Friday, January 17, 2014

Question from a Reader: Radioactive Dating, Part 1

When I'm discussing Evolution with people this is the topic that ALWAYS comes up. Supposedly, radioactive dating proves beyond a doubt that the Universe is billions of years old. What's the counter-argument?

Introduction


It was only a matter of time until this came up.  This is the most frequent question I receive, and it is almost always the first question asked after a live presentation.  Radioactive dating, or radiometric dating, is a technique used by paleontologists, geologists, archaeologists, and other scientists to try to determine the exact age of some things.  In the mind of the public, it seems to be the most compelling evidence that the earth and life came into being billions of years ago, as opposed to the ~6000 years that "young-earth" creationists say have passed since Creation.

I often hear people use "carbon dating" synonymously with "radiometric dating," but carbon dating is but one of numerous types of radiometric dating.  Carbon dating is only useful for materials that contain significant amounts of carbon, such as organic compounds, and it is only used to date objects believed to be less than about 50,000-60,000 years old for reasons which I will explain later.  When geologists date rocks, they use one or several other radioactive elements, such as uranium, thorium, lead, or potassium.  

How it works


The Atom
Diagram of a nucleus emitting an alpha particle.
Image source.
As you may recall from grade school, all matter is composed of atoms, which in turn are composed of protons, neutrons, and electrons.  The protons and neutrons are concentrated in the atom's nucleus, while the electrons buzz around them in a cloud.  The number of protons in an atom's nucleus determines how it behaves, and therefore what element it is.  As long as there is no net electric charge, the number of electrons matches the the number of protons (when it does not match, the atom becomes an "ion").  The neutrons, on the other hand, do practically nothing but add weight.  Because of this, a group of atoms can have the same number of protons, making them the same element, but different numbers of neutrons.  These different forms of the same element are called "isotopes."

Radioactivity
Most elements have one or more "preferred" isotopes—that is, they are stable and happy with a certain number of neutrons and are usually found that way in nature.  Many elements also have unstable isotopes that can be found in nature, in which case the atom is unbalanced, in a sense.  To balance itself out, the atom of an unstable isotope will release energy in various ways, such as by ejecting a neutron, an electron, or an alpha particle (composed of two protons and two neutrons), or by giving off gamma rays (very high-energy light).  This process is known as radioactive decay.  Depending on the type of decay, the atom may change to another isotope of the same element or to another element because the number of neutrons and protons changes.  The newly produced substance is referred to as the "daughter isotope," whereas the substance that produced it is the "parent isotope."

Half-life
For any particular atom, the timing of the decay cannot be predicted.  However, for any given isotope, the probability of decay is the same for all of the atoms.  This results in a statistical phenomenon called exponential decay.

To give a crude example, imagine an auditorium full of people, each with a six-sided die.  We have all of the people stand up and roll their die into a handheld tray, then tell everyone who rolled a 1 to sit down.  Because the probability of rolling a 1 is 1:6, about one sixth of the people will sit down.  We then do the same for everyone left standing, having them roll and sit if they get a 1, resulting in a sixth of the remaining standers to sit.  Suppose we repeat this process every five seconds until nobody is left standing.  If we started with a hundred people, the last person should sit down after about two and a half minutes.  If we started with a million people, the last person should sit down after about 6 minutes and 40 seconds.  However, the proportion of people left standing at any time is the same, regardless of how many people started.  For those who are more visually inclined, here is the proportion of people left standing plotted over time:


(anyone who has an aversion to math can skip this next paragraph)

The curve shown has a function of y = (5/6)x/5, where "5/6" is the number of people left after each roll, and "x/5" gives the number of times the dice have been rolled since the start.  If we want to know how long it would take (t) to arrive at a particular proportion of people (P), we can use the equation t = 5 log5/6 P.

A simple way to describe an exponential decay curve is to refer to its "half-life."  The half-life is the time it takes for the proportion to reach 50%, so that after one half-life, 50% remains; after two half lives, 25% remains; after three half lives, 12.5% remains, and so on.  In our example, the half-life of the auditorium full of people is just a tad over 19 seconds.  Knowing the half-life, any person can calculate the proportion of people left from the time, or vice versa, without needing to know the specifics of the type of die used or the frequency of rolling.

The Dating Game
Applying this back to radiometric dating, then, we see that using measured half-lives and proportions, a scientist can calculate the amount of time that a sample has been decaying, in theory.  The "beginning" point for inorganic rocks is the moment the rock hardened from magma/lava, and for carbon dating of organic material, the clock starts when an organism dies and is shut off from the atmosphere.  We can see, then, that sedimentary rocks, in which nearly all fossils are found, cannot be radiometrically dated.  Rather, nearby igneous rocks (either magma intrusions or ash layers, usually) are dated, and the fossil-bearing sedimentary layer is assigned a date based on relative position.  Radiometric dating can also be quite expensive, so it is not used nearly as frequently as the public seems to think it is used.

When radiometric dating is used, a scientist must select an appropriate element to measure.  This obviously depends somewhat on which elements are present in the sample, but in many cases there are numerous options.  Each radioactive isotope of each element has a specific lab-measured half-life, ranging from a few seconds to billions of years.  The isotope is chosen, then, by the scale that the isotope can measure.  After all, you would not use a car odometer to measure the length of a table, nor would you use a footlong ruler to measure the distance from Pittsburgh to Phoenix.  However, this reveals the first flaw of this technique—an age of a sample is already assumed to some extent, and the radiometric method is only being used to narrow it down.

Continue to Part 2 to learn the critical assumptions involved in radiometric dating →

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