Radiogenic nuclei decay at a rate calculated by the half-life rate where statistically 50% of the unstable nuclei decay to more stable isotopes by emitting particles, alpha, beta and gamma radiation, per unit of time.
Say we start with 100 nuclei that are unstable. After 1 half-life 50% decay to more stable isotopes. It is easily shown that this process completes at the 8th half-life. There is a problem, however, because the process is such that the last nuclei to decay has to be also the most stable of the nuclei of the ‘radiogenic’ isotopes. If the element is uranium and we consider its 238 isotope with a calculated half-life of 4,500 Ma. then we have the problem of explaining why one atom of U238 is stable for 8 times the half-life, or 36,000,000,000 years. And why is it more stable than, say, the first nuclei of U238 to decay? What’s the difference between the first and last nuclei? There has to be because the first one decayed while the last one has not.
Settled Science avoids this problem by escaping into ‘statistics’, which means we actually don’t understand the radiogenic decay process at all but ’statistically’ it’s true. However from first principles one must reject the present explanation for radiogenic decay and hence ‘absolute dates’.
Which leads me to paraphrase Charles Ginenthal’s conclusion that radiogenic dates are used to support chronological interpretations rather than to confirm them objectively.
And the problem with absolute dating lies in its fundamental presumption that there actually occurred an instant in the past when T= 0, when the atomic clock started ticking. Absolute dating is best viewed as unimpeachable authority, which makes it quite unscientific.
Update below the fold:
Where did uranium come from?
Cosmochemists have been concerned not only with patterns and secular trends of abundance of the elements in galaxies but also with the origins of abundance anomalies in particular stars and with theories on the synthesis of different nuclei to account for these observations. According to the theories developed, the Earth’s uranium was produced in one or more supernovae (“An explosive brightening of a star in which the energy radiated by it increases by a factor of ten billion … A supernova explosion occurs when a star has burned up all its available nuclear fuel and the core collapses catastrophically.” – Oxford Dictionary of Physics). The main process concerned was the rapid capture of neutrons on seed nuclei at rates greater than disintegration through radioactivity. The neutron fluxes required are believed to occur during the catastrophically explosive stellar events called supernovae. Gravitational compression of iron (the island of nuclear stability, incapable of further exothermic fusion reactions) and sudden collapse in the centre of a massive star triggers the explosive ejection of much of the star into space, together with a flood of neutrons. Remnants of hundreds of supernovae have been found, and we “witnessed” one in the Magellanic Clouds in 1987.
So, we know that the Earth’s uranium was produced through this process in one or more supernovae, and that this material was inherited by the solar system of which the Earth is a part.
We might further ask how long ago this synthesis of uranium occurred. Given
We can calculate the abundances of U-235 and U-238 at the time the Earth was formed. Knowing further that the production ratio of U-235 to U-238 in a supernova is about 1.65, we can calculate that if all of the uranium now in the solar system were made in a single supernova, this event must have occurred some 6.5 billion years ago.
This ‘single stage’ is, however, an oversimplification. In fact, multiple supernovae from over 6 billion to about 200 million years ago were involved. Additionally, studies of the isotopic abundances of elements, such as silicon and carbon in meteorites, have shown that more than ten separate stellar sources were involved in the genesis of solar system material. Thus the relative abundance of U-235 and U-238 at the time of formation of the solar system:
Which means a gravitationally compressing mechanism then suddenly explodes splattering the compressed elements into local space?
It’s more likely that radiogenic elements are produced in stellar Z-Pinches, or locally via electrical discharges, but the explanation above is not an explanation at all but a waffly guess.
So basically Settled Science doesn’t know how radiogenic elements are formed.