As seen in Figures 4.4—4.6, there are alpha decays in all decay series. The numbers of alpha decays are eight, seven, or six in the series of 238U, 235U, and 232Th isotopes, respectively. Since the alpha particles are the nuclei of helium, the quantity of the helium gas accumulated inside the rocks can be applied to estimate age. Of course, this method can give the right ages only if the helium gas has not escaped from the rock.

From 1 g of uranium or thorium, 1.195 X 10-4mm3 or 2.9 X 10-5 mm3 of helium gas is formed in a year. Therefore, this method requires the accurate deter­mination of small volumes of helium gas. For this purpose, the rock is dissolved in a mixture of H2SO4 + K2S2O8 or in an acidic oxidizing solution containing CuCl2 and KCl, avoiding the formation of hydrogen gas in significant volumes. The few hydrogen and nitrogen molecules that form are oxidized by palladium or barium
catalysts, respectively. The noble gases are separated by activated carbon in a chro­matographic procedure performed at the temperature of liquid nitrogen. In this way, the quantity of helium can be determined with an accuracy of about 2 X 10—7 cm3.

4.2.1 Radioactive Dating by Fission of Uranium

By spontaneous fission of uranium (discussed in Section 4.4.5), different xenon iso­topes (129, 131, 132, 133, 136Xe) are formed. The age of uranium-containing rocks or ores can be determined from the quantity of the xenon accumulated in the rocks.

Besides spontaneous fission, the neutrons coming from the cosmic ray also induce the fission of uranium in the silicates. The fission products destroy the silicate lattice. The fission tracks can be etched (e. g., by hydrogen fluoride) so that they can become visible through a microscope. The age can be estimated from the density of the fission tracks.

4.2.2 Radioactive Dating by Argon Concentration

The only source of 40Ar isotopes is branching decay (discussed in Section 4.1.4) of 40K isotopes:

в 40Ca

If all the argon gas stays trapped in the rock, the age of a potassium-containing rock can be estimated from the argon concentration:

where AEX+e+ and AEX+e++e— are the decay constants of 40K for the production of 40Ar and for the total decay, independent of the daughter nuclides, respectively. Since 40Ca may form via other routes, the quantity of 40Ca cannot be used for dating.