Radioactive Dating — How Knowledge Works

An element is described as radioactive if, in its natural state, its atoms have an unstable nucleus. Elements that are not radioactive have a structure that is strongly balanced and doesn't need to change to become more stable. General speaking radioactive elements emit particles to achieve stability and in so doing change to another element, or a more stable version of the same element.

If a radioactive element, like uranium, is present in a material, say a rock sample, We can work out when the rock originally formed by measuring how much of the radioactive element has decayed to a new stable element. So for example uranium decays to lead and the ratio of the two elements, together with the known rate of decay tells us how old the rock is.

The key to this calculation is knowing what the rate of decay is. The rate of decay we calculate is called the half-life, and requires an explanation before we can proceed.

What is a half-life

The interesting thing about radioactive elements is that it is impossible to predict when an individual atom of the element will decay (say uranium to lead). But you can work out the rate of decay of a large sample. In any large sample of a radioactive element a fraction of the atoms will decay in a given period of time. It will always be the the same fraction because all the atoms are identical, so the probability of decay will not change. For convenience we use the half-life. In other words how long will it take for half of the atoms to decay.

How the half life of Nickel to Copper works. Source - Me

The diagram left illustrates how this is used to work out time scales. Suppose the half life is 100 years. An unstable isotope of Nickel decays to copper in a half-life of almost exactly 100 years. You can see here how the ratio between the two elements changes over time. Theoretically there is no limit to how far back in time you can go because there will always be some of the original element left. In reality there is a limit because the remaining original element will get too small to detect with available technology and the margin of error becomes too great.

The ridiculously long decay chain from Uranium 238 to Lead 206. Source - Wikimedia, Tosaka

The other thing about half-life is that the rates of decay vary enormously from fractions of a second to billions of years. This is because there are degrees of instability. A highly unstable element will decay quickly, while a moderately unstable element will decay much more slowly.

Some elements, usually the heavier ones, go through many transitions to other unstable elements before arriving at a stable element. This is what happens to uranium. You can see from the chart on the left that half lives of the transition elements (also called decay products) range from a fraction of a second for polonium 214 to 75,380 years for Thorium 230. With this amount of detail available the half-life from uranium to lead can be very precise. Uranium is one of the longest half lives at 4.5 billion years for uranium 238, 700 million years for uranium 235 and 25 thousand years for uranium 234.

At this point it will be opportune to explain why elements have different versions. We need to talk about isotopes.

Isotopes

All atoms always have the same number of two things. Protons, which carry most of the mass and sit at the centre of the atom, and exactly the same number of the much lighter electrons that orbit the proton. The reason why this is a very stable arrangement is the the protons are positively charged and the electrons are negatively charged. The only thing that makes one element, say iron, different from another element, say carbon, is the number of protons (and electrons it has. Carbon has 6 protons and electrons each, while iron has 26.

Then we come to the third particle in most, but not all, atoms. The neutron is similar to the proton. It sits in the middle with the proton, but it has no charge, so it doesn't upset the balance of charge. The effect of a neutron on an atom is to change its mass. Each additional neutron make the element heavier. If we look at the lightest element, hydrogen, it has three versions. Deuterium has one extra neutron which doubles the atoms mass, and tritium has two extra neutrons, which triple the mass. What is interesting about these isotopes of hydrogen is that the first two are stable versions of hydrogen and tritium is radioactive. Tritium has a half-life of 12.32 years and it decays to a stable isotope of helium which has one extra neutron. The basic hydrogen atom (also called a protium) is 98.85% of all hydrogen on earth. For every 87 atoms only one is deuterium and tritium is just a trace because it doesn't hang around much. The Deuterium in water molecules turn ordinary water into heavy water and an attempt was made to accumulate large amounts of it by Germany during the second world war in its unsuccessful attempt to build an atomic bomb.

The atomic structure of Nickel showing the rings of electrons (2-8-16-2). Source - WIkipedia, Pumbaa and Greg Robson

As an aside, don't be fooled by the stylised image of the hydrogen atom. A hydrogen atom is 99.9999999999996% empty space. The only reason that stuff seems solid is that the outer face of atoms is so difficult to penetrate. The empty space is wrapped up tight. If a hydrogen atom was the length of a football pitch the proton in the middle of the centre circle would be 1.6 mm across or 1/16th of an inch. The electron would be orbiting roughly at the goal posts.

So lets look at the nickel atom we talked about above. Nickel has 28 electrons around a nucleus with, of course, 28 protons. Nickel has 5 stable isotopes and 30 unstable ones with neutron counts ranging from 20 to 80. The 5 stable version have 30, 32, 33, 34 and 36 neutrons. All the the rest have half-lives that range from tiny fractions of a second to 7,600 years.

