How dendrochronology works
Tree rings are not quite the only system that promises total accuracy to the nearest year. Varves are layers of sediment laid down in glacial lakes. Like tree rings, they vary seasonally and from year to year, so theoretically the same principle can be used, with the same degree of accuracy. Coral reefs, too, have annual growth rings, just like trees. Fascinatingly, these have been used to detect the dates of ancient earthquakes. Tree rings too, by the way, tell us the dates of earthquakes. Most of the other dating systems that are available to us, including all the radioactive clocks that we actually use over timescales of tens of millions, hundreds of millions or billions of years, are accurate only within an error range that is approximately proportional to the timescale concerned.
RADIOACTIVE CLOCKS
Let’s now turn to radioactive clocks. There are quite a lot of them to choose from, and, as I said, they blessedly cover the gamut from centuries to thousands of millions of years. Each one has its own margin of error, which is usually about 1 per cent. So if you want to date a rock which is billions of years old, you must be satisfied with an error of plus or minus tens of millions of years. If you want to date a rock hundreds of millions of years old, you must be satisfied with an error of millions. To date a rock that is only tens of millions of years old, you must allow for an error of plus or minus hundreds of thousands of years.
To understand how radioactive clocks work, we first need to understand what is meant by a radioactive isotope. All matter is made up of elements, which are usually chemically combined with other elements. There are about 100 elements, slightly more if you count elements that are only ever detected in laboratories, slightly fewer if you count only those elements that are found in nature. Examples of elements are carbon, iron, nitrogen, aluminium, magnesium, fluorine, argon, chlorine, sodium, uranium, lead, oxygen, potassium and tin. The atomic theory, which I think everybody accepts, even creationists, tells us that each element has its own characteristic atom, which is the smallest particle into which you can divide an element without it ceasing to be that element. What does an atom look like, say an atom of lead, or copper, or carbon? Well, it certainly looks nothing like lead or copper or carbon. It doesn’t look like anything, because it is too small to form any kind of image on your retina, even with an ultra-powerful microscope. We can use analogies or models to help us visualize an atom. The most famous model was proposed by the great Danish physicist Niels Bohr. The Bohr model, which is now rather out of date, is a miniature solar system. The role of the sun is played by the nucleus, and around it orbit the electrons, which play the role of planets. As with the solar system, almost all the mass of the atom is contained in the nucleus (‘sun’), and almost all the volume is contained in the empty space that separates the electrons (‘planets’) from the nucleus. Each electron is tiny compared with the nucleus, and the space between them and the nucleus is huge compared with the size of either. A favourite analogy portrays the nucleus as a fly in the middle of a sports stadium. The nearest neighbouring nucleus is another fly, in the middle of an adjacent stadium. The electrons of each atom are buzzing about in orbit around their respective flies, smaller than the tiniest gnats, too small to be seen on the same scale as the flies. When we look at a solid lump of iron or rock, we are ‘really’ looking at what is almost entirely empty space. It looks and feels solid and opaque because our sensory systems and brains find it convenient to treat it as solid and opaque. It is convenient for the brain to represent a rock as solid because we can’t walk through it. ‘Solid’ is our way of experiencing things that we can’t walk through or fall through, because of the electromagnetic forces between atoms. ‘Opaque’ is the experience we have when light bounces off the surface of an object, and none of it goes through.
Three kinds of particle enter into the makeup of an atom, at least as envisaged in the Bohr model. Electrons we have already met. The other two, vastly larger than electrons but still tiny compared with anything we can imagine or experience with our senses, are called protons and neutrons, and they are found in the nucleus. They are almost the same size as each other. The number of protons is fixed for any given element and equal to the number of electrons. This number is called the atomic number. It is uniquely characteristic of an element, and there are no gaps in the list of atomic numbers – the famous periodic table.* Every number in the sequence corresponds to exactly one, and only one, element. The element with 1 for its atomic number is hydrogen, 2 is helium, 3 lithium, 4 beryllium, 5 boron, 6 carbon, 7 nitrogen, 8 oxygen, and so on up to high numbers like 92, which is the atomic number of uranium.
