Incl. intelligent design, belief in divine creation

Moderators: Calilasseia, DarthHelmet86, Onyx8

Since one of the perennial canards that defenders of valid science have to endure on these forums, a canard that is practically a masturbatory obsession with creationists, is the "radionuclide dating is based upon assumptions" canard, I thought it apposite to produce this post, for the specific purpose of destroying this canard once and for all. This post was, needless to say, inspired by theropod's post on the rigour of the Earth sciences, and I owe him a debt for inspiring me to get off my backside and post this.

Given the nature of the material being covered, this will be a long post. Consequently, it will probably be spread over more than one post. However, I promise that persevering with it will be worth the effort.

Empirical Determination Of The Decay Law

Initially, the determination of the decay law was performed empirically, by observing the decay of various radionuclides in the laboratory, taking measurements of the number of decay events, and plotting these graphically, with time along the x-axis, and counts along the y-axis. Upon performing this task, the data for many radionuclides is seen to lie upon a curve, and determination of the nature of that curve requires a little mathematical understanding.

To determine the nature of a curve, various transformations can be performed upon the data. The result of each of these transformations is as follows:

[1] Plot loge(y) against x - if the result is a straight line, then the relationship is of the form:

loge(y) = kx + C (where C is some constant, in particular, the y-intercept of the straight line)

which can be rewritten:

loge(y) - loge(C0) = kx (where C = loge(C0))

which rearranges to:

y = C0ekx

where C0 is derived from the y-intercept of the straight line produced by the transformed plotting, and k is the gradient of the transformed line.

[2] Plot y against loge(x) - if the result is a straight line, then the relationship is of the form:

y = k loge(x) + C, where k is the gradient of the line, and C is the y-intercept of the straight line.

[3] Plot loge(y) against loge(x) - if the result is a straight line, then the relationship is of the form:

loge(y) = k loge(x) + C (where C is the y-intercept of the straight line thus produced)

This rearranges to:

loge(y) - loge(C0) = k loge(x) (where C = loge(C0))

Which in turn rearranges to:

loge(y/C0) = loge(xk)

Which finally gives us the relationship:

y = C0xk, where k is the gradient of the straight line produced by the transformed data, and C0 is derived from the y-intercept of the straight line produced by the transformed data.

The above procedures allow us to determine the nature of the mathematical relationships governing large bodies of real world data, when those bodies of real world data yield curves as raw plots of y against x. By applying the relevant transformations to radonuclide decay data, it was found that transformation [1] transformed the data into a straight line plot (within the limits of experimental error, of course), and consequently, this informed the scientists examining the data that the decay law was of the form:

N = C0ekt

where C0 and k were constants to be determined from the plot, and which were regarded as being dependent upon the particular radionuclide in question.

Now, if we are start with a known amount of radionuclide, and observe it decaying, then each decay event we detect with a Geiger counter represents one nucleus undergoing the requisite decay transformation. Since the process is random, over a long period of time, decaying nuclei will emit α or β particles in all directions with equal frequency, so we don't need to surround the material with Geiger counters in order to obtain measurements allowing a good first approximation to the decay rate. Obviously if we're engaged in precise work, we do set up our experiments to do this, especially with long-lived nuclei, because the decay events for long-lived nuclei are infrequent, and we need to be able to capture as many of them as possible in order to determine the decay rate with precision. Let's assume that we're dealing with a relatively short-lived radionuclide which produces a steady stream of decay events at a reasonably fast rate, in which case we can simply point a single Geiger counter at it, and work out what proportion of these events we are actually capturing, because that proportion will be the ratio of the solid angle subtended by your Geiger counter, divided by the solid angle of an entire sphere (this latter value being 4π). When we have computed this ratio (let's call it R), which will necessarily be a number less than 1 unless we have surrounded your sample with a spherical shell of Geiger counters, we then start collecting count data, say once per second, and plotting that data. In a modern setup we'd use a computer to collect this mass of data (a facility that wasn't available to the likes of Henri Becquerel, Röntgen and the Curies when they were engaged in their work), in order to have as large a body of data as possible to work with. Before working with the raw data, we transform it by taking each of the data points and dividing it by R to obtain the true count.

Once the data has been collected, transformed and plotted, the end result should be a nice curve. At this point, we're interested in knowing what sort of curve we have, and there are two ways we can determine this. One way is to take the transformed data set, comprising count values c1, c2, c3, ... , cn, where n is the number of data points collected, compute the following values:

r1 = c2 - c1
r2 = c3 - c2
r3 = c4 - c3
...
rn-1 = cn - cn-1

and then plot a graph with rk on the vertical axis, and ck on the horizontal axis. This should give a reasonable approximation to a straight line, and the slope of that straight line, obtained via regression analysis, will give the first approximation to the decay constant k. At this point, we know we are dealing with a relationship of the form dN/dt = -kN, and you can then apply the integral calculus to that equation (see below). Technically, what we are doing here is approximating the derivative by computing first differences.

However, as a double check, we can also perform a logarithmic regression on the data, plotting loge(ck) against time, which should also reveal a straight line, and again, the slope of that line will give you the value of k, which should be in good agreement with the value obtained earlier using the more laborious plot of rk against ck. In other words, applying the transformation [1] above to the data set, and extracting an exponential relationship from the data. Since we now know that the data is of the form:

logeN = -kt

we can then derive the exponential form and check that it tallies with the integral calculus result.

Once we have that function coupling the decay rate to time, we can then work backwards, and feed in the values of the known starting mass and the experimentally obtained decay constant k, and see if the function obtained reproduces the transformed data points. If the result agrees with observation to a very good fit, we're home and dry.

This is, essentially, how the process was done when the decay law was first derived - lots of data points were collected from observation of real radionuclide decay, and the above processes applied to that data, to derive the exponential decay law. When this was done for multiple radionuclides, it was found that they all obeyed the same basic law, namely:

N = N0e-kt

where N0 is your initial amount of radionuclide, N is the amount remaining after time t, and k is the decay constant for the specific radionuclide.

Now, having determined this decay law empirically, it's time to fire up some calculus, and develop a theoretical derivation of the decay law. Which I shall now proceed to do.

Theoretical Derivation Of The Decay Law And Comparison With The Above Empirical Result

Upon noting, using the calculation of first differences in the empirical determination above, that the rate of change of material with time, plotted against the material remaining, is constant, this immediately leads us to conclude that the decay law is governed by a differential equation. An appropriate differential equation is therefore:

dN/dt = -kN

which states that the amount of material undergoing decay is a linear function of the amount of material present (and furthermore, the minus sign indicates that the process results in a reduction of material remaining). Rearranging this differential equation, we have:

dN/N = -k dt

Integrating this, we have:

∫dN/N = - ∫ k dt

Our limits of integration are, for the left hand integral, the initial amount at t=0, which we call N0, and the amount remaining after time t, which we call Nt. Our limits of integration for the right hand integral are t=0 and t=tp, the present time.

