3 The Rb)Sr method
Rubidium, a group 1 alkali metal, has two
naturally occurring isotopes, 85Rb and 87Rb, whose
abundances are 72.17% and 27.83% respectively. These figures yield an atomic
abundance ratio of 85Rb/87Rb = 2.593 (Catanzaro et al., 1969), which is a constant
throughout the Earth, Moon and most meteorites due to isotopic homogenisation
in the solar nebula. 87Rb is radioactive, and decays to the stable
isotope 87Sr by emission of a $ particle and antineutrino (
<). The decay energy (Q) is shared as kinetic energy by these
3.1 The Rb decay constant
The low decay energy for this transformation (275 keV) has always caused problems in the accurate determination of the Rb decay constant. Because the decay energy is divided between the $ particle and anti-neutrino, the $ particles have a smooth distribution of kinetic energy from the total energy down to zero. When attempting to accurately determine the decay constant by direct counting, the low energy $ particles cause great problems because they may be absorbed by surrounding Rb atoms before they ever reach the detector. For example, in a thick (>1:m deep) solid Rb sample, attenuation is so severe that a false frequency maximum is generated at ca. 10 keV (Fig. 3.1).
Fig. 3.1. Plot of activity against kinetic energy for $ particles generated by 87Rb decay. Solid lines = solid Rb sources; dashed lines = liquid scintillator measurements. After Neumann and Huster (1976).
One way to avoid the attenuation problem is to use a photo- multiplier with a liquid scintillator solution doped with Rb. The $ particles will be absorbed by molecules of the scintillator (emitting light flashes) before they can be absorbed by other Rb atoms. The major problem with this method is that a low-energy cut-off at ca. 10 keV must be applied to avoid the high background noise associated with liquid scintillation. The consequent extrapolation of count-rate curves down to zero energy leads to a large uncertainty in the result (Fig. 3.1). Hence this method has given values for the 87Rb half-life from 47.0 " 1.0 Byr (Flynn and Glendenin, 1959) to 52.1 " 1.5 Byr (Brinkman et al., 1965).
Another approach to direct counting is to make measurements with progressively thinner solid Rb sources using a proportional counter. The results are then extrapolated to a theoretical source of zero thickness to remove the effect of self-absorption. The proportional counter has a much lower noise level, so the energy cut-off can be set as low as 0.185 keV. Rb films with thicknesses down to 1 :m were measured by Neumann and Huster (1974), and extrapolated to zero thickness by Neumann and Huster (1976) to derive an 87Rb half-life of 48.8 " 0.8 Byr (equivalent to a decay constant of 1.42 H 10!11 yr!1).
An alternative approach to determining the Rb decay constant is to measure the amount of 87Sr produced by decay of a known quantity of 87Rb in the laboratory over a known period of time. This method was first attempted by McMullen et al. (1966) on a rubidium sample they had purified in 1956, and was repeated on the same sample batch by Davis et al. (1977). Unfortunately, McMullen et al. omitted to measure the small but significant level of residual 87Sr present in their rubidium before they put it away on the shelf. Hence, the accuracy of their determination was compromised. However, this problem contributes less than 1% uncertainty to the later determination of Davis et al. (1977). Their proposed value for the 87Rb half-life (48.9 " 0.4 Byr, equivalent to a decay constant of 1.42 H 10!11 yr!1) can therefore be taken to support the value of Neumann and Huster (1976).
A third approach to the determination of the Rb decay constant is to date geological samples whose ages have also been measured by other methods with more reliable decay constants. This method has the disadvantage that it involves geological uncertainties, such as whether all isotopic systems closed at the same time and remained closed. However, it provides a useful check on the direct laboratory determinations. In this respect it is worth noting that Pinson et al. (1963) proposed a rubidium half-life of 48.8 Byr on the basis of Rb)Sr dating of stony meteorites.
During the last 30 years, values of the decay constant used in geological age calculations have varied between 1.47 and 1.39 H 10!11 yr!1 (t1/2 = 46.8 to 50.0 Byr). The most commonly used value of 1.42 H 10!11 yr!1 (t1/2 = 48.8 Byr) was adopted by international convention (Steiger and Jager, 1977), but probably needs to be revised. For example, very precise U)Pb and Rb)Sr isochrons for chondritic meteorites can only be made to agree if the 87Rb decay constant is reduced to 1.402 (" 0.008) H 10!11 yr!1, equivalent to a half-life of 49.4 " 0.3 Byr (Minster et al., 1982).
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