Page 130 - Radiochemistry and nuclear chemistry

116 Radiochemistry and Nuclear Chemistry

series. In such 2~ minerals if it is possible to determine the amount of the parent
nuclide 238U and of the end product 2~ the age of the mineral can be obtained from the
general equation

t= h -1 In(1 4- N d/Np) (5.10)

where Np is the number of parent atoms (e.g. 238U) and N O the number of radiogenic
daughter atoms (e.g. 2~ and X is the decay constant of the parent. The atomic ratios
between a number of isotopic pairs as a function of time is shown in Figure 5.7.
This method is more reliable than the helium method since there is very little possibility
of any of the lead that has been formed by radioactive decay having diffuse~ or been
leached from the mineral during its geologic age. Mineral samples from the earth have
yielded values as great as 3 x 109 y by the lead content method. Unfortunately, there is a
problem with this method also. The decay series all pass through isotopes of the inert gas
radon, and if some of the radon is lost from the mineral the 2~ content leads to an
erroneously low age. However, if relation (5.13) is used for different decay series (i.e. the
238 U and the 235 U series) and the same t is obtained, the data are said to be concordant.
Such data increases the confidence in the measured age.
Since the lifetimes of the uranium isotoj~es 238 U and 235U are different, the isotopic ratio
Pb can also be used for age determination. One
between their end products 206 Pb and 207r
can derive the relationship
207pbl206pb = (1/138)(e xesSt - 1)l(e ~8t- 1) (5.11)

where the factor 1/138 is the present isotopic abundance ratio of the uranium isotopes. This
method has given values of 2.6 x 109 y for uranium and thorium minerals. When applied
to stony meteorites, a somewhat longer age of (4.55 + 0.07) x 109 y is obtained.
When lead is extracted from the ore it is in secular equilibrium with its precursors radium
and uranium. The radium and most of its descendants are removed during processing while
the 210pb accompanies the other lead isotopes. The separation of radium from lead is not
always complete. Because of the long half-life of 226Ra (1600 y) as compared to the short-
lived 21~ (22.3 y), the determination of the excess 21~ over the equilibrium amount
received from 226Ra decay provides a scale for the time since the manufacture of the lead.
This was used to verify forgeries of paintings claimed to be made by the Dutch artist
Vermeer van Delft (1632 - 1675). The paintings were in fact made by H van Meegeren
(1889 - 1948), in the 1940's and were so excellent in style that every authority accepted
them as authentic. When threatened by the death penalty for selling such national treasures
to the Germans during World War II, van Meegeren confessed the forgery, and his story
was verified by dating the lead in the "lead white', PbSO 4, in the fake "Vermeers'.

5.9. Natural radioactivity of the oceans
The total amounts of 238U and 232Th in the ocean are 4.3 x 1012 kg (53 EBq) and 6.9 x
l0 l0 kg (0.3 EBq), respectively. The oceans contain a much higher concentration of
uranium than would be expected from its abundance in rocks. It also occurs at much larger