There are therefore a lot of opportunities to study radioactive elements for dating (not dinner dates obviously). So lets get started on some of the most useful ones.

How carbon 14 enters the environment and is fixed in living things through the absorption of carbon dioxide. Source - Flickr, Mrs Pugliano

Carbon 14 dating

Cosmic rays bombard the Earth all the time. A human body is struck by about 1,400 of them every second. When a cosmic ray strikes an atom in the atmosphere it produces an energetic neutron as a by product. When this neutron strikes a nitrogen atom it turns into a carbon 14 atom. Normal carbon is carbon 12. Carbon 14 is unstable but stays around long enough to get mixed up with ordinary carbon when it joins forces with two oxygen atoms to form carbon dioxide. Carbon 14 is now permanently fixed until the life form that absorbed it dies.

When plants absorb carbon dioxide and animals eat the plant, the result is that carbon 14 is fixed in living matter and the proportion of the two versions is also fixed. When the living organism dies the carbon 14 then starts to decay back to nitrogen with a half-life of 5,700 years.

Any nonliving organic material can therefore be dated back to when the plant or animal died. So the age of the sample can be dated back to its demise by measuring how the ratio between carbon 12 and 14 has changed. To do this we need to know what the proportion of carbon 14 was while the sample was living. This is where science deniers have a bit of a field day by claiming that carbon 14 levels fluctuate wildly over historical time and any measurement is therefore unreliable. Levels of carbon 14, and thus carbon dioxide with carbon 14, do indeed fluctuate. Fortunately though we know what these fluctuations are by a number of different and independent techniques, including two that I will be writing about shortly; tree ring and ice core analysis, but there are many others. Rock, fossils, corals and sediment deposits are just some of the ways we work out climate variations over time. Trapped pollen grains show which plants grew. this acts as a check as different plants thrive in different climatic conditions.

Carbon 14 decay can date back as far as 60,000 years at a pinch but more conservatively, 50,000 years.

Secular Equibrium. The balance maintained in the transition elements from uranium 238 to Thorium 230. Source - Wikimedia, Tosaka

Uranium-Thorium dating

This technique is different from the usual assessment of changed ratios between what are called parent and daughter isotopes. To illustrate this interesting difference I have cropped the image I used above showing the long-winded uranium to lead decay to show what is going on with this technique.

The transition is from uranium 234 to thorium 230. But you can see that uranium 234 is being constantly replenished by the decay of uranium 238 via two rather short lived isotopes, thorium 234 and protactinium 234. Thorium 230 is of course also decaying towards lead. The measure is therefore not the ratio between isotopes but the balance that is maintained between them through their respective decay rates. The way of measuring is called secular equilibrium and is significantly more accurate than usual. Also most importantly is can calculate the ages of samples that are also calculated using carbon 14 dating between 1000 and 50,000 years.

Potassium decaying to Argon and Calcium in volcanic rock - Source - Wikimedia, Dominic Vilsmeier

Potassium-Argon dating

Rock that forms from a molten precursor, like volcanic rock, loses all its argon to the atmosphere before it solidifies. If the rock contains any potassium it will replenish the rock with argon by radioactive decay. It also decays to calcium but this is pretty useless for dating because there is to much calcium in rock anyway, so its impossible to separate out. This technique is best at dating sedimentary deposits of volcanic origin, and can validate carbon 14 and uranium-thorium studies by dating the layers above and below fossil bones. It contributed to the dating of human remains in Olduvai Gorge.

Fission track dating

This method is unique because instead of measuring decay and proportions of isotopes it measures the very specific damage to crystals that have uranium 238 within them. The decay of uranium 238 causes what are called fission tracks within the crystal. Since these tracks cannot appear while the rock is molten or hot we know the tracks only start once the rock has cooled. By measuring the rate of crystal damage with powerful microscopes we get a pretty accurate estimate of how old the rocks are. The range of ages is 100,000 to 2 billion years.

The table of radiometric dating techniques that shows their range and how they overlap with each other. Source - Me

The four big ones

All of the remaining techniques on the chart below can date from 10 million to well beyond the 4.6 billion age of the earth and are sometimes used to date meteorites. Many of these can be calculated from the same cycle, especially if they are a part of a longer decay chain. The main thing to note is that from 500 to 4.6 billion years there are never less than two distinct techniques. In fact the important period from 10,000 to 50,000 has three. This is very similar to the Cosmic Staircase measuring distances to stars and galaxies. See my series of essays on this subject from the home page.

This is yet another example of the interconnectedness of knowledge, one of the main themes of these essays.

Note - Its worth mentioning that radioactive decay techniques aren't the only ones used to work out ages on earth. Dendrochronology, geology, genetic mutation, sedimentary rock, ice cores etc, could easily be added to this chart, increasing the number of techniques for any period of the Earth's history.