At the fastest end of our list of clocks was the decay of exotic subatomic particles like the delta particle or the Z boson, which have lifetimes measured in yactoseconds, 10−24 s. Deltas form due to the rearrangement of quarks within a proton or neutron, and the transition times are driven by the strong force, the force that binds quarks into the particles that we can see.
A great deal slower than strong transitions are atomic transitions, measured in nanoseconds, 10−9 s. These are the transitions that give us light to see by and also the cesium-133 clock. These transitions are driven by the electromagnetic force. The electromagnetic force is several orders of magnitude weaker than the strong force, so it is not surprising that its timescale is also much slower.
Our last timekeepers are based on the orbits of celestial bodies. It is the force of gravity that holds these systems together. And much like the trend between the strong and electromagnetic forces, gravity is much weaker and the timepieces are much slower.
We have, of course, skipped the weak force. The weak force is what causes radioactive decays. We will look at all the forces in detail in the next few chapters, but for now it is enough to know that the weak force has a problem: it is really weak. It is also very short range and so operates in a world within a neutron or proton, a region overwhelmingly dominated by the strong force. However, it does have a role. The strong force can hold together three quarks to make a neutron: an up and two down quarks. What the weak force can do, for example, is push one of those down quarks to decay into an up quark. In this case a neutron has become a proton, one of the most basic weak decays.
The weak decay can also happen between electrons and their exotic, heavier siblings, the muon and the tau particle. The decay of the muon is often considered the prototypical weak decay. This is because the muon decay is not buried inside of a bigger particle, and so it is free of strong-force complications. The lifetime of the muon is about 2 µ s (10−6 s), which fits in with our comparison to strong decays (10−24 s) and electromagnetic decays (10−9 s). It is a bit weaker than the electromagnetic force and much weaker than the strong force. But by itself that does not help us get to deep time.
When we look at the weak decay of the neutron to a proton we find a lifetime of nearly 14 min. This range represents a factor of a billion. But the weak decay exhibits even a broader range than that. At the fastest end of the scale is the tau particle, the electron’s heaviest sibling, with a lifetime of 3 × 10−13 s. A decay in a chain reaction can take a shake, or 10−8 s. But I am looking for a slower clock, one with which I can measure the age of stars and the universe.
Rubidium-86 decays in 18.6 days and americium-241, the heart of many smoke detectors, has a half-life of 432 years. Perhaps the most famous radioactive element is uranium-238 with a half-life of 4.47 billion years. We are now talking about timescales similar to the age of the Earth. If you had a kilogram of U-238 when the Earth was formed, you would now have half a kilogram left.
One of the slowest decays measured is vanadium-50 with a half-life of 1.5 × 1017 years. It may not actually be the slowest decay; it is just hard to measure these rare events. Actually you do not have to start with a kilogram and wait for half of it to go away. Instead you start with a known amount and watch the rate of decay particles coming out. For example, if I had a milligram of vanadium-50 (which is hard to obtain) and I watched it for a year I would see about 56 decay particles radiating out. When I compare the 56 I saw to the number we started with (think Avogadro’s number) we could work out the half-life. Measuring a long half-life comes down to isolating a good sample, and waiting for the occasional decays.
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Perhaps the most famous use of radioactive decay related to time is carbon-14 dating. But before we can look at this we need to understand a little bit about carbon and isotopes.
Most carbon is carbon-12, often written as 12C. In its nucleus are six protons and six neutrons. There are also six electrons orbiting the nucleus. It is those electrons that set carbon’s chemical properties and that is how we recognize it as carbon. In fact all carbon atoms have six electrons and therefore six protons because they are electrically neutral. But the number of neutrons is not so well determined. In nature there are carbon atoms with six, seven and even eight neutrons. These different variations all act essentially the same chemically, which is why we call them all carbon, but they have different masses. We call these variants isotopes, a term which is based on the Greek words for “same place,” meaning the same place on the periodic table of the elements. The 12 at the end of carbon-12 thus tells us the number of protons plus neutrons.
Carbon-13 has an extra neutron. It is like carbon-12: it is stable and will not decay and will participate in all the same chemical reactions as carbon-12. Carbon-14 has two extra neutrons that unbalance the nucleus a little and so it will eventually decay. A single carbon-14 atom has a 50% chance of decaying after 5730 years. That means that if I started out with a million atoms, after 5730 years I will have only 500,000 carbon-14 atoms left. After a further 5730 years I will be down to 250,000 atoms (see Figure 9.2). This is the basis for radiocarbon dating, which is so often used in archeology. If you know how many carbon-14 atoms an object started with, and you know how many it has now, you can figure out how long that bit of carbon has been around. The trick is to figure out how many were originally in the sample.
Figure 9.2 The decay of carbon-14 used for dating. Half of the carbon-14 in a sample decays after 5730 years, half of the remaining carbon decays over the next 5730 years and so forth.
