The Age of Elements as a Current Scientific Clock

By Matt Nipe

There are many tools scientists currently use to try to determine the specific age of the Earth. Over the years, many have been found to be unusable, such as Kelvin's cooling earth model, while other methods have proven very useful, such as radioactive decay. Determining the age of the elements that make up the solar system can also aid scientists in this pursuit of knowledge-not to give an exact date, but to provide a minimum age for earth and the other planets.

Estimating the age of the elements can be done by studying long-lived radioactive nuclei. This is done by the examining chronometer pairs. A chronometer pair is a pair of radioactive nuclei (or one stable, one radioactive) that is present now in a measurable abundance so their ratio can be obtained. The pair needs to include a radioactive isotope so the ratio of the two changes over time. Chronometer pairs are only useful, however, if three things are known: the ratio of the pair at the formation of the Solar System, the rate of production, and the production history.

The ratio of the chronometer pairs can be found by examining meteorites, lunar rocks and terrestrial samples (Dalrymple 2004). Finding the rate of production and history, however, is much more difficult.

At the beginning of the universe, during the Big Bang, only the two smallest elements were created: hydrogen and helium. Every heavier element has been generated from within stars, including nearly all of the material making up the earth. Heavy nuclides are created most effectively in large, short-lived stars that eventually explode as supernovae, thus distributing the nuclides back into space to be incorporated in new stars and planets. There are three major mechanisms of nuclide production within stars: nuclear burning, slow neutron capture, and rapid neutron capture. Nuclear burning is the process by which stars fuse nuclei to create successively larger nuclei: a star will first burn all hydrogen fuel, fusing it into helium, then it will burn the helium, then carbon, oxygen, etc. This burning results in the generation of elements up to iron (element number 26). After the generation of iron, stars are incapable of producing any heavier elements by this process (Dalrymple 2004).

The neutron capture processes are exactly what the name implies: lighter nuclides capturing passing neutrons. In slow neutron capture (the s-process) the rate of neutron capture is slow when considering the lifetime of the nuclide's eventual unstable product. As passing neutrons are captured by the nuclei, isotopes with a higher mass are produced. Eventually the s-process results in a radioactive isotope, at which time the isotope decays as quickly as it is formed, therefore blocking the generation of any heavier isotopes (Dalrymple 2004). The s-process can generate many nuclides, but because of the blocking, it cannot produce all elements. It is thought that the s-process occurs mainly in red giant stars, in which there are neutrons in high abundance, but not high enough to result in rapid neutron capture.

Rapid neutron capture (the r-process) is a faster version of s-process, in which neutrons are being captured faster than any unstable isotopes can decay. This circumvents the blocking found in the s-process and therefore produces nuclides of progressively higher masses until production and decay of a radioactive nuclide are in equilibrium. At that point, the r-process stops since equilibrium has been achieved. Rapid neutron capture can result in heavier nuclides than in the s-process, but it can only be found in areas of extreme neutron production. Supernovae are the only known events in which the r-process can proceed; other catastrophic events may also be a sight of rapid neutron capture, however (Dalrymple 2004). This is a very lucky coincidence because supernovae, which can produce the most elements, are also the most effective mechanism of new nuclide dispersal.

All nuclides found in nature can be accounted for by these three natural processes. Most formed as a byproduct of multiple events, such as a nuclide first going through nuclear burning and then rapid neutron capture. This can make obtaining exact production rates very difficult. To further complicate the matter, nuclides can be generated by the successive burning out of stars. Supernovae can provide material for new star formation, including heavier elements, and this results in heavier seed nuclei for the elemental production processes.

There are two hypotheses for production history of the nuclides. The first theory is that all elements were produced at the beginning of the galaxy or during the Big Bang. This was found to be inaccurate, however, because several short-lived radioactive nuclides produced through the r-process were incorporated into the Solar System's planets and meteorites during the Solar System's formation. Therefore, production cannot be a single early event, unless that event occurred immediately before the Solar System's formation. It is now believed that only hydrogen and helium were produced during the Big Bang. The second hypothesis is that nuclide production is uniform and ongoing throughout the stars of the universe. This second hypothesis is accepted as true and is used when working with chronometers.

