The ratios of U/Pb and Th/Pb must be quite large to maximize the sensitivity of these dating methods to radiogenically generated Pb.

Thus, they can only be applied to certain minerals such as zircon and monazite crystals.

Our investigation begins with the three “so called” isochron equations listed in a previous U to yield an isochron equation that only involves Pb isotope concentrations on one side of the equation: The result is a transcendental equation that cannot be solved for t (time).

Uranium comes in two common isotopes with atomic weights of 235 and 238 (we'll call them 235U and 238U).

Both are unstable and radioactive, shedding nuclear particles in a cascade that doesn't stop until they become lead (Pb).

In order for any of these methods to provide reasonable estimates of the age of a rock, all four basic assumptions made for radioisotope dating methods must be rigorously satisfied: (1) The rock/mineral must have remained closed to U, Th, Pb, and all intermediate daughters throughout its history.

(2) The decay constants of U, Th, Pb, and all intermediate daughters must be accurately known and constant over the entire history of the rock.

The two cascades are different—235U becomes 207Pb and 238U becomes 206Pb.

What makes this fact useful is that they occur at different rates, as expressed in their half-lives (the time it takes for half the atoms to decay).

The sixth assumption assumes that at the time a mineral was formed in a rock, the Pb it contains was separated from the U and Th parents, and thus its isotope ratio has remained constant.

How does one use radioisotope decay as a clock when it has been removed from the rock sample being dated?

They further reason that the loss of radiogenic Pb out of the rock formation causes discordant lines that intersect the ideal curve at the time of original crystallization and the time elapsed since complete closure to migration of any form, assuming all assumptions are rigorously satisfied.