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Clocks in Rocks: Isotopes and Age of Earth |
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Early thought
William Thompson (later Lord Kelvin) determined the age of the Sun by calculating the time it would take to cool to its present conditions. Later, Kelvin's calculations used Earth's temperature change with depth, thermal properties of rocks, and a planetary body that started as a molten mass, to produce ages in the range of 50-100 my. This determination was firmly grounded in the physics of late 19th Century, so its results were considered indisputable. We will not give its derivation, but we will experiment with Kelvin's calculation. The relationship is:
age = (To - T)2/ ( pi*K*GG2),
where To is the formation temperature, T is today's temperature, pi is 3.14, K is a material property called thermal diffusivity (we'll use 1mm2/sec) and GG is the Earth's geothermal gradient (25 C/km). If To ranges from 1500 to 2000 C, the age of the earth would range from 36-65 m.y. It was hard to argue with such sound physics, until a major discovery was made around the turn of the century: radioactivity.
Up to about silica, the number of protons in an element equals the number of neutrons. Heavier elements can have several isotopic numbers, meaning different numbers of neutrons, but the same number of protons. For example, the element rubidium has the isotopes 85/37 Rb and 87/37 Rb. The discovery of radioactivity was that the occurrence of some isotopes is unstable, such that a new element is formed spontaneously. Of the two Rb isotopes, 87/37 Rb is unstable and it changes to the element strontium (87/38 Sr) by the conversion of a neutron into a proton and an electron. The electron is expelled from the nucleus of the new element, which produces a dangerous side effect: radiation. This type of radioactive decay is called beta decay (b). There are several types of radioactive decay, which are illustrated in the Figure. A useful source of information is the Nuclear Wall Chart.
Types of radioactive decay. Alpha decay (a) is the emission of particles that contain two protons and two neutrons (He). This results in a daughter with a lower atomic number (-2) and a lower mass number (-4). Beta decay (b) describes the emission of an electron, which converts a neutron into a proton. The atomic number increases by 1, whereas the mass number remains the same. A another form of beta decay is when a nucleus catches an electron, resulting in the conversion of a proton to a neutron. This electron capture process, results in a decrease in atomic number, but no change in mass number. Gamma decay (g) produces gamma rays, which is electromagnetic radiation from photon emission. |
The half-lives of an element. |
In the language of radioactivity, rubidium would be called the parent
isotope and strontium the daughter isotope. The number of
isotopes that decay per unit time is proportional to the total number of
parent isotopes present. A convenient measure to express this property is
through the concept of the half-life (t½) of an isotope. The half-life is
the time required for half of a given number of parent isotopes to decay
to a daughter isotope.
The table below lists common radiogenic systems, their corresponding half-lives and decay constants. For example, it takes nearly 49 billion years to change 50% of Rb into Sr.
Commonly Used Long-Lived Isotopes in Geochronology
| Radioactive
Parent (P) |
Radiogenic
Daughter (D) |
Stable Reference (S) |
Half-life, t½
(109 y) |
Decay constant,
l (y-1) |
| 40K | 40Ar | 36Ar | 1.25 | 0.58x10-10 |
| 87Rb | 87Sr | 86Sr | 48.8 | 1.42x10-11 |
| 147Sm | 143Nd | 144Nd | 106 | 6.54x10-12 |
| 232Th | 208Pb | 204Pb | 14.01 | 4.95x10-11 |
| 235U | 207Pb | 204Pb* | 0.704 | 9.85x10-10 |
| 238U | 206Pb | 204Pb* | 4.468 | 1.55x10-10 |
Note: * 204Pb is not stable, but has an extremely long half life of ca. 1017 years.
A useful analogy to illustrate the fundamentals of geochronology is an hourglass. If we start with one side of the hourglass full (containing the 'parent') and the other side empty (containing the 'daughter'), we only need to know the rate at which the sands moves from one chamber to the other (represented by the half-life) and the amount of sand in the daughter chamber or the amount of parent remaining to determine how much time has passed. However, in reality matters are more complex.
A complication occurs in natural samples because at the time the radiogenic clock starts ticking, the sample already contains some daughter material; in other words, some sand is already present in the daughter chamber even before we begin measuring time. This amount of daughter is referred to as the initial daughter. Therefore, when we measure the amount of daughter product in our specimen we are combining the amounts of daughter from decay of the parent and initial daughter. The amount of initial daughter, however, needs to be subtracted for age determination.
The solution to this problem lies in first determining the amount of initial daughter. The actual method is a little tricky, but basically what we need is to find a part of the sample that contains no radiogenic 87Rb. The measured 87Sr in that part of the sample must therefore be initial daughter (i.e., non-radiogenic in origin). The tricky part comes from the fact that such a component cannot be found, but the same result may be obtained using components (minerals) of the sample that contain different amounts of 87Rb.
