Radiocarbon Dating Discussion with candle2

• Message 656 by PaulK
• Message 657 by Tanypteryx
• Message 658 by Pollux
• Message 660 by dwise1
• Message 661 by Pollux
• Message 662 by Tanypteryx

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There are only three quite technical instances where a half-life changes, and these do not affect the dating methods we have discussed.

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1. Only one technical exception occurs under terrestrial conditions, and this is not for an isotope used for dating. According to theory, electron-capture is the most likely type of decay to show changes with pressure or chemical combination, and this should be most pronounced for very light elements. The artificially-produced isotope, beryllium-7 has been shown to change by up to 1.5%, depending on its chemical environment (Earth Planet. Sci. Lett. 171, 325-328, 1999; see also Earth Planet. Sci. Lett. 195, 131-139, 2002). In another experiment, a half-life change of a small fraction of a percent was detected when beryllium-7 was subjected to 270,000 atmospheres of pressure, equivalent to depths greater than 450 miles inside the Earth (Science 181, 1163-1164, 1973). All known rocks, with the possible exception of diamonds, are from much shallower depths. In fact, beryllium-7 is not used for dating rocks, as it has a half-life of only 54 days, and heavier atoms are even less subject to these minute changes, so the dates of rocks made by electron-capture decays would only be off by at most a few hundredths of a percent.

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2. { pressures and temperatures in the center of the sun, which cannot be produced naturally on earth }

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3. { relativistic effects on time in space vehicles traveling very fast }

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These cases are very specialized, and all are well understood. None of these cases alter the dates of rocks either on Earth or other planets in the solar system. The conclusion once again is that half-lives are completely reliable in every context for the dating of rocks on Earth and even on other planets. The Earth and all creation appears to be very ancient.

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4. The decay rates are poorly known, so the dates are inaccurate.

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Most of the decay rates used for dating rocks are known to within two percent. Uncertainties are only slightly higher for rhenium (5%), lutetium (3%), and beryllium (3%), discussed in connection with Table 1. Such small uncertainties are no reason to dismiss radiometric dating. Whether a rock is 100 million years or 102 million years old does not make a great deal of difference.

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5. A small error in the half-lives leads to a very large error in the date.

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Since exponents are used in the dating equations, it is possible for people to think this might be true, but it is not. If a half-life is off by 2%, it will only lead to a 2% error in the date.

