Page 128 - Radiochemistry and nuclear chemistry

114 Radiochemistry and Nuclear Chemistry

XEC = 0.578 X 10 l0 y-l, ;k B = 4.837 x 10 -10 y-l, Emax 1.32 MeV. Because the 4~
half-life is of the same magnitude as the age of the earth, measurement of the 40K/Ar ratio
can be used to determine ages of the oldest K-containing minerals (for notation, see {}2.3.2).
From the decay scheme one can derive the equation

t= ;k -1 ln[{4~ + 11 (5.6)

where X is the total decay constant (= XEC + XB; see w 4oAr re~resents the
concentration of 4oAr-atoms in the sample (i.e. number of radiogenic atoms of 4oAr per unit
sample weight), and 40K is the present atomic abundance of 40K-atoms. This equation
assumes that all 4oAr in the mineral is radiogenic. Any amount of non-radiogenic 4oAr
present initially (e.g. dissolved in the magma from which the mineral formed) is denoted
as 4oAr i. Thus the present amount of 4oAr is the sum of the radiogenic amount and that
originally present:

40Ar = 40Ari + )kEC X -1 40K (e 1~- 1) (5.7)

The problem is that both t and 4oAr i are unknown. This can be solved by dividing equation
(5.7) by the number of 36Ar atoms in the sample, yielding

40Ar/36Ar = (40Ar/36Ar)i + (~kEC/ h)(4~ hi- 1} (5.8)

Because 36Ar is a stable non-radiogenic isotope, its amount in the sample should not
change by time. Thus the measured 4~ ratio is the sum of the original and the
radiogenic contributions from 4~ Mineral samples of the same origin (so-called
cogenetic) should have the same initial 4~ ratio and be of the same age (same t),
40
36
40 36
though the K~ Ar may vary. Thus for cogenetic samples a plot of 'Arl Ar versus
40 36
KI Ar should yield a straight line, from the slope of which t is calculated. This line is
referred to as an isochron. From the isochron for the rock sample from Tanzania in Figure
5.6, its age is calculated to be (2.04 + 0.02) x 10 6 y, which is an interesting result as
remains of early humans has been found in the same tuff matrix.

5.8.3. Dating by Rb- Sr method

Some uncertainty is associated with the use of the 40K/4OAr ratio because of the possibility
of the loss of gaseous argon from minerals. An alternative method is based on 87Rb/Sr
system:

87Rb .......... ~ 87Sr (7.00% of natural Sr) (5.9)
4.8 x 10 l0 y

The measurement of the 87Rb/87Sr ratio by isotope dilution and mass spectrometry is one
of the most reliable methods for geologic age determinations. Meteorite values as high as
4.7 x 109 y have been obtained, indicating that this is the age of the solar system. For the