From the age of meteorites from the asteroid belt between Mars and Jupiter, we
conclude that the solar system must be 4.56 Ga as they were formed from
the original cloud that formed the solar system. Chondrules represent the
earliest products of the solar nebula, which is supported by their
chemistry. Thus, the age of meteorites equals that of the formation of the
planets and, within a few million years, that of the formation of the Sun.
Radiogenic age measurements on rock and minerals from Earth are not that old. The oldest rock, found in northern Canada, is about 4 Ga, whereas the oldest mineral is about 4.3 Ga. Samples collected through the lunar program of the late 60s and early seventies, however, support older ages. The first moon rock picked up was dated at 3.6 billion years old! All moon rocks examined to date are in the range 3.1 - 4.6 billion years old.
Take a trip with Berkeley's geological time machine to learn about Earth's long and varied history.
The age of the Earth is estimated by using the principles of radioactive decay to date meteorites. This technique is also applied to date rocks and minerals. The Earth is estimated to be ~4.56 Ga and therefore formed long after the Big Bang.
Radioactive decay is the spontaneous decay of an isotope (the parent) to a new isotope (the daughter), which is accompanied by radiation. This process is usually described in terms of its half-life (t½), which is the amount of time that it takes for half of the initial parent to decay. Since half-lives can be calculated from laboratory experiments, the only other information needed to determine the age is the amount of parent and daughter isotopes present in the sample.
If the Universe is about 15 Ga old, our solar system must have been formed long after the Big Bang. Supporting evidence for this conclusion can also be found in the chemistry of our solar system, where we find elements that cannot be formed by the fusion process that fuels our Sun.
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Earth's Early Years:
Differentiation, Water and Early Atmosphere |
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| Internal Structure of Earth |
Earth's solid body is composed of several layers of varying density (see Figure). The Earth's core is composed of two portions, an inner core of solid iron and an outer core of molten iron (perhaps with some S). Above the core lies the mantle, which is made up of dense silicates, and the crust, which is the outer layer of the solid Earth. The oceans and atmosphere are the outermost layers.
Differentiation in the first few 100's of millions of years led to the formation of the core and the mantle and a crust, and initiated the escape of gases from the moving interior that eventually led to the formation of the atmosphere and oceans.
1. Accretion. Impacting bodies bombard the Earth and convert their energy of motion (kinetic energy) into heat. In recent years we also learned that an early collision with a very large object was responsible for the "extraction" of the Moon from Earth.
2. Self-compression. As the Earth gets bigger, the extra gravity forces the mass to contract into a smaller volume, producing heat (just like a bicycle pump gets hot on compression).
3. Differentiation. Conversion of gravitational potential energy to heat during core formation
3. Short-lived radiogenic isotopes. The surrounding material absorbs the energy released in radioactivity, heating up. Today this is a very slow but steady source of heat. About 20 calories of heat are generated by 1 cubic centimeter of granite in the course of a million years. It would take this amount of rock 500 million years to brew a cup of coffee!
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The melting
of iron leads to the formation of a heavy liquid layer. Drops begin to develop in later stages and sink toward the center. |
The Figure below compares the elemental
abundances for the Earth's crust with the whole Earth, showing that
the crust has a quite different composition from the rest of the Earth,
with abundant oxygen and silicon. About 90% of the
Earth is made of the four elements iron, oxygen, silicon and magnesium.
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For the Early Earth, extreme volcanism occurred during differentiation, when massive heating and fluid-like motion in the mantle occurred. It is likely that the bulk of the atmosphere was derived from degassing early in the Earth's history. The gases emitted by volcanoes today are in Table 1 and in Figure.
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Composition of volcanic
gases for three volcanoes |
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Volcanic outgassing |
Stromatolite and Banded-iron Formation (BIF)
Life started to have a major impact on the environment once photosynthetic organisms evolved. These organisms, blue-green algae (picture of stromatolite, which is the rock formed by these algae), fed off atmospheric carbon dioxide and converted much of it into marine sediments consisting of the shells of sea creatures.
While photosynthetic life reduced the carbon dioxide content of the atmosphere, it also started to produce oxygen. For a long time, the oxygen produced did not build up in the atmosphere, since it was taken up by rocks, as recorded in Banded Iron Formations (BIFs; picture) and continental red beds. To this day, the majority of oxygen produced over time is locked up in the ancient "banded rock" and "red bed" formations. It was not until probably only 1 billion years ago that the reservoirs of oxidizable rock became saturated and the free oxygen stayed in the air.
Once oxygen had been produced, ultraviolet light split the molecules, producing the ozone UV shield as a by-product. Only at this point did life move out of the oceans and respiration evolved. We will discuss these issues in greater detail later on in this course.
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Cumulative history of O2 by photosynthesis over geologic time. The start of free O is likely earlier than shown. |
Additional Work
Run through and complete Virtual Dating - Isochron to learn more about isotopic dating.
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