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1. Notation for an atom is its elemental abbreviation which appears in the Periodic Table of Elements; eg, C for carbon, U for uranium, Fe for iron, Au for gold, etc.
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   Notation of a molecule (a combination of atoms) uses the same abbreviations followed by a subscript giving the number of that element's atom in the molecule. For example, water consisting of two hydrogen (H) and one oxygen (O) is H₂O, an oxygen molecule is O₂, carbon dioxide is CO₂, glucose (a simple carbohydrate) is C₆H₁₂O₆.
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2. On the most basic level, an atom consists of a nucleus surrounded by shells of electrons:
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   1. Basically, the nucleus contains two types of particles: protons and neutrons. Collectively they are called nucleons and hence the total number of protons and neutrons is the atom's nucleon count (term will be used below).
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   2. Almost all of an atom's mass is in its nucleus. Assigning a mass of one (1) to a nucleon, the number of nucleons will be about its Atomic Weight. One mole of a substance (6.02214076×10²³ atoms or molecules, AKA Avogadro number) will weigh its atomic weight in grams. For example, the atomic weight of a molecule of water is 18.0154, so one mole of water would weight 18.0154 grams (and have a volume of 18.0154 milliliters which is 3.655 teaspoons or 1.218 tablespoons).
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   3. Neutrons have no electrical charge and protons have a positive electrical charge. Therefore, the positive charge of the protons give the nucleus a positive electrical charge. Since particles with the same polarity repel (postive attracts negative, but positive repels positive as negativ repels negative), it is the neutrons that hold the nucleus together (as I recall from half a century ago in high school chemistry).
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   4. By definition, the element that that atom is of is determined entirely on the number of protons it has, which is its Atomic Number. Change the number of protons and you've changed the element.
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   5. The chemical reactions that an atom will engage in depends on its electrons (basically, on the extra electrons in the outer shells which are not stable since they are not complete).
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   6. The number of electrons that an atom has is normally the same as the number of protons, but it is possible for an atom to have a different number of electrons than protons, which are ions. More electrons than protons makes for a negative ion, fewer electrons than protons makes for a positive ion, and the number of electrons being the same as the number of protons makes for an electrically neutral atom. We commonly encounter ions in solutions (eg, table salt, NaCl, dissolved it water forming sodium (Na+) and clorine (Cl-) ions).
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   7. When we look at the nucleons, we find that the number of neutrons can be different in an element's atoms. When viewed in this way, those atoms are called isotopes, even those isotopes in which the number of neutrons is that same as the number of the protons.
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      1. An isotope is identified by its proton count (the Atomic Number) and the its nucleon count (ie, the sum of its protons and neutrons).
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      2. There are a few different forms of notation for isotopes:
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         • Preface the element symbol with the proton-plus-neutron count (superscripted) and the proton count (subscripted); eg, carbon ¹²₆C, radiocarbon ¹⁴₆C.
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         • That notation can be simplified by leaving out the proton count, which is the same as the element's Atomic Number. Therefore the examples above would be written as ¹²C for carbon and ¹⁴C for radiocarbon. I seem to recall seeing this used without superscripting so that carbon would be written as 12C and radiocarbon as 14C.
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         • An even simpler notation which does not require special formatting is to write the nucleon count after the elemental symbol, connecting them with a hyphen. Hence the examples above would be written as C-12 and C-14.
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           I tend to use that last notation.
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      3. Since all isotopes of an element have the same number of protons and electrons, they will all react chemically in an identical manner. For example, water (H₂O) can also be formed with one of those hydrogen atoms being replaced with deuterium (H-2) to form a molecule of heavy water.
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      4. Since the isotopes of an element have different numbers of nucleons, they will all have a different atomic weight. Because of that fact, we can differentiate between different isotopes, something that is important in radiometric methods.
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         The differences in mass can change the isotope's physical properties. In some cases, greater mass can make that isotope less likely to be incorporated in a compound. Also, heavy water is less suseptible to electrolysis, which is how we obtain heavy water (ie, use electrolysis to split the regular water molecules into hydrogen and oxygen, and when all the regular water has been split what remains is heavy water which occurs naturally).
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      5. Some isotopes are stable and some are unstable (and hence radioactive). Some are naturally occuring and some are produced by radiation (eg, C-14) and some are radiogenic (ie, produced by the decay of a heavier element).

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Assumption 3: No Daughter Element Existed at the Beginning

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To date rocks using any radiometric dating system, a person must assume that the daughter element in the sample was not there in the beginning. However, that claim cannot be proven. Who is to say that the rock did not start out with 23 ounces of lead already in it? The lead could have been in the rock from the beginning (and so could the uranium). To illustrate this point, suppose you go to a swimming pool and find a hose that is pumping water into the pool at a rate of 100 gallons an hour. You discover that the pool has 3,000 gallons of water in it. You calculate that the hose must have been running for 30 hours. However, when you ask the owner of the pool how long she has been running the hose, she tells you that she has been running it for only one hour. Most of the water was already in the pool due to a heavy rain the night before. If you assumed that all the water came from the hose, your calculations would be way off—29 hours off to be exact. Assumption three, that no daughter element existed at the beginning, simply cannot be granted.

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• P_now - The quantity of the parent isotope that remains now. This is measured directly.
• D_now - The current quantity of the daughter isotope.
• P_orig - The quantity of the parent isotope that was originally present. This is computed from the current quantity of parent isotope plus the accumulated quantity of daughter isotope.
• halflife - The half-life of the parent isotope. Standard values are used, based on direct measurements. (Constancy of decay rate is covered in the Age of the Earth FAQ.)
• age - The value computed from the equation and the other three quantities, is the amount of time which has passed.

