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Dating - Radioactive and Other Techniques


Carbon-14 Dating
Potassium-Argon Dating
Isochron Dating
Optical Dating
Rehydroxylation Dating

Carbon-14 Dating

Radioactive Decay Carbon 14 Dating Before the advent of carbon 14 dating, estimate of age is a rather hazardous undertaking. The age of a piece of antique can be determined by its style in certain period, the age of fossil is related to the stratification etc. Discovery of radioactive elements provides the mean to date objects in term of years. The radioactive isotope carbon-14 is especially suitable for dating organic matter because the initial quantity N0 and its half-life t1/2 are known in the decay formula :

N = N0e-kt ---------- (1)

where k = ln(2)/t1/2, and t is the time variable (Figure 01). Further details are provided in the followings :

Figure 01 Radioactive Decay [view large image]

Figure 02 Carbon-14 Dating [view large image]

Potassium-Argon Dating

Carbon-14 seems to be the only radioactive element that betrays its initial number N0 in Eq.(1). The potassium-argon dating gets around this problem by using the ratio between the daughter and parent numbers (N0-N)/N = (ekt -1), which yields the age with no trace of N0 :

K40 Dating K40 Decay t = (1/k)ln(1+D/P) ---------- (2)

where D and P denote the daughter and parent numbers respectively. Since the daughter product argon-40 is not incorporated into minerals, all such atoms in a rock must have come from the decay of K-40 that was there originally. That is, the age can be measured from the ratio D/P using AMS. However, this assumption may not be valid as shown in Figure 06. The measurements obtain three different ages depending on the hydrothermal condition in the magma (from the 1986

Figure 06 K-40 Dating
[view large image]

Figure 07 K-40 Decay
[view large image]

Mt. St. Helen eruptions). It demonstrates that excessive argon (radiogenic and/or primeval) can yield erroneous ages - a problem readily exploited by creationists.

Debates between the rival factions aside, the formula for age estimate from K-40 decay has to be modified because it decays by two modes. Only 10.72% produces argon-40, the rest goes to calcium-40 as shown in Figure 07. Therefore, the formula in Eq.(2) should be re-written as :

t = (1/k)ln[1+D/(0.1072xP)] ---------- (3)

Isochron Dating

Isochron Dating For cases where the initial quantity of the radioactive isotope is not available, the method of isochron (equal time) can also bypass the problem with the ratios of parent and daughter to the non-radiogenic isotope of the daughter element as illustrated in Figure 08. The formula corresponds to the plot is in the form :

(D + d)/S = (D/P)(P/S) + d/S ---------- (4)

where P is the number of the parent atoms, D for the daughter, S (assumed to be constant) is the

Figure 08 Isochron Dating [view large image]

non-radiogenic isotope of D, and d is the initial number of D. The formula in Figure 08 is for the case where the horizontal axis is displaced upward by an amount d corresponding to equate d = 0 in Eq.(4).

The process involves measuring the D/S and P/S ratios from different minerals inside a rock (assumed to form at the same time) by AMS. Since the amount of the constituents are not exactly the same in the various minerals, the plot of D/S vs P/S would spread out in different points - on a straight line in this case. A horizontal line along the x-axis signifies the beginning of the decay when D = 0; the slope of the line becomes steeper as the disintegration progresses; finally, the line moves to a vertical position when P = 0 at the end of the decay. The dating is determined by the slope G = (D/S)/(P/S) using the formula :

t = (1/k)ln(1 + G) ---------- (5)

in which the initial parent number disappears altogether. One of the best known isotopic systems for isochron dating is the rubidium-strontium system (as shown in Figure 08). Other systems include samarium-neodymium (t1/2=106 BY), and uranium-lead (t1/2=4.468 BY). Other shorter half-life radionuclides include 53Mn (t1/2=3.7 MY), 26Al (t1/2=0.717 MY), 129I (t1/2=15.7 MY), 60Fe (t1/2=2.6 MY). They are used for dating events (e.g., origin of the meteorite) in the early history of the solar system, which has an age of about 4.5 BY, the proliferation of multicellular life occurred around 500 MY (BY = Billion Years, MY = Million Years).

Table 01 below lists some radiometric systems and the range of dates that can be measured. The lower and upper limits are determined by the presence of enough number of the daughter and parent atoms to obtain sufficient signals. Ultimately it is the quality of the equipments in the laboratory, which impose the sensitive limit.

Table 01 Radiometric Systems and Dating Ranges

Optical Dating

Luminescence Dating Optical (Luminescence) Dating utilizes a principle opposite to the radioactive method. Whereas the latter measures the diminished amount of the decaying material, optical dating relies on the accumulation of electrons trapped inside minerals such as quartz and feldspar (the major composition of sediment). The electrons come from the background radioactive elements in the solid, they are trapped in the crystal lattice in the absence of Sun light, which would set the dating clock back to zero by evicting the electrons from the sites. The amount of such electrons measured in the laboratory from a sample is proportional to its age since the last exposure to Sun light. Followings is a summary of such age determination procedure (Figure 09).

Figure 09 Optical Dating
[view large image]

Rehydroxylation Dating

Rehydroxylation Dating Rehydroxylation (RHX) Dating also utilizes the concept of the regular accumulation of something inside the material to determine its age. In this case, it is observed that the mass of fired-clay ceramics, brick, tile etc. is reduced by heating. The subsequent re-absorption of moisture from the environment produces water mass gain, which is found to follow a power law of the time after the initial heating. This dating method is still under development following its introduction in early 21st century. It has been shown to reproduce accurate dates comparing to the known ages of antique artefacts, ancient ruins, etc. Following is a brief description of this method.

Figure 10 Rehydoxylation Dating [view large image]

Figure 12 shows the kinds of materials that have been dated by various methods over the entire history of the Earth :

Figure 12 Dating the Earth