Thus, we end up with:

logeN -logeN0 = -ktp

By an elementary theorem of logarithms, this becomes:

loge(N/N0) = -ktp

Therefore, exponentiating both sides, we have:

N/N0 = e-kt

or, the final form:

N = N0e-kt
The half-life of a radionuclide is defined as the amount of time required for half the initial amount of material to decay, and is called T½. Therefore, feeding this into the equation for the decay law,

½N0 = N0e-kt

Cancelling N0 on both sides, we have:

½ = e-kt

loge½ = -kt

By an elementary theorem of logarithms, we have:

loge2 = kt

Therefore T½ = loge2/k

Alternatively, if the half-life is known, but the decay constant k is unknown, then k can be computed by rearranging the above to give:

k = loge2/T½

Which allows us to move seamlessly from one system of constants (half-lives) to another (decay constants) and back again.

If the initial amount of substance N0 is known (e.g., we have a fresh sample of radionuclide prepared from a nuclear reactor), and we observe the decay over a time period t, then measure the amount of substance remaining, we can determine the decay constant empirically as follows:

N = N0e-kt

N/N0 = e-kt

loge(N/N0) = -kt

Therefore:

(1/t) loge(N0/N) = k

On the left hand side, the initial amount N0, the remaining amount N and the elapsed time t are all known, therefore k can be computed using the empirically observed data.

Once again, this agrees with the empirical data from which the law was derived in the earlier exposition above, and consequently, we can be confident that we have alighted upon a correct result.

Once we have the decay law in place, it simply remains for appropriate values of k to be determined, which will be unique to each radionuclide. This work has been performed by scientists, and as a result of decades of intense labour in this vein in physics laboratories around the world, vast bodies of radionuclide data are now available.

Kaye & Laby's Tables of Physical & Chemical Constants, devised and maintained by the National Physical Laboratory in the UK, contains among the voluminous sets of data produced by the precise laboratory work of various scientists a complete table of the nuclides, which due to its huge size, is split into sections to make it more manageable, in which data such as half-life, major emissions, emission energies and other useful data are included. The sections are:

[1] Hydrogen to Flourine (H1 to F24)

[2] Neon to Potassium (Ne17 to K54)

[3] Calcium to Copper (Ca35 to Cu75)

[4] Zinc to Yttrium (Zn57 to Y101)

[5] Zirconium to Indium (Zr81 to In133)

[6] Tin to Praesodymium (Sn103 to Pr154)

[7] Neodymium to Thulium (Nd129 to Tm177)

[8] Ytterbium to gold (Yb151 to Au204)

[9] Mercury to Actinium (Hg175 to Ac233)

[10] Thorium to Einsteinium (Th212 to Es256)

[11] Fermium to Roentgenium (name not yet officially recognised by IUPAC) (Fm242 to Rg272)

Now, the above exhaustively compiled data gives rise to yet more data, in the form of the tables covering the major decay series. These arise from the observation of which radionuclides decay into which other radionuclides (or in the case of certain radionuclides, which stable elements are formed after decay), and all of these decay events follow specific rules, according to whether α decay, β- decay, or one of the other possible decay modes for certain interesting radionuclides, takes place. Again, data is supplied in the above tables with respect to all of this.

Now, we come to the question of how this data is pressed into service. Since the above work couples radionuclide decay to time, via a precise mathematical law, we can use this data to provide information on the age of any material that contains radionuclides. This can be performed by performing precise quantitative measurements of parent radionuclides and daughter products, all of which is well within the remit of inorganic chemists (since the chemistry of the relevant elements has been studied in detail, in some cases for over 200 years) and of course, modern gas chromatograph mass spectrometry can be brought to bear upon the process, yielding results with an accuracy that past chemists reliant upon earlier techniques could only dream of. Consequently, it is now time to cover the business of dating itself.

With the data obtained above, it becomes possible to trace the decay of suitably long-lived elements in geological strata, locate specific isotopes, determine by precise quantitative analysis the amounts present in a given sample, and compare these with calculations for known decay observations in the laboratory, whence the time taken for the observed isotope composition of the sample can be determined. Given that several isotopes have extremely long half-lives, for example, U238 has a half-life of 4,500,000,000 years, and Th232 has a half-life of 14,050,000,000 years, and several of the daughter isotopes also have usefully long half-lives, one can determine the age of a rock sample, where multiple isotopes are present, by relating them to the correct decay series and utilising the observed empirically determined half-lives of laboratory samples to determine the age of a particular rock sample, cross correlating using multiple isotopes where these are present and enable such cross correlation to be performed. Thus, errors can be eliminated in age determinations by the use of multiple decay series and the presence of multiple long-lived isotopes - any errors arising in one series will yield a figure different from that in another series, and the calculations can thus be cross-checked to ensure that they are consilient.

Referring to the data tables above, I have selected a number of isotopes of interest. These are isotopes whose half-lives have been determined to lie within a specific range, and which moreover are not known to be produced in the Earth's crust by any major synthesis processes (except for the various Technetium isotopes, which can arise if Molybdenum isotopes are coincident with Uranium isotopes in certain rocks, but this exception is rare and well documented). The isotopes in question, in increasing atomic mass order, are:

Al26 : 740,000 years
Cl36 : 301,000 years
Ca41 : 103,000 years
Mn53 : 3,740,000 years
Fe60 : 1,500,000 years
Kr81 : 213,000 years
Zr93 : 1,530,000 years
Nb92 : 34,700,000 years
Tc97 : 2,600,000 years
Tc98 : 4,200,000 years
Tc99 : 211,000 years
Pd107 : 6,500,000 years
Sn126 : 100,000 years
I129 : 15,700,000 years
Cs135 : 2,300,000 years
Sm146 : 103,000,000 years
Gd150 : 1,790,000 years
Dy154 : 3,000,000 years
Hf182: 9,000,000 years
Re186m : 200,000 years
Pb205 : 15,200,000 years
Bi208 : 368,000 years
Bi210m : 3,040,000 years
Np236 : 154,000 years
Np237 : 2,140,000 years
Pu242 : 373,300 years
Pu244 : 81,700,000 years
Cm247 : 15,600,000 years
Cm248 : 340,000 years

The reason I have chosen these isotopes is very simple. Namely, that they would all be present in measurable quantities in the Earth's crust, and detectable by modern mass spectrometry among other techniques, if the planet was, say, only 6,000 years old, as various enthusiasts for mythology continue to assert. This is because because the half-lives of all these radionuclides are a good deal longer than 6,000 years. So, what do we find when we search for these isotopes in Earth rocks?

NONE of them are present in measurable quantities.

Now, one can safely assume that at the end of 20 half-lives, any measurable amount of a particular radionuclide has effectively vanished - the amount left is ½20, or just 0.000095367% of the original mass that was present originally. So even for isotopes of common elements, this fraction represents a vanishingly small amount of material that would test even the world's best mass spectrometer labs to detect in a sample. So, what does the observation of no measurable quantity of the above isotopes mean? It means that at least 20 half-lives of the requisite isotopes must have elapsed for those isotopes to disappear. Taking each isotope in turn, this means that:

[1] Sn126, being absent, must have disappeared over a period of 20 half lives = 20 × 100,000 years = 2,000,000 years. Therefore the Earth must be at least 2,000,000 years old for all the Sn126 to have disappeared.

[2] Ca41, being absent, must have disappeared over a period of 20 half lives = 20 × 103,000 years = 2,060,000 years. Therefore the Earth must be at least 2,060,000 years old for all the Ca41 to have disappeared.