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Potential problems for generic dating

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Some assumptions have been made in the discussion of generic dating, for the sake of keeping the computation simple. Such assumptions will not always be accurate in the real world. These include:

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• The amount of daughter isotope at the time of formation of the sample is zero (or known independently and can be compensated for).
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• No parent isotope or daughter isotope has entered or left the sample since its time of formation.

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If one of these assumptions has been violated, the simple computation above yields an incorrect age.

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Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless. In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable. However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age... especially in absence of cross-checks by different methods, or if presented without sufficient information to judge the context in which it was obtained.

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Isochron methods avoid the problems which can potentially result from both of the above assumptions.

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Isochron methodology

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Isochron dating requires a fourth measurement to be taken, which is the amount of a different isotope of the same element as the daughter product of radioactive decay. (For brevity's sake, hereafter I will refer to the parent isotope as P, the daughter isotope as D, and the non-radiogenic isotope of the same element as the daughter, as D_i). In addition, it requires that these measurements be taken from several different objects which all formed at the same time from a common pool of materials. (Rocks which include several different minerals are excellent for this.)

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Each group of measurements is plotted as a data point on a graph. The X-axis of the graph is the ratio of P to D_i. The Y-axis of the graph is the ratio of D to D_i. For example, an Rb/Sr isochron plot looks like this:

Figure 1. Example isochron plot.
P = Rb-87; D = Sr-87; D_i = Sr-86.
The X-axis (horizontal) is the ratio of (Rb-87 / Sr-86); ie, P / D_i, ratio of parent and the NON-radiogenic isotope
The Y-axis (vertical) is the ratio of (Sr-87 / Sr-86); ie, D / D_i, ratio of the radiogenic and NON-radiogenic isotopes
Three samples are plotted on the graph

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What does it mean?

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The intent of the plot is to assess a correlation between:

1. The level of P (X-value of the data points), and
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2. Any enrichment in D (Y-value of the data points):

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Figure 2. Meaning of the plot axes.

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Increasing abundance of P moves the plot point to the right
Increasing enrichment in D moves the plot point up

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If the data points on the plot are colinear, and the line has a positive slope, it shows an extremely strong correlation between:

1. The amount of P in each sample, and
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2. The extent to which it is enriched in D, relative to D_i.

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This is a necessary and expected consequence, if the additional D is a product of the decay of P in a closed system over time. It is not easily explained, in the general case, in any other way.

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Why isochron data are colinear

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The data points would be expected to start out on a line if certain initial conditions were met. Consider some molten rock in which isotopes and elements are distributed in a reasonably homogeneous manner. Its composition would be represented as a single point on the isochron plot:

Figure 3. Global composition of the melt.
Plots a single plot based on the composition of the melt; subsequent graphs are derived from this one

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As the rock cools, minerals form. They "choose" atoms for inclusion by their chemical properties.

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Since D and D_i are isotopes of the same element, they have identical chemical properties*. Minerals may include varying quantities of that element, but all will inherit the same D/D_i ratio as the source material. This results in an identical Y-value for the data points representing each mineral (matching the Y-value of the source material).

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* Note that the above is somewhat simplified. There are minor differences between isotopes of the same element, and in relatively rare circumstances it is possible to obtain some amount of differentiation between them. This is known as isotope fractionation. The effect is almost always a very small departure from homogeneous distribution of the isotopes -- perhaps enough to introduce an error of 0.002 half-lives in a non-isochron age. (It can happen... but it is rare and the effect is not large enough to account for extremely old ages on supposedly young formations.)

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In contrast, P is a different element with different chemical properties. It will therefore be distributed unequally relative to D & D_i as minerals form. This results in a range of X-values for the data points representing individual minerals.

