The Meoto-Iwa, or Wedded Rocks, Shima Peninsula. Legend holds that the spirits of Izanagi and Izanami, Japan's creator gods, are housed in the rocks, which are connected to one another by a straw rope.
Courtesy Corbis
Clocks in Rocks: 
Isotopes and Age of Earth

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In this lecture we learn:

09/21/11                                                                            

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. 

The Atom and Radiogenic Dating

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 (t) 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, t
(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.

Age of Earth and the Solar System

UCMP's Geological Time MachineFrom 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.

Summary

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 (t), 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

We learn:

Differentiation: A Molten Planet

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. 

Heating of Early Earth 

The earliest Earth was probably an unsorted conglomeration, mostly of silicon compounds, iron and magnesium oxides, and smaller amounts of all the natural elements. It became increasingly hotter as the protoplanet grew. Four different effects led to the heating of our planet: 

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! 

Iron Melts

At some point, probably within the first few hundred million years of Earth, the surface down to a depth of about 500 km became so hot that iron (a plentiful element) started to melt. The molten iron collected and began to sink under its own great weight. About one third of the primitive planet's material sank to the center, and in the upheaval, heating rates increased and most of the planet was liquified. There might well have been an early ocean of molten rock -- a magma ocean more than 100 km deep. The formation of a molten iron core was the first stage of the differentiation of the Earth, in which it was converted from a homogenous body, with roughly the same kind of material at all depths, to a layered body, with a dense iron core, a crust composed of lighter materials with relatively lower melting points, and between them the mantle. 
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. 
 


Comparison of relative abundances of elements in (a) the Earth's crust and (b) the whole Earth. 

Compare the abundance of elements in the crust with the values for the Earth as a whole. Because most of the iron sank to the core, that element drops to fourth place. Conversely, silicon, aluminum, calcium, potassium, and sodium are far more abundant in the crust than in the whole Earth.  The reason for the different make up is that the elements favored in the crust form light-weight chemical compounds, which are easily melted. Materials such as these melted early during the differentiation, rose to the surface by convective overturning and accumulated. 

The Earliest Atmosphere, Oceans and Continents

After loss of the hydrogen, helium and other hydrogen-containing gases from early Earth due to the Sun's radiation, primitive Earth was devoid of an atmosphere. The first atmosphere was formed by outgassing of gases trapped in the interior of the early Earth, which still goes on today in volcanoes. 

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.

Composition of volcanic
gases for three volcanoes

 

Volcanic outgassing

Oxygen in the Atmosphere

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. 

Early Oceans

The Early atmosphere was probably dominated at first by water vapor, which, as the temperature dropped, would rain out and form the oceans. This would have been a deluge of truly global proportions an resulted in further reduction of CO2. Then the atmosphere was dominated by nitrogen, but there was certainly no oxygen in the early atmosphere. The dominance of Banded-Iron Formations (BIFs; see picture) before 2.5Ga indicates that Fe occurred in its reduced state (Fe2+). Whereas reduced Fe is much more soluble than oxidized Fe (Fe3+), it rapidly oxidizes during transport. However, the dissolved O in early oceans reacted with Fe to form Fe-oxide in BIFs. As soon as sufficient O entered the atmosphere, Fe takes the oxidized state and is no longer soluble. The first occurrence of redbeds, a sediments that contains oxidized iron, marks this major transition in Earth's atmosphere.
Cumulative history of O2 by photosynthesis over geologic time.  The start of free O is likely earlier than shown.

Early Continents

Lava flowing from the partially molten interior spread over the surface and solidified to form a thin crust. This crust would have melted and solidified repeatedly, with the lighter compounds moving to the surface. This is called differentiation.  Weathering by rainfall broke up and altered the rocks.  The end result of these processes was a continental land mass, which would have grown over time. The most popular theory limits the growth of continents to the first two billion years of the Earth. 

Clocks in Rocks Self Test

 

Additional Work

Run through and complete Virtual Dating - Isochron to learn more about isotopic dating.

 

All materials the Regents of the University of Michigan unless noted otherwise.