[3] Np236, being absent, must have disappeared over a period of 20 half lives = 20 × 154,000 years = 3,080,000 years. Therefore the Earth must be at least 3,080,000 years old for all the Np236 to have disappeared.

[4] Re186m, being absent, must have disappeared over a period of 20 half lives = 20 × 200,000 years = 4,000,000 years. Therefore the Earth must be at least 4,000,000 years old for all the Re186m to have disappeared.

[5] Tc99, being absent, must have disappeared over a period of 20 half lives = 20 × 211,000 years = 4,220,000 years. Therefore the Earth must be at least 4,220,000 years old for all the Tc99 to have disappeared.

[6] Kr81, being absent, must have disappeared over a period of 20 half lives = 20 × 213,000 years = 4,260,000 years. Therefore the Earth must be at least 4,260,000 years old for all the Kr81 to have disappeared.

[7] Cl36, being absent, must have disappeared over a period of 20 half lives = 20 × 301,000 years = 6,020,000 years. Therefore the Earth must be at least 6,020,000 years old for all the Cl36 to have disappeared.

[8] Cm248, being absent, must have disappeared over a period of 20 half lives = 20 × 340,000 years = 6,800,000 years. Therefore the Earth must be at least 6,800,000 years old for all the Cm248 to have disappeared.

[9] Bi208, being absent, must have disappeared over a period of 20 half lives = 20 × 368,000 years = 7,360,000 years. Therefore the Earth must be at least 7,360,000 years old for all the Bi208 to have disappeared.

[10] Pu242, being absent, must have disappeared over a period of 20 half lives = 20 × 373,000 years = 7,460,000 years. Therefore the Earth must be at least 7,460,000 years old for all the Pu242 to have disappeared.

[11] Al26, being absent, must have disappeared over a period of 20 half lives = 20 × 740,000 years = 14,800,000 years. Therefore the Earth must be at least 14,800,000 years old for all the Al26 to have disappeared.

[12] Fe60, being absent, must have disappeared over a period of 20 half lives = 20 × 1,500,000 years = 30,000,000 years. Therefore the Earth must be at least 30,000,000 years old for all the Fe60 to have disappeared.

[13] Zr93, being absent, must have disappeared over a period of 20 half lives = 20 × 1,530,000 years = 30,600,000 years. Therefore the Earth must be at least 30,600,000 years old for all the Zr93 to have disappeared.

[14] Gd150, being absent, must have disappeared over a period of 20 half lives = 20 × 1,790,000 years = 35,800,000 years. Therefore the Earth must be at least 35,800,000 years old for all the Gd150 to have disappeared.

[15] Np237, being absent, must have disappeared over a period of 20 half lives = 20 × 2,140,000 years = 42,400,000 years. Therefore the Earth must be at least 42,400,000 years old for all the Np237 to have disappeared.

[16] Cs135, being absent, must have disappeared over a period of 20 half lives = 20 × 2,300,000 years = 46,000,000 years. Therefore the Earth must be at least 46,000,000 years old for all the Cs135 to have disappeared.

[17] Tc97, being absent, must have disappeared over a period of 20 half lives = 20 × 2,600,000 years = 52,000,000 years. Therefore the Earth must be at least 52,000,000 years old for all the Tc97 to have disappeared.

[18] Dy154, being absent, must have disappeared over a period of 20 half lives = 20 × 3,000,000 years = 60,000,000 years. Therefore the Earth must be at least 60,000,000 years old for all the Dy154 to have disappeared.

[19] Bi210m, being absent, must have disappeared over a period of 20 half lives = 20 × 3,040,000 years = 60,800,000 years. Therefore the Earth must be at least 60,800,000 years old for all the Bi210m to have disappeared.

[20] Mn53, being absent, must have disappeared over a period of 20 half lives = 20 × 3,740,000 years = 74,800,000 years. Therefore the Earth must be at least 74,800,000 years old for all the Mn53 to have disappeared.

[21] Tc98, being absent, must have disappeared over a period of 20 half lives = 20 × 4,200,000 years = 84,000,000 years. Therefore the Earth must be at least 84,000,000 years old for all the Tc98 to have disappeared.

[22] Pd107, being absent, must have disappeared over a period of 20 half lives = 20 × 6,500,000 years = 130,000,000 years. Therefore the Earth must be at least 130,000,000 years old for all the Pd107 to have disappeared.

[23] Hf182, being absent, must have disappeared over a period of 20 half lives = 20 × 9,000,000 years = 180,000,000 years. Therefore the Earth must be at least 180,000,000 years old for all the Hf182 to have disappeared.

[24] Pb205, being absent, must have disappeared over a period of 20 half lives = 20 × 15,200,000 years = 304,000,000 years. Therefore the Earth must be at least 304,000,000 years old for all the Pb205 to have disappeared.

[25] Cm247, being absent, must have disappeared over a period of 20 half lives = 20 × 15,600,000 years = 312,000,000 years. Therefore the Earth must be at least 312,000,000 years old for all the Cm247 to have disappeared.

[26] I129, being absent, must have disappeared over a period of 20 half lives = 20 × 15,700,000 years = 314,000,000 years. Therefore the Earth must be at least 314,000,000 years old for all the I129 to have disappeared.

[27] Nb92, being absent, must have disappeared over a period of 20 half lives = 20 × 34,700,000 years = 694,000,000 years. Therefore the Earth must be at least 694,000,000 years old for all the Nb92 to have disappeared.

[28] Pu244, being absent, must have disappeared over a period of 20 half lives = 20 × 81,700,000 years = 1,634,000,000 years. Therefore the Earth must be at least 1,634,000,000 years old for all the Pu244 to have disappeared.

[29] Sm146, being absent, must have disappeared over a period of 20 half lives = 20 × 103,000,000 years = 2,060,000,000 years. Therefore the Earth must be at least 2,060,000,000 years old for all the Sm146 to have disappeared.

This is an inescapable conclusion from observational reality, given that these isotopes are not found in measurable quantities in the Earth and would be found in measurable quantities if the Earth was only 6,000 years old, indeed, hardly any of the Sm146 would have disappeared in just 6,000 years, and it would form a significant measurable percentage of the naturally occurring Samarium that is present in crustal rocks. The fact that NO Sm146 is found places a minimum limit on the age of the earth of 2,060,000,000 years - over two billion years - and of course, dating using other isotopes with longer half lives that can be measured precisely has established that the age of the Earth is approximately 4.5 billion years. Now since the decay of these isotopes obeys a precise mathematical law as derived above, and this law has been established through decades of observation of material of known starting composition originating from nuclear reactors specifically for the purpose of determining precise half-lives, which is one of the tasks that the UK National Physical Laboratory (whose data I cited above) performs on a continuous basis in order to maintain scientific databases, the provenance of all of this is beyond question. The tables I have linked to above are the result of something like half a century of continuous work establishing half-lives for hundreds upon hundreds of radionuclides, and not ONE of them has EVER been observed to violate that precise mathematical law which I opened this post with under the kind of conditions in which those materials would exist on Earth if they were present. The majority of those isotopes are nowadays ONLY obtained by synthesis within nuclear reactors, and observation of known samples of these materials confirms again and again that not only does the precise mathematical law governing radionuclide decay apply universally to all of these isotopes, but that the half-lives obtained are valid as a consequence. The laws of nuclear physics would have to be rewritten wholesale for any other scenario to be even remotely valid, and that rewriting of the laws of nuclear physics would impact upon the very existence of stable isotopes including stable isotopes of the elements that make up each and every one of us, none of which would exist if the various wacky scenarios vomited forth on creationist websites to try and escape this were ever a reality.