The 232Th/238U chronometer pair is the best known chronometer for determining the age of our Milky Way Galaxy. Its initial ratio can be determined by observing meteorites, lunar rocks and terrestrial samples ; the production history is known to be ongoing; and most importantly, both nuclides are produced solely through the r-process which gives a much more definite rate of production. By using the 232Th/238U chronometer pair, an age of 12.± to 13.0 ± 3 billion years has been calculated for the elements of the Milky Way galaxy (Dalrymple 2004).

In addition to chronometer pairs, there is another line of evidence to consider when seeking an age for the elements. Of all of the known radioactive nuclides, only thirty-four have half-lives over one million years. Of those thirty-four, twenty-three are found in nature, with five of the twenty-three being continually produced through natural processes. The remaining seventeen all have half-lives of greater than 82 million years. The other eleven elements are extinct in nature (Dalrymple 1991; see table below).

Table of radioactive nuclides with half lives greater than one million years (after Dalrymple 2004).
A "P" indicates that the element is still being produced by natural means.
Nuclide Halflife (years) Found in Nature?
V-50 6 x 1015 Yes
Nd-144 2.4 x 1015 Yes
Hf-174 2.0 X 1015 Yes
Pt-192 1 x 1015 Yes
In-115 6 x 1014 Yes
Gd-152 1.1 x 1014 Yes
Te-123 1.2 x 1013 Yes
Pt-190 6.9 x 1011 Yes
La-138 1.12 x 1011 Yes
Sm-147 1.06 x 1011 Yes
Rb-87 4.88 x 1010 Yes
Re-187 4.3 x 1010 Yes
Lu-176 3.5 x 1010 Yes
Th-232 1.40 x 1010 Yes
U-238 4.47 x 109 Yes
K-40 1.25 x 109 Yes
U-235 7.04 x 108 Yes
Pu-244 8.2 x 107 Yes
Sm-146 7 x 107 No
Pb-205 3.0 x 107 No
U-236 2.39 x 107 Yes-P
I-129 1.7 x 107 Yes-P
Cm-247 1.6 x 107 No
Hf-182 9 x 106 No
Pd-107 7 x 106 No
Mn-53 3.7 x 106 Yes-P
Cs-135 3.0 x 106 No
Tc-97 2.6 x 106 No
Np-237 2.14 x 106 Yes-P
Gd-150 2.1 x 106 No
Be-10 1.6 x 106 Yes-P
Zr-93 1.5 x 106 No
Tc-98 1.5 x 106 No
Dy-154 1 x 106 No

There are three hypotheses to explain the extinction of the eleven radioactive nuclides. First, the extinction may only be a result of chance, i.e. the elements were not evenly distributed and are not found in our area of observation. This hypothesis, although not impossible, is highly improbable. Dalrymple (2004) gives a probability of only one in 1021.

The second hypothesis is that the extinct nuclides were never actually produced. This hypothesis is also easily discredited. The s and r-processes should have produced each radioactive nuclide successively, therefore none of the steps would be skipped. Also, there have been daughter products found for some radioactive nuclides-Dalrymple (2004) notes the increased abundance of 129Xe in meteorites from the decay of 129I (a missing nuclide)-which indicates their presence at an earlier time.

Finally, there is a hypothesis that the radioactive nuclides were produced, but after such a long period of time, they have now completely decayed to extinction. This seems the most likely answer. This hypothesis also proves that the Solar System is older than 4.5 billion years, but less than 10 billion years. A solar system younger than 4.5 billion years should include many of the missing nuclides. Any age older than 10 billion years would have resulted in the extinction of radioactive nuclides with half-lives greater than 82 million years (Dalrymple 2004).

In conclusion, the age of the elements is a natural clock, and it gives science another tool to decipher the age of the earth and the universe. However, it is unable to give an exact date-instead giving only a range of ages for the materials that make up the stars and planets. Based on this method the Solar System appears to be older than 4.5 billion years, but less than 10 billion, and the Milky Way Galaxy is between 9.5 and 16 billion years old. These dates indicate an old universe and lead one to believe that the earth is also quite old, since the earth is thought to have formed soon after the Solar System.

Sources:
  1. Dalrymple, Brent G. 1991. Age of the Earth. Stanford University Press, 474 p.
  2. Dalrymple, Brent G. 2004. Ancient Earth, Ancient Skies. Stanford University Press, 247 p.