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Since the data points have the same Y-value and a range of X-values, they initially fall on a horizontal line:

Figure 4. Differential migration of elements as minerals form.
Shows that minerals which incorporate D better than P will plot to the left of the initial melt while those that incorporate P better than D will plot to the right
All points start out on a horizontal line for zero-age

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A horizontal line represents "zero age." *

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* More precisely, a horizontal line represents an age which is indistinguishable from zero. In most cases, any age less than about 10^-3 P half-lives will include zero within its range of uncertainty. (The range of uncertainty varies, and may be as much as an order of magnitude different from the approximate value above. It depends on the accuracy of the measurements and the fit of the data to the line in each individual case.) For example, with Rb/Sr isochron dating, any age less than a few tens of millions of years is usually indistinguishable from zero. That encompasses the entire young-Earth timescale thousands of times over.

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As more time passes and a significant amount of radioactive decay occurs, the quantity of P decreases by a noticeable amount in each sample, while the quantity of D increases by the same amount. This results in a movement of the data points to the left (decreasing P) and upwards (increasing D). Since each atom of P decays to one atom of D, the data point for each sample will move along a path with a slope of -1.

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Decay occurs in a proportional manner (that is, when 20% of the P in one sample has decayed, 20% of the P in every sample will have decayed). As a result, the data points with the most P (the right-most ones on the plot) move the greatest distance per unit time. The data points remain colinear as time passes, but the slope of the line increases:

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Figure 5. Movement of data points as decay occurs.
Illustrates the movement of the data points as they age

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The slope of the line is the ratio of enriched D to remaining P. It can be used in place of "D_now/P_now" in the decay equation.

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Miscellaneous notes

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Age "uncertainty"

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When a "simple" dating method is performed, the result is a single number. There is no good way to tell how close the computed result is likely to be to the actual age.

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An additional nice feature of isochron ages is that an "uncertainty" in the age is automatically computed from the fit of the data to a line. A routine statistical operation on the set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an uncertainty in the age). The better the fit of the data to the line, the lower the uncertainty.

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General comments on "dating assumptions"

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All radiometric dating methods require, in order to produce accurate ages, certain initial conditions and lack of contamination over time. The wonderful property of isochron methods is: if one of these requirements is violated, it is nearly certain that the data will indicate the problem by failure to plot on a line. (This topic will be discussed in much more detail below.) Where the simple methods will produce an incorrect age, isochron methods will generally indicate the unsuitability of the object for dating.

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Avoidance of generic dating's problems

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Now that the mechanics of plotting an isochron have been described, we will discuss the potential problems of the "simple" dating method with respect to isochron methods.

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Initial daughter product

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. . .

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Contamination - parent isotope

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Contamination - daughter isotope

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Exceptions for loss of daughter

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. . .

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These exceptions should be of little comfort to young-Earthers, for (1) they are uncommon (extremely uncommon in the case of partial resetting); and (2) the result in both cases is an isochron age which is too young to represent the time of formation. Young-Earthers necessarily insist that all ancient isochron ages are really much too old.

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Are Radioactive Dates Wrong?

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John Woodmorappe (1979) went through the scientific literature looking for radioactive dates which are 20% too old or too young. He specifically excluded from his search any date which matched the expected age. This type of selective editing is exactly what Young earth Creationists charge the Evolutionists with. Woodmorappe says

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"An objective comparison between the number of fitting vs. the number of anomalous dates in the Phanerozoic is hindered (if not prevented) by the fact that anomalous dates frequently (or usually) are not reported in scientific journals." (Woodmorappe 1979, p. 113)

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Thus while he criticizes the old-earther for selectively publishing radioactive dates, he does the very same thing by only publishing bad dates. This seriously hurts his credibility. In his article he listed these bad dates but did not plot them. If he had, he would have seen something remarkable. Above the 350 dates are plotted . A perfect dating result should appear on the line. Note that there are more dates under the line than above the line. If radioactivity is producing dates which are too old, you would expect that there would be more dates above the line than below the line. What this proves is that if a radioactive date is wrong it is far more likely to be too young than too old! Young earth creationists need the dates to be too old if their viewpoint is correct.

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