Now, having covered this, it's time to deal with a topic of importance, and one that constitutes another of those epistemological bones creationists love to chew upon, without realising that the questions surrounding this topic have already been answered. That question is ...

Transport - And How Scientists Deal With It

Even in the very early days of the development of radionuclide dating techniques, scientists were aware that chemical elements in rock samples might be subject to various chemical processes resulting in the transport of material in or out of a given rock sample. After all, inorganic chemists had been performing detailed investigations of the aqueous chemistry of geologically significant elements for the best part of a century before the development of radionuclide dating. Scientists interested in utilising radionuclides for dating purposes, therefore had a vast body of knowledge from inorganic chemistry to draw upon, in order to determine whether or not transport was likely to take place in a given rock stratum, and given the known behaviour of the relevant elements and their various salts in aqueous conditions, they were able to devise means of testing whether transport was likely to be a significant factor in a given rock stratum of interest. Which they promptly set about doing. For example, a geologist can reasonably conclude that virtually zero transport has taken place in a sample where the radionuclides are found as sulphide salts, because the only sulphides that are soluble in water are those of the alkali metals - ALL other sulphides are insoluble, with solubility constants that are extremely low. Lead (II) sulphide, for example (known geologically as the mineral galena), has a Ksp of 3.4 × 10-28, mercury (II) sulphide (cinnabar) has a Ksp of around 4 × 10-53, and silver sulphide (acanthite or argentite) has a Ksp of 1.6 × 10-49.

Indeed, thanks to the large body of knowledge bestowed upon geologist by inorganic chemists, all manner of tests can be performed in order to determine if transport is likely to be a problem before a sample is submitted for dating analysis, so that this can be taken into account and proper corrections applied to the material in question. Indeed, scientists have spent time devising a technique, known as isochron dating, whose purpose is specifically that of checking whether the isotopes used for dating have been subject to transport, and developing appropriate corrections to the dates that would have been obtained without such checking. This technique takes advantage of the fact that many radionuclides produce a stable decay product that is isotopically different from a typical sample of the daughter element arising non-radiogenically, and appropriate comparisons of the amounts of non-radiogenic daughter element with that of the radiogenic daughter element can be used to determine if transport took place.

Let's see how isochron dating works, shall we?

When an igneous stratum is formed (and dating techniques tend to focus upon igneous strata, because the deep mantle of the Earth is the primary source of the radionuclides required), molten material solidifies, and as it does so, the chemical compounds of various elements crystallise out of the melt differentially, resulting in the formation of well-defined mineral species. Moreover, some melts possess a greater chemical affinity for some elements than others, and consequently, there will be further differentiation, based upon those chemical affinities. Zircons, for example, have a chemical affinity for uranium, and incorporate uranium salts into their crystals far more readily than, say, lead salts. Likewise, some other crystalline formations will incorporate other elements preferentially, including elements that are of utility value in dating. A typical element that is of use is rubidium, with the Rb87 isotope having a half-life of 4.75 × 1010 years. This decays via β- decay into Sr87, an isotope of strontium, and this decay product is stable. However, a non-radiogenic isotope of strontium, namely Sr86, also exists in geological strata. The utility of this will become apparent shortly.

Now, any melt starting off with a quantity of Rb87 will, after sufficient time has elapsed, start to acquire quantities of Sr87. This will take time, given the long half-life of Rb87, and indeed, detectable quantities of Sr87 amenable to mass spectrometry will only start to appear after 0.001 half-lives have elapsed. In the case of Rb87, this is 45 million years, so a sample that has an Rb87 age that is indistinguishable from zero could be as much as 40 million years old, which means that this is no indication of an allegedly "young" Earth. The moment any detectable traces of Sr87 appear in a sample, however, then we're dealing with a rock that is at least 45 million years old, which flushes blind assertions about the Earth being only 6,000 years old down the toilet to begin with. But, this isn't the point: the point is, that any mineral that acquires quantities of strontium upon formation will acquire a specific ratio of the two isotopes Sr86 and Sr87, and that ratio can be used to determine the initial amount of Rb87 that was acquired during formation as well. Which means that no "assumptions" about initial material present are needed.

Now, since all the minerals that acquire strontium will acquire the same ratio of Sr86 to Sr87 at the start, we can use that ratio as the y-axis for a plot. However, different minerals within the sample will acquire different quantities of Rb87, and we can use the ratio of Rb87 to Sr86 to form the x-axis of the plot. If our initial values are:

P = amount of Rb87 at the time of stratum formation
D1 = amount of Sr86 at the time of stratum formation
D2 = amount of Sr87 at the time of stratum formation

then we plot an x-y plot consisting of:

x = P/D1, y = D2/D1

the axes therefore correspond to:

x = increasing enrichment of Rb87 in the sample with increasing value
y = increasing enrichment of Sr87 in the sample with increasing value

Now, the global composition of the melt, from which the stratum eventually forms, will have a given point value on this plot. As the melt cools, and minerals crystallise out, different minerals will migrate along a straight line in this plot, as all the minerals will inherit the same value of y (= D2/D1), but inherit different values of x (=P/D1). The result will be, at zero age, a horizontal line connecting the points for those minerals in the plot.

Now, as the Rb87 decays in each mineral, it will produce Sr87. Therefore, over geological time, the data points will move upwards and to the left.

Now, because decay occurs in a proportional manner, courtesy of the decay law derived above, when 20% of the Rb87 has decayed in one mineral, then 20% of the Rb87 will have decayed in all the minerals present in the stratum. This means that all the points will move upwards and to the left of the plot. This means that those points corresponding to the minerals with the greatest initial Rb87 concentration will move the farthest, and the movement will be such that all of the points will remain on a straight line. Indeed, those familiar with Monte Carlo simulation methods can produce a computer simulation that reproduces this exact result. As a consequence, any stratum containing the appropriate minerals will yield, for a given age, a line of points whose slope increases with time, and the slope of that line can be used to determine the age of the sample.

Note that we don't need to know the initial amounts of any of the elements present in the sample in order for this to work. All we need to know is the present-day ratios of those elements. And, from that data, we can reconstruct the original composition of the melt.

Now, here is the fun part. If the sample suffered any transport, then this will become immediately apparent because the points will deviate significantly from a straight line plot. This is because the minerals containing the various elements will undergo transport differentially. For example, if the minerals lost Rb87 due to various processes of aqueous chemistry, then this would shift all of the points to the left, but because different minerals are involved in the process, each with a different chemistry, and a different response to the aqueous processes that could remove Rb87 from them, the amount of x-shift will be different for each mineral, and as a consequence, straight line correlation will be destroyed. Immediately scientists see this, they know that something unusual has happened to the sample after formation, and that dates obtained from it are unlikely to be reliable.