Protons and electrons carry an electric charge, of opposite sign – we call one of them positive and the other negative by arbitrary convention. These charges are important when elements form chemical compounds with each other, mostly mediated by electrons. The neutrons in an atom are bound into the nucleus together with the protons. Unlike protons they carry no charge, and they play no role in chemical reactions. The protons, neutrons and electrons in any one element are exactly the same as those in every other element. There is no such thing as a gold-flavoured proton or a copper-flavoured electron or a potassium-flavoured neutron. A proton is a proton is a proton, and what makes a copper atom copper is that there are exactly 29 protons (and exactly 29 electrons). What we ordinarily think of as the nature of copper is a matter of chemistry. Chemistry is a dance of electrons. It is all about the interactions of atoms via their electrons. Chemical bonds are easily broken and remade, because only electrons are detached or exchanged in chemical reactions. The forces of attraction within atomic nuclei are much harder to break. That’s why ‘splitting the atom’ has such a menacing ring to it – but it can happen, in ‘nuclear’ as opposed to chemical reactions, and radioactive clocks depend upon it.
Electrons have negligible mass, so the total mass of an atom, its ‘mass number’, is equal to the combined number of protons and neutrons. It is usually rather more than double the atomic number, because there are usually a few more neutrons than protons in a nucleus. Unlike the number of protons, the number of neutrons in an atom is not diagnostic of an element. Atoms of any given element can come in different versions called isotopes, which have differing numbers of neutrons, but always the same number of protons. Some elements, such as fluorine, have only one naturally occurring isotope. The atomic number of fluorine is 9 and its mass number is 19, from which you can deduce that it has 9 protons and 10 neutrons. Other elements have lots of isotopes. Lead has five commonly occurring isotopes. All have the same number of protons (and electrons), namely 82, which is the atomic number of lead, but the mass numbers range between 202 and 208. Carbon has three naturally occurring isotopes. Carbon-12 is the common one, with the same number of neutrons as protons: 6. There’s also carbon-13, which is too short-lived to bother with, and carbon-14 which is rare but not too rare to be useful for dating relatively young organic samples, as we shall see.
Now for the next important background fact. Some isotopes are stable, others unstable. Lead-202 is an unstable isotope; lead-204, lead-206, lead-207 and lead-208 are stable isotopes. ‘Unstable’ means that the atoms spontaneously decay into something else, at a predictable rate, though not at predictable moments. The predictability of the rate of decay is the key to all radiometric clocks. Another word for ‘unstable’ is ‘radioactive’. There are several kinds of radioactive decay, which offer possibilities for useful clocks. For our purposes it isn’t important to understand them, but I explain them here to show the magnificent level of detail that physicists have achieved in working out such things. Such detail casts a sardonic light on the desperate attempts of creationists to explain away the evidence of radioactive dating, and keep the Earth young like Peter Pan.
All these kinds of instability involve neutrons. In one kind, a neutron turns into a proton. This means that the mass number stays the same (since protons and neutrons have the same mass) but the atomic number goes up by one, so the atom beco
mes a different element, one step higher in the periodic table. For example, sodium-24 turns itself into magnesium-24. In another kind of radioactive decay, exactly the reverse happens. A proton turns into a neutron. Again, the mass number stays the same, but this time the atomic number decreases by one, and the atom changes into the next element down in the periodic table. A third kind of radioactive decay has the same result. A stray neutron happens to hit a nucleus and knocks out one proton, taking its place. Again, there’s no change in mass number; again, the atomic number goes down by one, and the atom turns into the next element down in the periodic table. There’s also a more complicated kind of decay in which an atom ejects a so-called alpha particle. An alpha particle consists of two protons and two neutrons stuck together. This means that the mass number goes down by four and the atomic number goes down by two. The atom changes to whichever element is two below it in the periodic table. An example of alpha decay is the change of the very radioactive isotope uranium-238 (with 92 protons and 146 neutrons) to thorium-234 (with 90 protons and 144 neutrons).