Carbon in a piece of wood comes from the atmosphere at the time the tree was growing. In the process of photosynthesis carbon dioxide (CO2) was absorbed by the tree’s leaves and was synthesized into sugar and then into cellulose. If all carbon-14 on Earth dated from the time of the origin of our planet, it would all have essentially decayed away by now. But carbon-14 is constantly being produced in the upper atmosphere. When a high-energy cosmic ray collides with a nitrogen atom it might transform that atom into carbon-14. This means that there are always new carbon-14 atoms being created and the number in the atmosphere is nearly constant. Our atmosphere has one carbon-14 for every trillion carbon-12 atoms. So by measuring the ratio 14C:12C in your sample now, and knowing that it was originally one to a trillion, you can figure out how old the sample is.
This whole technique seems almost too clever. It is also true that people have been tweaking it since Willard Libby developed it in 1949. For instance, if the object is an important artifact, such as the Shroud of Turin, you will want to use as little of a sample as you can. Also, how do we know that the production of 14C has been constant? We can actually confirm this number by looking at the carbon-14 content of objects with a known history. Libby was able to get a scrap of wood from an ancient Egyptian barge, the age of which was known from written records. He could also confirm the technique by looking at the heartwood of a redwood tree that had been cut in 1874. By counting tree rings he could independently determine the age of the heart wood as 2900 years old, in agreement with the carbon-14 dating results.
Actually, by looking at tree rings people have found slight variations of the trillion-to-one number over time and in various locations, but nothing dramatic. With a lifetime of 5730 years, carbon-14 is well suited to dating objects through the history of modern man. In fact we can date samples back to about 63,000 years, but not much beyond.
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We now enter realm of geologic time, the time it takes to build mountains, cut valleys, or even form the Earth itself.
Once you have watched a flood carve out a new channel, or a volcano erupt and new rocks appear it soon becomes apparent that the world is in flux. When you look at the side of a mountain, especially in a dry region or if it is very steep and so not hidden beneath trees, there is a story to read. Layers of sandstone, limestone, or schist must be telling us something, if only we knew how to read it.
Figure 9.3 The layers or strata of the Grand Canyon. Fossi
ls in each layer order and date the rock. Radiometric dating is also used.
One of the first people to try and read these layers was Nicholas Steno (1638–1686), a Danish naturalist and later a priest and bishop. He recognized some of the most basic principles of stratigraphy, principles like: strata are laid down horizontally, even if later they are tilted. Also, newer layers must be formed on top of older layers. So when you see a deep cut through the Earth, like the Grand Canyon (see Figure 9.3), the newest rocks are on top, near the canyon’s rim, and the oldest are at the bottom. The rimrock is Kaibab limestone, which is about 250 million years old. At the bottom of the canyon, near the Colorado River, is the Vishnu schist, which is almost two billion years old.
Strata are not always simple to read. Over time a layer may be eroded before a new layer caps it, such that a layer might be thinner than it was originally, or even missing. As continents collide and mountain ranges push up layers can get twisted, tilted, or even inverted. But the general trend is old on bottom and new on top, a feature which geologists use to decipher the history of the Earth.
In the century following Steno, people were collecting rocks and also fossils, but it would be a mining and canal engineer in England who really saw the important relationship between strata and fossils. William “Strata” Smith (1769–1839) realized that the same fossils show up in the same strata. He also realized that the same strata existed all across the British Isles, but sometimes tipped, so that what was near the surface in Wales was buried deep under London. This meant that once the fossil record was established where rocks were undisturbed, then rocks that were broken, tilted, or even inverted elsewhere could be dated by their fossils, at least in a relative sense.
When you start to read the fossil record as a book the story has a curious structure. The fossils change slowly as you move through a stratum, but then there are jumps. A species might disappear, or sometimes a whole group of species became extinct. These chapter breaks are distinct and are seen across the world. Slowly geologists pieced together the pages, sections, chapters and volumes of geologic history. The time units that were established were the period, which was greater than the era, and which was in turn greater than the eon (see Table 9.3).
Table 9.3 Present geologic time.
Eon
Phanerozoic
540 million years
Era
Cenozoic
65 million years
Period
Quaternary
2.6 million years
Epoch
Holocene
12,000 years
Our present eon is the phanerozoic (from the Greek for “visible life”) and for a long time it was thought that this time period spanned the whole of the fossil record, from 540 million years ago to the present. There are no hard-shelled, macroscopic fossils before it. The oldest period in the Phanerozoic eon is called the Cambrian period (541–485 million years ago). Cambria is the Roman name for Wales, at the west end of William Smith’s survey. It was also about the end of the hard-shelled fossil record. So the time before the Phanerozoic eon is called Precambrian eon. By the end of the Precambrian super-eon the world was already old. The Earth was covered with bacteria and some multicellular life, but these do not make the sort of fossils rock hounds would like to hunt.
Using stratification and the fossil record, geologists and paleontologists could name and identify the various times in geological history. They could also order the eras. They could even make estimates of lengths of time by noting how fast a modern lake or sea will acquire silt or sand and then extrapolating that knowledge to the thicknesses of shales and sandstones. But these were crude estimates, subject to numerous unknown factors and assumptions.