Indeed, if the Earth were only 6,000 years old, not only would ALL isochron plots involving minerals with long half-lives be flat, horizontal lines, but random loss or gain of the parent nuclide would not affect those results. If the Earth were only 6,000 years old, any "contamination" that creationists assert would be present that would render radionuclide dating methods invalid, would not even be noticeable on a purported "young Earth". Contamination would only ever be noticeable if the Earth was old. Which means that far from "invalidating" radionuclide dating, detectable contamination in a sample via the isochron method actually reinforces an old age for the Earth.

Worse still, from the creationist standpoint, the known possibilities for systematic alteration of an isochron plot, that results in modification of the data points such that they remain collinear, result in an underestimate of the age of the sample - in other words, the isochron plot records them as being younger than they actually are, not older. Complete homogenisation of the stratum with respect to the content of Sr87 will reset the isochron 'clock' to zero, and partial homogenisation will result in a line of lower slope than previously, causing the technique to underestimate the true age.

Once such a plot is complete, any strong correlation to a straight line (as yielded by regression analysis, which will give us an indication how much we can trust a date from the plot, and what value of error to apply to the plot), will yield the following values:

[1] the y-intercept of the line is the value of D2/D1 at solidification;

[2] the slope of the line is equal to ΔP/(P - ΔP), where ΔP is the amount of Rb87 lost to decay, and thus allows us to determine the age of the sample, given the known half-life of Rb87 (we can back-calculate using the decay law to determine what value of P was initially present to produce the observed result).

There is a body of technical literature on the subject of isochron dating, and, needless to say, it requires a fair amount of work to plough through, but for those who have acquired the relevant scientific and mathematical background, it is well worth exerting this effort, not least in order to prepare oneself for the inevitable quote mining of the scientific papers that will arise in creationist circles.

And now, I'd like to turn attention to this:

Purported "Exceptions" To The Decay Law

One of the more interesting findings of recent years was that rhenium-187, a radionuclide that undergoes decay by electron capture, can have its half-life altered under laboratory conditions. However, the mechanism of alteration offers no hope to anyone entertaining fantasies about a 6,000 year old Earth, for the following reasons:

[1] The mechanism only applies to isotopes that decay via electron capture, and both α decaying and β- decaying isotopes are unaffected by this mechanism;

[2] The mechanism only has a small effect upon the half-life of Re187 unless extreme conditions are applied (and the scientists had to resort to extreme measures to determine this);

[3] The conditions required to produce this mechanism in Re187 atoms on Earth are physically unreal.

What the relevant scientists did, was to take Re187 atoms, and subject them to ever more extreme levels of ionisation. In order to do this, they had to resort to a particle accelerator, and use large amounts of energy to ionise the Re187 atoms to the required amount. As any student of basic physical chemistry understands, it takes a certain amount of energy to remove one electron from a neutral atom, but, once that electron is removed, it requires more energy to remove a second electron, because that electron is now being removed from a positively charged ion, and more energy is needed to overcome the additional electrostatic attraction now present. Consequently, as one removes yet more electrons, more energy is needed for each subsequent electron. In order to speed up the decay process of Re187, scientists stripped all of the electrons from the Re187 atoms, making them extremely highly ionised. Extreme states of ionisation of this sort only occur in nature within the confines of extremely hot incandescent plasmas, with temperatures well beyond that required to turn elements such as rhenium into gases, and rhenium has the highest boiling point of all the elements, at a whopping 5,600°C (courtesy of Kaye & Laby again). Even this temperature isn't enough to strip 75 electrons off a rhenium atom, and the temperature required is more likely to be of the order of 65,000 Kelvins or beyond, which means that trying to invoke this mechanism as a means of "accelerating" nuclear decay involves heating the Earth's crust to temperatures more normally associated with the chromospheres of supergiant O class stars.

Apart from the fact that this mechanism requires ludicrously absurd conditions to have occurred in the Earth's crust in order for it to happen, and apart from the fact that this mechanism is useless for U238 and several other important isotopes used in radionuclide dating, because they do not decay via electron capture, it's actually a waste of time trying to argue against the constancy of the decay law under normal conditions, because this one exception requires such extreme conditions that the Earth would not have remained a solid planet if they had been present. Plus, the mere fact that the half-life for Re187 is of the order of 4.16 × 1010 years, means that the presence of any detectable Re187 in the Earth's crust means that the planet is ancient. If by some bizarre freak of physics, Re187 decay had been sped up by this mechanism without vaporising the Earth's crust, the anomaly would have been so immediately detectable alongside the other radionuclides, that scientists would have noticed something was amiss long ago. That word 'consilience' is back to haunt those who prefer mythology to reality.

I think this covers relevant bases for now.
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Calilasseia
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### Re: RADIONUCLIDE DATING IS RIGOROUS

Hehe i love this post. I copied it from the old forum a while back
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### Re: RADIONUCLIDE DATING IS RIGOROUS

Excellent stuff; but it would be alot better for topics like these if there were pictures to help explain (esp the graphing and math bit dealing with linear regression) for those not very aquainted with that sort of material.

Also, if god was magiking the universe into existance (high energy situation like the big bang) and molding the earth out of plasma and all that, the modified decay rate because of electron capture due to high energy (?) seems apologeticable.. you have to accept the absurd premise though.

I'm not very learned in nuclear chemistry but do you have a resource that deals with that special exception because of ionization thingy, because i can't really see how that occurs and why Re187 has to be super duper ionized for that all to occur??
Ryan
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### Re: RADIONUCLIDE DATING IS RIGOROUS

An apposite paper on Re187 is this one:

Observation Of Bound-State β- Decay Of Fully Ionised Re187: Re187-Os187 Cosmochronometry by F. Bosch, T. Faestermann, J. Friese, F. Heine, P. Kienle, E. Wefers, K. Zeitelhack, K. Beckert, B. Franzke, O. Klepper, C. Kozhuharov, G. Menzel, R. Moshammer, F. Nolden, H. Reich, B. Schlitt, M. Steck, T. Stöhlker, T. Winkler and K. Takahashi, Physical Review Letters, 77(26): 5190-5193 (December 1996)

Bosch et al, 1996 wrote:We observed the bound-state β- decay of fully ionized 187Re nuclei circulating in a storage ring. With two independent methods the time dependent growth of hydrogenlike 187Os ions has been measured and a half-life of 32.9±2.0yr for bare 187Re nuclei could be determined, to be compared with 42 Gyr for neutral 187Re atoms. With the resulting logft value of 7.87±0.03 the half-life of 187Re ions in any ionization state can be calculated. Thus one can correct the 187Re-187Os galactic chronometer calibration, by taking account of the β- decay enhancement in stellar interiors, which will lead to a more accurate estimate of the galactic age.
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Calilasseia
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### Re: RADIONUCLIDE DATING IS RIGOROUS

But, we all know that radioactive decay occurred faster in the past, as was the speed of light. Just a little over 6000 years ago, the decay was many magnitudes higher than it is today, but in such a synchronous way that even today certain dating lines appear to line up when dating old rocks with Uranium, etc. Now don't start with that crap that faster decay or faster speed of light would result in a hotter planet. Scientists are now discovering dark matter and energy, an energy that seems to behave the opposite of regular energy. Regular matter has attraction towards each other (gravity). Dark matter has the opposite, and pushes matter apart, as is evidenced by our expanding universe. In the same way, even though the radioactive decay was many magnitudes higher in the past just before 6000 years ago, dark energy was also more prevalent and therefore prevented the super heating of our planet during the time that caused billions of years of apparent decay in just the first day when Gob created the earth.