Now we approach the nub of the whole matter. Every unstable or radioactive isotope decays at its own characteristic rate which is precisely known. Moreover, some of these rates are vastly slower than others. In all cases the decay is exponential. Exponential means that if you start with, say, 100 grams of a radioactive isotope, it is not the case that a fixed amount, say 10 grams, turns into another element in a given time. Rather, a fixed proportion of whatever is left turns into the second element. The favoured measure of decay rate is the ‘half-life’. The half-life of a radioactive isotope is the time taken for half of its atoms to decay. The half-life is the same, no matter how many atoms have already decayed – that is what exponential decay means. You will appreciate that, with such successive halvings, we never really know when there is none left. However, we can say that after a sufficient time has elapsed – say ten half-lives – the number of atoms that remains is so small that, for practical purposes, it has all gone. For example, the half-life of carbon-14 is between 5,000 and 6,000 years. For specimens older than about 50,000–60,000 years, carbon dating is useless, and we need to turn to a slower clock.
The half-life of rubidium-87 is 49 billion years. The half-life of fermium-244 is 3.3 milliseconds. Such startling extremes serve to illustrate the stupendous range of clocks available. Although carbon-15’s half-life of 2.4 seconds is too short for settling evolutionary questions, carbon-14’s half-life of 5,730 years is just right for dating on the archaeological timescale, and we’ll come to it presently. An isotope much used on the evolutionary timescale is potassium-40, with its half-life of 1.26 billion years, and I’m going to use it as my example, to explain the whole idea of a radioactive clock. It is often called the potassium argon clock, because argon-40 (one lower in the periodic table) is one of the elements to which potassium-40 decays (the other, resulting from a different kind of radioactive decay, is calcium-40, one higher in the periodic table). If you start with some quantity of potassium-40, after 1.26 billion years half of the potassium-40 will have decayed to argon-40. That’s what half-life means. After another 1.26 billion years, half of what remains (a quarter of the original) will have decayed, and so on. After a shorter time than 1.26 billion years, a proportionately smaller quantity of the original potassium will have decayed. So, imagine that you start with some quantity of potassium-40 in an enclosed space with no argon-40. After a few hundreds of millions of years have elapsed, a scientist comes upon the same enclosed space and measures the relative proportions of potassium-40 and argon-40. From this proportion – regardless of the absolute quantities involved – knowing the half-life of potassium-40’s decay and assuming there was no argon to begin with, one can estimate the time that has elapsed since the process started – since the clock was ‘zeroed’, in other words. Notice that we must know the ratio of parent (potassium-40) to daughter (argon-40) isotopes. Moreover, as we saw earlier in the chapter, it is necessary that our clock has the facility to be zeroed. But what does it mean to speak of a radioactive clock’s being ‘zeroed’? The process of crystallization gives it meaning.
Like all the radioactive clocks used by geologists, potassium/ argon timing works only with so-called igneous rocks. Named after the Latin for fire, igneous rocks are solidified from molten rock – underground magma in the case of granite, lava from volcanoes in the case of basalt. When molten rock solidifies to form granite or basalt, it does so in the form of crystals. These are normally not big, transparent crystals like those of quartz, but crystals that are too small to look like crystals to the naked eye. The crystals are of various types, and several of these, such as some micas, contain potassium atoms. Among these are atoms of the radioactive isotope potassium-40. When a crystal is newly formed, at the moment when molten rock solidifies, there is potassium-40 but no argon. The clock is ‘zeroed’ in the sense that there are no argon atoms in the crystal. As the millions of years go by, the potassium-40 slowly decays and, one by one, atoms of argon-40 replace potassium-40 atoms in the crystal. The accumulating quantity of argon-40 is a measure of the time that has elapsed since the rock was formed. But, for the reason I have just explained, this quantity is meaningful only if expressed as the ratio of potassium-40 to argon-40. When the clock was zeroed, the ratio was 100 per cent in favour of potassium-40. After 1.26 billion years, the ratio will be 50–50. After another 1.26 billion years, half of the remaining potassium-40 will have been converted to argon-40, and so on. Intermediate proportions signify intermediate times since the crystal clock was zeroed. So geologists, by measuring the ratio between potassium-40 and argon-40 in a piece of igneous rock that they pick up today, can tell how long ago the rock first crystallized out of its molten state. Igneous rocks typically contain many different radioactive isotopes, not just potassium-40. A fortunate aspect of the way igneous rocks solidify is that they do so suddenly – so that all the clocks in a given piece of rock are zeroed simultaneously.
