. Concordant and discordant ages based on four dating methods. *NOTE: Adapted, with permission, from Hamilton, E. I. Applied geochronology. London: Adcademic Press Inc.; 1965. © 1965 E. I. Hamilton. Table 2.5 400dpi 275k
It has been charged that since some of the noble gases found on the lunar surface have been derived from the solar wind (a constant stream of particles from the sun), the potassium-argon dating of moon rock is unreliable (44). However, the potassium-argon dating was done with the interior portions of the crystalline rocks thus avoiding the outer portion of the rocks that may have been contaminated by the solar wind. Moreover, analysis of the ratios of the noble gases in the lunar surface showed that their concentrations were inversely proportional to the particle size. However, these ratios were significantly different from solar values. The ratios of the isotopes, on the other hand, were found to be similar to those in meteorites. Corrections using the solar values measured in the outer portions of crystalline rocks were routinely done in the potassium-argon dating method, and these solar corrections were found to be negligible in almost all cases (45, 46, 47).
The moon was believed to have been heated up "recently" to temperatures
between 1000°C and 1300°C. At such heat all the elements used in
radiometric dating would have been melted, thus rendering the dating methods
useless (44). This view apparently was not held in high
regard by the moon-rock scientists, for none of the articles in the "Moon"
issue of Science
(30 January 1970) referred to it. It was estimated,
Table 2.6. Comparison of ages obtained by radiocarbon dating with material of known ages. L (50, 51); B (52); C (53).* the moon was crystallized at a temperature range of 1140°C to 1170°C and that it had been reduced to a greater extent during crystallization than had the earth (48). The assumptions in the radiometric dating were apparently that the radiogenic elements were derived from components that surfaced during the process of crystallization. Since the surface of the moon is atmosphere-free (49), the erosion and diffusion processes that are usually associated with the contamination and loss of radioactive atoms in a sample rock are minimized. The remarkable agreement of the age of moon rock with that of earth rock increased the credence of the radioactive dating methods.
*NOTE: Reprinted, with permission, from Hamilton, E. I. Applied geochronology.
London: Academic Press Inc.; 1965. © 1965 E. I. Hamilton.
A comparison of the carbon-14 dated samples with known ages also indicated that the method is reliable within the limits of experimental errors (Table 2.6). Recently a new carbon-14 dating method was introduced that utilizes a cyclotron that increases the maximum determinable age to 100,000 years while reducing the sample size required. Scientists hope that this will increase the efficiency of the carbon-14 method (54).
A new method of dating human fossils too old for C-14 that depends on the constant rate of the racemization of amino acids has also been developed. This process changes an optically active compound that can rotate plane polarized light into an optically inactive or racemic mixture. Since only L-amino acids are found in living organisms, the D-amino acids detected on human fossils can be attributed to the process of racemization. Of particular interest in dating because of its long-time constant and ease of measurement is the reaction involving L-isoleucine and D-allo-isoleucine. L-isoleucine and D-allo-isoleucine are separable on the buffered columns of the automatic amino acid analyzer.
Constant temperature is the critical requirement in dating by racemization of amino acids. Using this method, fossils found in caves with relatively constant environments can be dated with only Å5 to 10% uncertainty. Samples within the C-14 range dated by this method have yielded concordant ages with those using C-14 dating. The maximum age that can be obtained by this method for caves with temperatures of 10°C and 20°C would be approximately 1.3 x 106 and 1.9 x 105 years respectively. This method has become quite useful for dating human fossils between 40,000 and 1 million years of age (55).
Each geological stratum in the earth's crust (geological column) has
been correlated with quantitative measurements of radiometric data, resulting
in the construction of a geologic time scale. Dated materials are used
as tiepoints between geologic strata in constructing the time scale. The
best candidates for tiepoints are layered volcanics, which consist of lava
flows and deposits of volcanic ash. They have the advantage of having 
Table 2.7. Radiometric dates that have been applied to geologic time scale.*
*NOTE: Reprinted, by permission, from Harbaugh, J. W. Stratigraphy and the geologic time scale. 2nd ed. Dubuque, IA: Wm. C. Brown Co. Publishers; 1974. © 1974 Wm. C. Brown Co. Table 2.7a 400dpi 520k Table 2.7b 400dpi 404k
 been deposited quickly, and often they occur interstratified within a sequence of fossiliferous sedimentary rocks, permitting an establishment of their position in relation to the layers of rock.
Furthermore, layered volcanics frequently contain minerals used in several radioactive dating techniques. Many volcanic rocks have yielded concordant ages, lending credence to the geological time scale. Other rocks, such as bracket intrusives and glauconites, are used occasionally as tiepoints. However, they are problematic either because they span too many stratigraphic layers, or they are continually being formed after the sedimentation of the layer has been completed. Despite these shortcomings, the geological time scale has as much validity as is allowed by the current stratus of geochronological science. Table 2.7 summarizes the geological column as correlated by representative samples to the absolute radiometric age.