pcCoder

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### Re: RADIONUCLIDE DATING IS RIGOROUS

pcCoder wrote:But, we all know that radioactive decay occurred faster in the past, as was the speed of light. Just a little over 6000 years ago, the decay was many magnitudes higher than it is today, but in such a synchronous way that even today certain dating lines appear to line up when dating old rocks with Uranium, etc. Now don't start with that crap that faster decay or faster speed of light would result in a hotter planet. Scientists are now discovering dark matter and energy, an energy that seems to behave the opposite of regular energy. Regular matter has attraction towards each other (gravity). Dark matter has the opposite, and pushes matter apart, as is evidenced by our expanding universe. In the same way, even though the radioactive decay was many magnitudes higher in the past just before 6000 years ago, dark energy was also more prevalent and therefore prevented the super heating of our planet during the time that caused billions of years of apparent decay in just the first day when Gob created the earth.

Which is why God created Radon gas.
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### Re: RADIONUCLIDE DATING IS RIGOROUS

I sure hope that's a Poe.
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OgreMkV

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### Re: RADIONUCLIDE DATING IS RIGOROUS

That is actually similar to what someone told me once, something about how dark matter/energy prove that the dating methods are wrong. I don't think I could never be a very effective Poe though.
pcCoder

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### Re: RADIONUCLIDE DATING IS RIGOROUS

pcCoder wrote:That is actually similar to what someone told me once, something about how dark matter/energy prove that the dating methods are wrong. I don't think I could never be a very effective Poe though.

Fallible wrote:Don't bacon picnic.

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### Re: RADIONUCLIDE DATING IS RIGOROUS

stijndeloose wrote:
pcCoder wrote:That is actually similar to what someone told me once, something about how dark matter/energy prove that the dating methods are wrong. I don't think I could never be a very effective Poe though.

Thanks to the Firefox spellchecker. Sometimes I find myself a bit obsessive about checking my grammar and spelling and every time I go over a writing I end up changing something only to review it again and eventually find it worse than it was to start with, so I try not to review it as much especially if it is just an online forum post. Technical reports and such I check more thoroughly.
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### Re: RADIONUCLIDE DATING IS RIGOROUS

OgreMkV wrote:I sure hope that's a Poe.

Don't know if that was for me or someone else but I like radon gas arguments as the gas kills mostly innocent people and yet it is the byproduct of a decay chain from the longest lived chains (the disintegration chain of U 238). We're talking billions of years here and it'll be doing this for billions of years to come.

So when talking to a YEC who is mangling the decay chains I usually bring up Radon gas because of the usefulness of the gas in highlighting the absurdities. The YEC is kind of doomed to the following style of arguments,

Either God accelerated the decay chains so messing up radionuclide dating systems and forgot about radon gas or God knows about radon gas but failed to highlight the dangers in the Bible (though other dangerous stuff got a mention). Or God knows about Radon gas and doesn't care that innocent people get lung cancer, or God couldn't work out how to get rid of Radon gas in the disintegration chain no matter how hard God tried. Or God just wanted more jobs for the Radon gas membrane and sensor manufacturers and installers unions.
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byofrcs wrote:Either God accelerated the decay chains so messing up radionuclide dating systems and forgot about radon gas or God knows about radon gas but failed to highlight the dangers in the Bible (though other dangerous stuff got a mention). Or God knows about Radon gas and doesn't care that innocent people get lung cancer, or God couldn't work out how to get rid of Radon gas in the disintegration chain no matter how hard God tried. Or God just wanted more jobs for the Radon gas membrane and sensor manufacturers and installers unions.
You forget that bad things only happen to people because of their sins... If they weren't sinfull then they wouldn't get lung cancer from radon gas

No, seriously... Just bookmarking this for potential subsequent use.
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tnjrp

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### Re: RADIONUCLIDE DATING IS RIGOROUS

OK, here's a question - why should the Earth contain any radionuclides at all?
Do we know what proportions of isotope to parent element are created in a supernova explosion (assuming, for now, that that is where they originate from) ?
If a supernova occurred, say, 4 billion years before the Earth formed, then wouldn't all but the longest-lived isotopes have decayed by then? Is it legitimate to consider the supernova as being contemporary to the formation of the Earth?
Just asking, as I'm sure others have thought of similar questions...

Beelzebub

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### Re: RADIONUCLIDE DATING IS RIGOROUS

Beelzebub wrote:OK, here's a question - why should the Earth contain any radionuclides at all?
Do we know what proportions of isotope to parent element are created in a supernova explosion (assuming, for now, that that is where they originate from) ?
If a supernova occurred, say, 4 billion years before the Earth formed, then wouldn't all but the longest-lived isotopes have decayed by then? Is it legitimate to consider the supernova as being contemporary to the formation of the Earth?
Just asking, as I'm sure others have thought of similar questions...

No. The initial Big Bang formed quite light weight elements and isotopes. Subsequent stellar nucleosynthesis formed all the heavier elements. The thing is that we're dealing with half-lifes and these are a binary progressions not straight-line reductions.

I used radon gas as an example to show the perversity of creationism but the most unusual is for 209-Bismuth which has a proven half-life of 1.9 × 1019 years - or roughly a billion times longer than the current age of the universe.

The U-238 to Th-234 has a halflife of 4,460,000,000 years so if at about 4 billion years ago you had 1 ton of U238 then now you would have about 1/2 a ton. Then in another 4 billion years you would have 1/4 ton and then so on for trillions of trillions of years into the future until the last Uranium atom split (more or less).

The current understanding is that the earth's core is hot mainly because of radioactive decay and of these Uranium is the most important. By looking at the ratios of uranium-238 and uranium-235 on Earth and as these have different halflifes then by comparing the ratios with what is calculated to be the ratios in supernova we can calculate, as a rough guess, that the Uranium on Earth dates from a supernova about 6.5 billion years ago (so about 2 billion years before the Earth was formed) though the actual picture if we look at all elements is that the Earth, and so each of us, contains elements formed in a number of supernova.

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### Re: RADIONUCLIDE DATING IS RIGOROUS

byofrcs wrote:
Beelzebub wrote:OK, here's a question - why should the Earth contain any radionuclides at all?
Do we know what proportions of isotope to parent element are created in a supernova explosion (assuming, for now, that that is where they originate from) ?
If a supernova occurred, say, 4 billion years before the Earth formed, then wouldn't all but the longest-lived isotopes have decayed by then? Is it legitimate to consider the supernova as being contemporary to the formation of the Earth?
Just asking, as I'm sure others have thought of similar questions...

No. The initial Big Bang formed quite light weight elements and isotopes. Subsequent stellar nucleosynthesis formed all the heavier elements. The thing is that we're dealing with half-lifes and these are a binary progressions not straight-line reductions.

I used radon gas as an example to show the perversity of creationism but the most unusual is for 209-Bismuth which has a proven half-life of 1.9 × 1019 years - or roughly a billion times longer than the current age of the universe.

