Geochronology - The Solid Earth - page 257

such as these need to be made with caution and with as much knowledge of the
origin and chemistry of the rocks as possible.
The beta decays of rhenium to osmium ( 187 Re to 187 Os) and lutetium to hafnium
( 176 Lu to 176 Hf ) mean that these isotopes can be used as geochronometers in the
same way that the decays 87 Rb to 87 Sr and 147 Sm to 143 Nd are used. Lutetium, a
rare-earth element, occurs in most rocks as a trace element with an abundance of
less than 1 ppm. Rhenium and osmium are metals - their abundance is generally
very low, less than 10 ppb. However, rhenium occurs in some ores at a sufficient
level to be used to date them and has been used to date 0.5-ppm-metallic mete-
orites. Isochrons and isotopic evolution diagrams are constructed in an analogous
manner to the rubidium-strontium and samarium-neodymium methods. A nota-
tion similar to Eq. (6.52) can be used to express deviations of the Lu-Hf and
Re-Os systems from their bulk reservoirs and these deviations then used in an
analogous way to ε Nd . These isotopes, though rarely used yet as geochronome-

ters, are useful in the study of mantle evolution and the origin of magmas and
will become more popular in the near future.

6.9 Fission-track dating
As well as undergoing a series of radioactive decays to stable lead-206, uranium-
238 is also subject to spontaneous fission . 12 That is, the nucleus can disintegrate
into two large but unequal parts, releasing two or three neutrons and considerable
energy (about 150 MeV). The decay constant for this spontaneous fission of 238 U
is 8.46 10 − 17 yr − 1 ,very much less than the decay constant for the decay to

206 Pb. Thus, fission of

×

238 U occurs only rarely; the ratio of spontaneous fission

10 − 7 only. The
decay products from the fission of 238 U are of such energy that they are able to
travel through minerals for about 10

10 − 17 ) 10 − 10 )

to -particle emission is (8.46 × / (1.55 × = 5 ×

10 − 6 m).
The passage of a charged particle through a solid results in a damaged zone
along its path. This is one of the ways by which cosmic rays 13 can be studied. If
a singly charged particle passes through a photographic emulsion that is subse-
quently developed, the track of the particle can be seen under the microscope as

m(1 m =

12

Spontaneous fission occurs only in nuclei over a critical size (about atomic number 90). It is the
principal decay method for some of the synthesized transuranium elements.

13

Cosmic rays are very-high-velocity nuclei that constantly bombard the Earth. Their flux is about
1 particle cm − 2 s − 1 , about the same energy flux as starlight. Most cosmic rays are protons, and
10% are 3 He and 4 He. The remainder are heavier elements (with B, C, O, Mg, Si and Fe being
prominent); in fact, iron has an abundance of ∼ 3 × 10 − 4 that of the protons by number or ∼ 1.7%
by mass. The abundance of the heaviest nuclei, with charge greater than 70, is ∼ 3 × 10 − 9 that
of the protons. The boron and similar nuclei are fragments of the original carbon and oxygen that
underwent collision with interstellar hydrogen during their 10 7 -yr journey to Earth at ∼ 90% of

the speed of light.