First of all, I'd like to know how the authors of that tripe came up with the figure of 28 billion years, because I've never seen anything like it in any actual scientific literature.
Let's take an example of an isotope with a suitably long half-life - Thorium 232. This has a half-life of 14 billion years. Its decay products are well known -
this diagram from Kaye & Laby illustrates the decay sequence nicely. Ultimately,
232Th decays, via a chain of short-lived intermediates, to
208Pb, which is stable. Consequently, measuring the ratio of
232Th to
208Pb in a rock sample gives you a reasonable indication of its age. Indeed, from the decay equation, you can work out how much of an initial sample of
232Th would be converted to
208Pb, after a given amount of elapsed time. We start with:
N = N
0e
-ktNoting that the half-life is 14 billion years, we therefore have:
½N
0 = N
0e
-kTwhere T is the half-life. Cancelling out the N
0 on both sides and rearranging gives us:
k = ln(2)/T
where ln(x) is the natural logarithm function. So, knowing the half-life, we calculate the decay constant k, which for
232Th becomes:
k = ln(2) ÷ (441,882,000,000,000,000) = 1.568 × 10
-18In case you're wondering where I got that huge number on the left hand side from, it's the number of seconds in 1.4×10
10 years.
Right, so armed with this information, we can now work out how much
232Th would be converted to
208Pb in 4.4 billion years. Starting with a 100 Kg sample of
232Th, we would have, after this amount of time, the following amount:
N = 100×e
-(kt) = 100×e
-0.217 = 80.4 Kg
So, a little under 20% of the sample would have been converted in that time.
As a check to see if the numbers are indeed correct, we should, after a 28 billion year period (which is two half-lives of
232Th, which is why I chose this isotope), have just 25% of our original
232Th left. Let's run the numbers:
N = 100×e
-(kt) = 100×e
-1.385 = 25 Kg
Bingo.
Now, we'll move on to molar ratios, because these are independent of the masses of the atoms in question. One mole of
232Th is 232 grams, and 1 mole of
208Pb is 208 grams. The calculations still give us the same relationships for the
232Th atoms that have disappeared, and the same equation can still be used, but the advantage of moving to molar ratios, is that the amount of
208Pb produced, when couched in molar ratios, doesn't involve tedious mass conversions. Consequently, for a sample that's 4.4 billion years old, one mole of
232Th will be converted to 0.804 moles of
232Th, and 0.196 moles of
208Pb. Since chemists routinely work with molar ratios, this makes everything more convenient from the calculation side, but still allows us to analyse actual raw data. Consequently, if we alight upon a sample in which the molar ratios of
232Th and
208Pb are 0.804 and 0.196 respectively, then we know we're dealing with a likely primordial sample. Molar ratios biased toward the
232Th side will indicate a sample that solidified at some younger age than 4.4 billion years, again calculable in the above manner.
Now comes the fun part. Scientists don't just happily assume that their samples will always yield nice data like this, regardless of lies peddled to the contrary by creationists. Instead, they perform
other tests in order to ensure that they have as much information about the provenance of the sample as possible. So, for example, with a terrestrial sample here on Earth, scientists would check other isotopes and their parent/daughter nuclide ratios, to provide cross-checking, and would also perform tests
to determine if the sample had been subject to other phenomena affecting molar ratios of substances of interest. Earth provides a number of these, one important one being groundwater movement dissolving out soluble minerals, and transporting them to lower strata. Geologists could probably cite several other processes that could exert similar effects upon molar ratios, but since I'm not a geologist, I'll leave it to them to come here and discuss this.
As a consequence, if one set of parent/daughter nuclides occurs in molar ratios that are consonant with a given age, but one outlier exists yielding a different age, then this is a clue to the scientists, that something of interest happened to that sample. Either it began with an anomalous composition of elements, or it acquired one via other processes before being collected. Which is usually what tends to be reported in the literature,
specifically to alert other future scientists to the possibility of anomalous compositions and their effect upon the data. This is reported perfectly honestly in the literature, specifically to warn other researchers to check their samples for such anomalous compositions before performing any actual calculations, and quite often, examples of anomalous results arising from calculations
not taking account of said checks, are provided to illustrate the errors that can arise if one does not apply due diligence and rigour.
It would not surprise me in the least, if [1] this is precisely what happened with the lunar rock samples, and [2] the resulting reporting had been duplicitous quote mined by creationists, leaving out all the important caveats that would inevitably appear in any genuine scientific reportage. Indeed, I can imagine one entirely plausible scenario that would result in an anomaly of this very sort with
232Th, namely,
the rock sample was formed with additional 208Pb in its matrix. Now here on Earth, this would become apparent early on in the testing, because here on Earth, that initial additional
208Pb would form easily recognisable crystalline minerals, and the presence of those would be an immediate pointer to the fact that this sample began with additional lead.
Lunar rocks, on the other hand, are subject to somewhat different weathering processes to those on Earth. Earth's atmosphere and magnetic field, together attenuate cosmic rays and charged particles from the solar wind, more or less eliminating weathering processes arising from those sources, whilst the atmosphere provides a different set of weathering phenomena of its own. On the surface of the Moon, however, the rocks are exposed to the vacuum of space, and to direct weathering by the solar wind. NASA has already alighted upon the results of this, in the form of nanophase iron, which occurs in measurable quantities in lunar rock samples, but which is only seen on Earth in artificially irradiated mineral samples. Now, of course, it's not just iron that's subject to cosmic ray and charged particle spallation of this sort - other elements will also be subject thereto. Consequently, I would expect any primordial lunar samples containing enhanced initial
208Pb to contain that lead in a nanophase form, which, lo and behold, would be distributed in the rock sample in a manner difficult to distinguish from the distribution arising from
232Th decay. Of course, I'll await some suitably informed words from actual analysts of the samples in question before suggesting that this
is what happened, but the fact that I can alight, with relatively little effort, upon a plausible natural mechanism for the appearance of skewed molar ratios in a lunar rock sample, should be telling you
that the actual scientists can think of a lot more, and go looking for them.
I think this covers the bases fairly neatly.