# How does isochron dating work

Note that uranium-238 and uranium-235 give rise to two of the natural radioactive series , but rubidium-87 and potassium-40 do not give rise to series. They each stop with a single daughter product which is stable. Some of the decays which are useful for dating, with their half-lives and decay constants are:

* Note that 40 K also decays to 40 Ca with a decay constant of 4.962 x 10 -10 yr -1 , but that decay is not used for dating. The half-life is for the parent isotope and so includes both decays.

There are powerful rationales for using lead isotopes as indicative of concentrations at the point when the lead-containing mineral was in the molten state. Since the isotopes of lead are chemically identical, any processes that brought lead into the mineral would be completely indiscriminate about which isotope was brought in. The forming mineral will incorporate lead-204, lead-206 and lead-207 at the ratio at which they are found at that location at the time of formation. Any departure from the original relative concentrations of lead-206 and lead-207 relative to lead-204 could then be attributed to radioactive decay.

Making use of the decay constants of both 238 U and 235 U, plus the fact that the consistent isotopic ratio of 238 U/ 235 U = 137.88 is found, Holmes and Houtermans developed a system to use the ratios of the lead isotopes to produce Pb-Pb isochrons for dating minerals. This approach is generally considered to be the most precise for determining the age of the Earth.

Potassium-Argon dating has the advantage that the argon is an inert gas that does not react chemically and would not be expected to be included in the solidification of a rock, so any found inside a rock is very likely the result of radioactive decay of potassium. Since the argon will escape if the rock is melted, the dates obtained are to the last molten time for the rock. The radioactive transition which produces the argon is electron capture .

The rubidium-strontium pair is often used for dating and has a non-radiogenic isotope, strontium-86, which can be used as a check on original concentrations of the isotopes. This process is often used along with potassium-argon dating on the same rocks. The ratios of rubidium-87 and strontium-87 to the strontium-86 found in different parts of a rock sample can be plotted against each other in a graph called an isochron which should be a straight line. The slope of the line gives the measured age. The oldest ages obtained from the Rb/Sr method can be taken as one indicator of the age of the earth .

This is a rubidium-strontium isochron for a set of samples of a Precambrian granite body exposed near Sudbury, Ontario. The data is from T. E. Krogh, et al., Carnegie Institute Washington Year Book, Vol 66, 1968, p. 530.