Ideally, one would like to use a technique like radiocarbon dating to establish the age of a rock. The difficulty is that you need to know how much of an isotope there was in a rock initially. You also need an isotope with a very long lifetime, and there are many that meet that criterion. Actually, several techniques have been devised but I will only describe one based on the potassium and argon levels in a rock.
Argon is an inert gas that would not bind to a rock if it was fluid, so a new igneous rock will be argon-free. However the potassium-40 in the rock can decay into calcium and argon and after the rock has solidified that argon will be trapped within the rock. So a geologist can break open a rock and measure the ratio of potassium-40 to argon-40. By knowing the lifetime of potassium, and what percentage of it decays into argon and to calcium, the age of the rock, or at least the time since solidification can be calculated. Since the half-life of potassium is 1.25 billion years, this technique will work across a wide range of times, but with less precision than carbon-14. Still, it is well matched to geological eons/eras/periods.
So now we can put absolute dates on geological time. The great dinosaur extinction shows up as the border between the Cenozoic and Mesozoic eras, about 65 million years ago. The start of the hard-shelled fossils, the Cambrian revolution is about 540 million years ago. The oldest microscopic fossils are about 3.5–4 billion years old.
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The life of the Earth is not just about life on the Earth. The Earth itself evolves and changes shape. Continents have merged into supercontinents and then split apart. Oceans have swelled and vanished. It is not that hard to believe that the eastern most point of South America, Cabo de Sao Roque in Brazil, would fit into the Gulf of Guinea in Africa, but when Alfred Wegener first suggested continental drift in 1912 it was seen as radical. However, we now realize that it is not just that the coastlines seem to match, but also that the mid-Atlantic ridge is made of young rocks, and we have actually measured the spreading of the Atlantic. We can measure the motion of all the continents and extrapolate back 200–300 million years ago when they were joined together into one supercontinent called Pangaea (see Figure 9.4).
Figure 9.4 The supercontinent Pangaea about 200–300 million years ago.
The Earth seems so solid and rocks seem so rigid and permanent. But given enough time—and we are talking about hundreds of millions of years—and the heat that rises up from the core of the Earth, the continents are plastic and malleable. We should think of the Earth as being in a slow—very slow—boil, with rocks rising in one place and being drawn down in another. Giant convection currents exist, only with continental plates instead of air or water.
Pangaea was not the first and only supercontinent. Earlier in geologic time there were Rodinia, Columbia, Kenorland and Vaalbara as well as a number of other continents and fragments (see Table 9.4). Throughout the history of the Earth the continents bump into each other every few hundred million years, stick together for a while, and then move apart.
The further back in time we go the harder it is to piece together the evidence about the continents, but we can still date rocks. Some of the oldest rocks found are from Australia and Canada. In Canada, the Acasta gneiss, an outcropping in the Northwest Territories has been dated to 4 billion years old. Also the Nuvvuagittuq greenstone, from near Hudson Bay may be older, but having more complex chemistry, its radiometric date is still being studied. Older than these two are small crystals of Zircon found in the Jack Hills of Western Australia, which date back 4.4 billion years.
Table 9.4 Supercontinents through the history of the Earth.
Supercontinent
Millions of years ago
Vaalbara
3,100–2,800
Kenorland
2,700–2,500
Columbia/Nuna
1,900–1,400
Rodinia
1,100–750
Pangaea
300–200
The list is incomplete.
There are in fact older rocks on Earth, but not of Earthly origins. Famous among these is the Genesis rock, which was brought back from the Moon by the Apollo 15 mission. It has been dated at 4.46 billion years. And even older than that are meteorites. We think that meteors were formed at about the same time as the Earth
and solar system and have remained unchanged since then. While the Earth has continued to roil, these meteorites have remained intact for 4.54 billion years. In fact 4.54 billion years (or 1.43 × 1017 s) is our best measurement of the age of both the solar system and the Earth, to within about 1%.
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We have walked back about a third of the way to the Big Bang. The universe is about three times older than the solar system. This comes as no surprise when you realize that at a time shortly after the Big Bang the universe was essentially made of only hydrogen. Yet here on Earth we have heavier elements; we have lead and gold and uranium.
A few stars can actually be dated with radiometric techniques. This is difficult since the isotopes generally appear as faint lines within the stars’ spectra, especially compared to more common and stable isotopes. Still, the ratio of 232Th:238U has been measured in a few stars, yielding ages of over 13 billion years.
Radiometric techniques only work because we can measure the lifetimes of these isotopes here on Earth. Also the more we have learned about nuclear physics in laboratories the better we are able to construct models of how fusion works within stars, how fast elements are formed and what happens in a supernova. Our present models of the universe start out with the Big Bang. A few hundred million years later the universe was made primarily of hydrogen and a bit of helium. Stars were formed and started to burn that hydrogen. Through nuclear fusion those hydrogen atoms combined into helium and released energy, in the same way our Sun works today. This process of creating heavier elements is called nucleosynthesis: helium burns to form beryllium, and then carbon, nitrogen, oxygen and other elements. But the process of fusion can only go so far up the periodic table and it stops at iron. You cannot fuse iron with another atom and get energy. Iron is the most stable element. Yet we have heavier elements around us.
How Big is Big and How Small is Small Page 16