With the exception of Carbon-14, radiometric dating is used to date either igneous or metamorphic rocks that contain radioactive elements such as uranium. Now when the uranium or thorium disintegrates, the alpha particles which are emitted are slowed down by the crystals in which the grains of the uranium- or thorium-bearing minerals are embedded.
And even though various radioactive elements have been used to "date" these rocks, for the most part, the methods are basically the same. This means that if you had some pure uranium-238 with no lead in it, 4.5 billion years later one half of it would have decayed into its stable daughter product (lead-206). Where these alpha particles finally stop, crystal deformation occurs (and) shows up as a discolouration or a darkening of the crystals.
They consist of measuring the amount of radioactive (mother) element and comparing it to the amount of stable (daughter) element. Uranium is radioactive, which means it is in the process of changing from an unstable element into a stable one. And after 9 billion years there would be 75% lead and 25% uranium, and so on. (an) episode of drastically accelerated decay has ... When the crystal is looked at under a microscope, these discolourations appear as dark ringshence the name "pleochroic halo".
In other words, the magnitude of the radius of a pleochroic halo in a particular crystal depends on the half-life of the decay responsible for the alpha particle emission. the radii of pleochroic haloes corresponding to a definite decay in a particular mineral are ...
(the same) size, then it can be safely assumed that the half-life of that decay is a constant.