Only igneous rocks provide radioactive clocks, but fossils are almost never found in igneous rock. Fossils are formed in sedimentary rocks like limestone and sandstone, which are not solidified lava. They are layers of mud or silt or sand, gradually laid down on the floor of a sea or lake or estuary. The sand or mud becomes compacted over the ages and hardens as rock. Corpses that are trapped in the mud have a chance of fossilizing. Even though only a small proportion of corpses actually do fossilize, sedimentary rocks are the only rocks that contain any fossils worth speaking of.
Sedimentary rocks unfortunately cannot be dated by radioactivity. Presumably the individual particles of silt or sand that go to make sedimentary rocks contain potassium-40 and other radioactive isotopes, and therefore could be said to contain radioactive clocks; but unfortunately these clocks are no use to us because they are not properly zeroed, or are zeroed at different times from each other. The particles of sand that are compacted to make sandstone may originally have been ground down from igneous rocks, but the igneous rocks from which they were ground all solidified at different times. Every grain of sand has a clock zeroed at its own time, and that time was probably long before the sedimentary rock formed and entombed the fossil we are trying to date. So, from a timekeeping point of view, sedimentary rock is a mess. It can’t be used. The best we can do – and it is a pretty good best – is to use the dates of igneous rocks that are found near sedimentary rock, or embedded in it.
To date a fossil, you don’t literally need to find it sandwiched between two slabs of igneous rock, although that is a neat way to illustrate the principle. The actual method used is more refined than that. Recognizably similar layers of sedimentary rock occur all over the world. Long before radioactive dating was discovered, these layers had been identified and given names: names like Cambrian, Ordovician, Devonian, Jurassic, Cretaceous, Eocene, Oligocene, Miocene. Devonian sediments are recognizably Devonian, not only in Devon (the county in south-west England that gave them their name) but in other parts of the world. They are
recognizably similar to each other, and they contain similar lists of fossils. Geologists have long known the order in which these named sediments were laid down. It’s just that, before the advent of radioactive clocks, we didn’t know when they were laid down. We could arrange them in order because – obviously – older sediments tend to lie beneath younger sediments. Devonian sediments, for example, are older than Carboniferous (named after the coal which is frequently found in Carboniferous layers) and we know this because, in those parts of the world where the two layers coincide, the Devonian layer lies underneath the Carboniferous layer (the exceptions to this rule occur in places where we can tell, from other evidence, that the rocks have been tilted aslant, or even turned upside down). We aren’t usually fortunate enough to find a complete run of layers, all the way from Cambrian at the bottom up to Recent at the top. But because the layers are so recognizable, you can work out their relative ages by daisychaining and jigsawing your way around the world.
So, long before we knew how old fossils were, we knew the order in which they were laid down, or at least the order in which the named sediments were laid down. We knew that Cambrian fossils, the world over, were older than Ordovician ones, which were older than Silurian; then came Devonian, then Carboniferous, Permian, Triassic, Jurassic, Cretaceous, and so on. And within these major named layers, geologists also distinguish sub-regions: upper Jurassic, middle Jurassic, lower Jurassic, and so on.
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