## Tuesday, September 21, 2010

### Basic Insights into Radioactive Decay

While teaching evolutionary biology in Barbados, I found that in more than one place of the syllabus there was provision to introduce physics concepts. One of these is the use of radio-isotope dating, with which every budding evoutionist needs to be familiar. At the very least, this allows the more accurate placing of fossil finds in relation to others, after they have been subject to geological disturbances or long term processes.

In this blog I want to give some basic background on radio-nuclide dating. For reference, the fundamental law of radioactive decay, based on some original number of N(o) atoms decaying with an activity a over time t to a number N atoms, is:

N = N(o) exp (-at)

The ‘half-life’ is the time for half of the original (N(o)) atoms to disintegrate, or for

N(o) -> N(o)/2

Thus:

N(o)/ 2 = N(o) exp(-a T ½)

where the half-life: T ½, has been inserted into the exponent for the time t.

After canceling N(o) from both sides of the above equation, and taking natural logarithms (base e)[1]:

a T ½ = ln 2 = 0.693

or T ½ = 0.693/ a

Using this basis, any sample or fossil, with even a minuscule amount of radioactive element can be dated. All we need to know is that over the period T ½, half of the number of remaining atoms decay and the current activity in Becquerels. Thus, if T ½ = 15,000 yrs. for a = 200 Bq, then if a = 50 Bq now, we may deduce the sample is ~ 45,000 yrs. old. (E.g. three half-lives decaying)
A graphical depiction of a generic radio-nuclide decay is shown in the accompanying diagram. Here, the left side of the graph shows a relative scale for amounts (masses) of an unnamed, decaying radioactive isotope which starts at some specified value (1 gram) then decreases to half the original amount each half life. The time axis is given in millions of years (mY). It’s easy to see here that the half life for this hypothetical isotope is about 1 million years.[2]

The problem of dating ancient fossils or other specimens is really a problem of finding the radioactive isotope with half-life long enough to provide a reasonably accurate measure of the age. For fossils one would look first for isotopes that have half-lives in the millions, or at least hundreds of thousands of years. Failing that, one would wish to have available some kind of correction method, say to correct for extraneous effects like the atmosphere might impose on samples.

For many applications, potassium-argon dating methods are important. These are based on the relative compositions of Potassium –40 to Argon-40, a gas. Typically when rocks or other items are tested, the sample obtained is split between the potassium content on the one hand, and the argon on the other. The instrument of choice to assess the ratio of K-40 content/mass to Ar-40 (or other combinations in the relevant radioactive series) is the mass spectrometer.

Exotic isotopes of carbon can also be used if the measurement technique is sufficiently refined. In a recent use of the isotope delta 13C, evidence has been found for the existence of life on Earth at least 3, 850 million (or 3.85 billion) years ago.[3] Quartz (zircon, zirconium) crystals have often found to be of use, since they may harbor small amounts of uranium or thorium at the level of ‘parts per billion’.[4] For dating in the millions of years – particularly for igneous rocks and fossils embedded within, isotopes of lead and strontium are ideal, being the ‘daughters’ from millions of years of radioactive decay.

Despite some drawbacks to the use of fossils and the fossil record, we see that radioactive isotope dating is an excellent means of enhancing their quality assurance. The use of such methods (e.g. using delta 13C) to show that life existed on Earth nearly four billion years ago, for example, controverts the thesis claimed by most creationists: that life arose barely 6 millenia ago. The fact it ties to a primitive bacterium discloses humans didn't appear first but rather bacteria, which makes sense given the human genetic associations to assorted bacteria.

Even if creationists dispute the underlying explanation for what the delta 13C dating reveals, they are left to account for it on their own. That the ancient organisms were likely methanotrophs – living on methane gas, a toxin to humans - makes their challenge even more interesting and their solutions less probable. Beyond this, the many differing layers of the fossil record revealed show that any special creationist explanation either approaches nonsense, infringes credulity or both. For instance, multiple layers disclose multiple ‘creations’ in the creationists’ framework. And it certainly begs both reason and credulity that any deity requiring so many ‘creations’ can possibly command our attention. At the very least, it ought to be ‘fired’ for gross inefficiency!

[1] Of course I am leaving out a large amount of mathematics here, especially the calculus aspects related to rate of decay, e.g. dN/dt and how various forms are obtained, also equations linking up the daughter nuclei produced from the original nuclei. I am hoping readers will avail themselves of many fine resources to broaden their perspectives on this, and reinforce what I’ve given here.

[2] The real life isotope that most closely matches is Zirconium 93.

[3] Holland, H.D.: Evidence for Life on Earth More Than 3850 Million Years Ago, in Science, Vol. 275, 3 January, 1997, p. 38.

[4] The Dating Game, Research in Review, Summer/Fall 1990, p. 5.