The U-238 to Th-234 has a halflife of 4,460,000,000 years so if at about 4 billion years ago you had 1 ton of U238 then now you would have about 1/2 a ton. Then in another 4 billion years you would have 1/4 ton and then so on for trillions of trillions of years into the future until the last Uranium atom split (more or less).

The current understanding is that the earth's core is hot mainly because of radioactive decay and of these Uranium is the most important. By looking at the ratios of uranium-238 and uranium-235 on Earth and as these have different halflifes then by comparing the ratios with what is calculated to be the ratios in supernova we can calculate, as a rough guess, that the Uranium on Earth dates from a supernova about 6.5 billion years ago (so about 2 billion years before the Earth was formed) though the actual picture if we look at all elements is that the Earth, and so each of us, contains elements formed in a number of supernova.

This message was brought to you from the You-are-but-an-insignificant-mote-in-the-universe Ministries.

Ah, but the 'Big Bang' doesn't enter into it - it only produced H, He and Li - all the elements we are addressing come from nucleosynthesis in stars and supernovae!
Now, my argument would be this - assume an ancient universe, billions of years old, but a young Earth (some 6000 years old) - now, if the supernovae that produced the heavy elements, and their isotopes, exploded 2 billion years before the Earth formed then all the elements listed by Calilasseia would have decayed already. So the creationists, if they can stomach an old universe, could make a case for a radiologically consistent young Earth!!
Of course, there are other evidences for an old Earth, but, at least at a superficial level, radiological dating doesn't necessarily mean an old Earth

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### Re: RADIONUCLIDE DATING IS RIGOROUS

Beelzebub wrote:
byofrcs wrote:
Beelzebub wrote:OK, here's a question - why should the Earth contain any radionuclides at all?
Do we know what proportions of isotope to parent element are created in a supernova explosion (assuming, for now, that that is where they originate from) ?
If a supernova occurred, say, 4 billion years before the Earth formed, then wouldn't all but the longest-lived isotopes have decayed by then? Is it legitimate to consider the supernova as being contemporary to the formation of the Earth?
Just asking, as I'm sure others have thought of similar questions...

No. The initial Big Bang formed quite light weight elements and isotopes. Subsequent stellar nucleosynthesis formed all the heavier elements. The thing is that we're dealing with half-lifes and these are a binary progressions not straight-line reductions.

I used radon gas as an example to show the perversity of creationism but the most unusual is for 209-Bismuth which has a proven half-life of 1.9 × 1019 years - or roughly a billion times longer than the current age of the universe.

The U-238 to Th-234 has a halflife of 4,460,000,000 years so if at about 4 billion years ago you had 1 ton of U238 then now you would have about 1/2 a ton. Then in another 4 billion years you would have 1/4 ton and then so on for trillions of trillions of years into the future until the last Uranium atom split (more or less).

The current understanding is that the earth's core is hot mainly because of radioactive decay and of these Uranium is the most important. By looking at the ratios of uranium-238 and uranium-235 on Earth and as these have different halflifes then by comparing the ratios with what is calculated to be the ratios in supernova we can calculate, as a rough guess, that the Uranium on Earth dates from a supernova about 6.5 billion years ago (so about 2 billion years before the Earth was formed) though the actual picture if we look at all elements is that the Earth, and so each of us, contains elements formed in a number of supernova.

This message was brought to you from the You-are-but-an-insignificant-mote-in-the-universe Ministries.

Ah, but the 'Big Bang' doesn't enter into it - it only produced H, He and Li - all the elements we are addressing come from nucleosynthesis in stars and supernovae!
Now, my argument would be this - assume an ancient universe, billions of years old, but a young Earth (some 6000 years old) - now, if the supernovae that produced the heavy elements, and their isotopes, exploded 2 billion years before the Earth formed then all the elements listed by Calilasseia would have decayed already. So the creationists, if they can stomach an old universe, could make a case for a radiologically consistent young Earth!!
Of course, there are other evidences for an old Earth, but, at least at a superficial level, radiological dating doesn't necessarily mean an old Earth

No that would not work at all. The isotopes all decay at different rates. It's like those questions when one passenger leaves on a train travelling at 50 Mph from Boston and another leaves on a Train travelling at 30 Mph from New York, where will they overlap ? In this case we're at the crossing point and knowing the speed of the trains we can backtrack to where they started.

(Similar to last-Thursdayism) To get the values right God would have to have created the isotopes in the right quantities and moreover God would have also had to have created the Radon gas (which kills innocent people). YEC is a travesty to common sense and though a YEC could argue for their rather devious form of last-Thursdayism, it comes with a monkey on it's back. One almost imagines God running the timeline forward and then notices Radon, works out it'll kill people but as God hasn't created people yet, doesn't think much of it at the time. When Adam and Eve are kicked out for a minor misunderstanding God also fails to mention this product defect (and forgets to mention Bacteria but given both are invisible then who the heck will notice, thinks God ?).
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### Re: RADIONUCLIDE DATING IS RIGOROUS

Beelzebub wrote:OK, here's a question - why should the Earth contain any radionuclides at all?
Do we know what proportions of isotope to parent element are created in a supernova explosion (assuming, for now, that that is where they originate from) ?
If a supernova occurred, say, 4 billion years before the Earth formed, then wouldn't all but the longest-lived isotopes have decayed by then? Is it legitimate to consider the supernova as being contemporary to the formation of the Earth?
Just asking, as I'm sure others have thought of similar questions...

In the case of elements produced by a supernova detonation, what happens is that they are formed in stages by neutron absorption followed by beta decay along the neutron drip line. The immediate environment surrounding a supernova detonation is nicely rich in neutrons, facilitating the building of the requisite elements. Indeed, the relevant physical theories governing this have been given a nice evidential boost courtesy of long term observation of SN1987A, which has yielded the spectra of new elements appearing over time.

The next matter to consider is the vast mass of material involved. Stars that produce supernova detonations at the end stages of their lives are massive - the minimum mass is of the order of 8 solar masses, and quite a few stars that evolve to the supernova stage are a good deal more massive than that. So there's quite a lot of material shed into the surroundings when a supernova detonates. If that material then comes into contact with a relatively close gas cloud of light elements such as hydrogen and helium, it can form the basis for an accretion disc should the interaction trigger star formation within the light gas cloud. A compression wave travelling through the gas cloud as a result of the interaction would introduce density inhomogeneities in the gas cloud, and gravity would then do the rest.

Turning to Kaye & Laby, we have a nice table featuring the abundances of the elements. The column for the Solar System is represented in rather odd units: the figure is the number of atoms present for each 106 atoms of silicon (which is a nice, easily measured, relatively abundant element). So, for every 106 atoms of Si in the Solar System, there are 2.8 × 1010 atoms of hydrogen. However, there are a lot more than 106 atoms in the Solar System in total. For example, the mass of the Sun is 1.9891 × 1030 Kg, of which 75% is hydrogen. A mole of hydrogen atoms (note: NOT hydrogen molecules!) has a mass of 1 gram, therefore 1 kilogram of hydrogen atoms equals 1,000 moles, and each mole comprises 6.023 × 1023 atoms, so this gives us that the Sun alone contains around 8.985 × 1056 hydrogen atoms. Since the Sun comprises 99.86% of the entire mass of the Solar System, that means that the total abundance of hydrogen in the Solar System is around 8.997 × 1056 atoms. Divide this by 2.8 × 1010 to obtain our multiplying factor, and use this to multiply the entries in the table to obtain the actual total number of atoms in the Solar System, and we have, for uranium, 5.785 × 1044 atoms throughout the Solar System, the majority of which are concentrated in rocky bodies such as the Earth. Apparently, the spectrum of the Sun contains no measurable lines for uranium, though oddly enough it does contain measurable lines for thorium, and the abundance of thorium in the Sun is slightly higher than that for the Solar System as a whole - a little puzzle that should keep some researchers happy for a while.

