|
Clocks in Rocks: Isotopes and Age of Earth |
format
for printing| 04/17/06 |
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.
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.
