The actual underlying assumption is that, if those requirements have not been met, there is no reason for the data points to fall on a line.
The resulting plot has data points for each of five meteorites that contain varying levels of uranium, a single data point for all meteorites that do not, and one (solid circle) data point for modern terrestrial sediments.
Over time, the amounts of Pb-206 and Pb-207 will change in some samples, as these isotopes are decay end-products of uranium decay (U-238 decays to Pb-206, and U-235 decays to Pb-207).
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Further, the processes of erosion and crustal recycling have apparently destroyed all of the earliest surface.
The oldest rocks which have been found so far (on the Earth) date to about 3.8 to 3.9 billion years ago (by several radiometric dating methods).
The higher the uranium-to-lead ratio of a rock, the more the Pb-206/Pb-204 and Pb-207/Pb-204 values will change with time.
If the source of the solar system was also uniformly distributed with respect to uranium isotope ratios, then the data points will always fall on a single line.
The most direct means for calculating the Earth's age is a Pb/Pb isochron age, derived from samples of the Earth and meteorites.
This involves measurement of three isotopes of lead (Pb-206, Pb-207, and either Pb-208 or Pb-204).
(I believe this argument was originally put forth by Mormon young-Earther Melvin Cook, in a letter to the editor which was published in .) But helium can and does escape from the atmosphere, at rates calculated to be nearly identical to rates of production.
In order to obtain a young age from their calculations, young-Earthers handwave away mechanisms by which helium can escape.
) and they are historically the ones posted to talk.origins more than any others.
The young-Earth argument goes something like this: helium-4 is created by radioactive decay (alpha particles are helium nuclei) and is constantly added to the atmosphere.
Some of these rocks are sedimentary, and include minerals which are themselves as old as 4.1 to 4.2 billion years.