Now, given that we can plot the distribution of stars of various masses, and indeed, astronomers have already done this, it transpires that something of the order of 0.1% of all stars in the current population are of 8 solar masses or greater, and therefore destined to end in supernova detonations, but of course that's the stars extant after 13.6 billion years of the life of the universe - things become more complicated when we consider the first population of stars to form early in the life of the universe, but that's a separate topic properly deserving its own thread. Basically, something like 0.1% of all stars have masses greater than 8 solar masses (if you want the precise figure, find a tame astrophysicist!) and these stars have lifetimes of only 10 million years or so. For example, Zeta Orionis is a hot blue supergiant whose mass is around 28 solar masses, and Zeta Puppis is an extreme example of this sort of star, with a whopping 64 solar masses to its credit. Nearing the end of its life is Antares, a red supergiant with a mass of 15.5 solar masses, and since Antares is only 600 light years from Earth, when it blows, it'll light up the night sky in spectacular fashion. It will also send a fair amount of matter our way, and that matter will form a nebula of truly stupendous proportions visually as it grows, becoming the dominant feature of the night sky for millennia. But I digress. If you want to find out more about this, useful links include this one and this one. But if you want the current record holder, that will be Eta Carinae, a star that is estimated to possess a mass of as much as 150 solar masses, and when that goes supernova, we'll certainly know about it, even though it's 8,000 light years from Earth.

Basically, stars of the size of Eta Carinae and Zeta Puppis will dump a LOT of heavy element debris into the surroundings. Untold trillions of tons of the stuff. Even a more modest supernova will dump something like 5 × 1030 Kg of material into space. That's a lot of atoms. Even if only one kilogram in 1010 Kg of that material ends up as a uranium atom, you're still going to end up with 5 × 1020 Kg of uranium. After 4.5 billion years, you'll still be left with around 2.5 × 1019 Kg. So you shouldn't be surprised that there's still useful amounts of uranium available for us to pop into nuclear reactors.
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Calilasseia
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Fascinating Calilasseia, the amount of heavy elements formed since the earliest supernovae began to detonate must be truly astounding - enough, surely, for untold numbers of metal-rich stars and planetary systems to form.

Alas, all this does not address the primary question - why should we expect to find isotopes with half-lives shorter than, say, 100 million years on a planet created only 6000 years ago? - If the matter it was created from originated from a supernova > 2 billion years ago? (more than 20 half-lives).
So long as a creationist is prepared to accept an old Universe, then a young Earth would not be contradicted by the absence of < 100 million year half-life isotopes.

Though I doubt any of them would like this scenario - if an old Universe, then why not an old Earth?

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### Re: RADIONUCLIDE DATING IS RIGOROUS

I can think of one reason why we can find isotopes with shorter half-lives than 100 million years. They're the decay products of some of those longer-lived isotopes. That's why we find radium in coal dust - it's a decay product of uranium. Any reasonably ancient piece of rock containing uranium will also contain radium in small but measurable quantities. Since uranium percolates through geological water flows into coal seams and becomes resident in the coal in measurable quantities, radium appears in the coal as well. It's one of the reasons that ash from coal burning is a quantifiable radiological hazard. Find out more about this from this scientific paper among others.

Then, some of those longer-lived isotopes induce other elements alongside them to become radioactive. Neutron activation is a well-known phenomenon arising from nuclear reactors. My old favourite resource, Kaye & Laby, has a nice long article on neutron activation cross sections. Basically, what happens is this. Long-lived alpha-decay emitters such as uranium and thorium emit alpha particles (helium nuclei). In the case of 232Th, these have an energy of around 35.4 MeV, whilst those for 238U have an energy of 47.3 MeV. These can interact with other nuclei via collisions, producing an effect known as spallation, where the collision results in the liberation of a neutron or other fragment from the target nucleus. That neutron, in turn, can be absorbed by a stable nucleus, and transformed into a radioactive nucleus. For example, a stable 58Ni nucleus can absorb a spallation neutron, becoming 59Ni, which is radioactive, decaying via electron capture to the stable 59Co, with a half-life of 75,400 years.

Of course, which of the surrounding stable nuclei absorb the spallation neutron is dependent upon several factors, but this mechanism produces elements such as technetium in tiny quantities in appropriate geological strata. No isotope of technetium has a half life greater than 4.2 million years (this is an element with no stable isotopes), so its detection in a natural rock sample indicates that it was produced by neutron activation of molybdenum followed by beta decay (typically neutron activation of 98Mo to become 99Mo, which beta-decays with a half-life of 65 hours to produce 99Tc, which has a half-life of 211,000 years. Other technetium isotopes are produced by spontaneous fission of uranium, such as that occurring in the Oklo natural nuclear reactor.

Incidentally, a tiny fraction of 238U nuclei can undergo spontaneous fission, not only producing elements such as technetium directly, but producing other elements via neutron activation (three neutrons are released by the fissioning nucleus). However, a comparison of the interaction cross sections shows that this is a very infrequently occurring process - the cross section for 238U fission is around 4 × 10-6 barns (which means it doesn't happen very often). Compare this with the fission cross section for 235U, which is 583 barns, or 239Pu, which is 748 barns (both are fissile materials capable of being utilised in a nuclear reactor or a nuclear weapon as a result).
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Calilasseia
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### Re: RADIONUCLIDE DATING IS RIGOROUS

Thanks Calilasseia,
The problem is, that the argument for an old Earth is precisely that we don't find isotopes with half-lives shorter than ~100 million years - therefore the Earth must be older than, say, 20 half-lives.

But the isotopes in question were not created when the Earth formed, but when the 'progenitor' supernova(e) exploded. If this event took place billions of years beforehand, then these same isotopes would have long decayed before the Earth even started to form - hence, whether we consider an old or a young Earth, these isotopes would still be missing (except, of course, for those that are continuously generated by the decay of much longer-lived isotopes (as you mention) or cosmic-ray events (14C))

Now, all is not lost, as we could measure the relative abundance of these continuously generated isotopes to their own daughter products - this would give a minimum time for the age of the particular sample.
Let's say that a lump of primordial 238U, say, produced a quantity of 59Ni, this then decays to 59Co with a half-life of 76,000 years - this decay chain could then be used to place a minimum limit to the age of this sample.

Actually, checking up on this example seems to show that the only detectable amounts of 59Ni, are those found in nuclear reactors - but I'm sure other chains could be found?

(My use of the term 'Isotope' is a bit sloppy, - All forms of an element are, of course, isotopes. Please take the term here to mean the unstable, radioactive, nuclides of an element)

Beelzebub

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