How do we know radiometric dating is reliable

As one example, the first minerals to crystallize (condense) from the hot cloud of gasses that surrounded the Sun as it first became a star have been dated to 4568 plus or minus 2 million years....!! Other events on earth can be dated equally well given the right minerals.

There are about two dozen decay pairs used for dating.

Uranium 235 decay to lead has a half-life of 713 million years, so it is well suited to dating the universe.

For example, the element Uranium exists as one of several isotopes, some of which are unstable.

When an unstable Uranium (U) isotope decays, it turns into an isotope of the element Lead (Pb).

For example, a problem I have worked on involving the eruption of a volcano at what is now Naples, Italy, occurred 38500 years ago with a plus or minus of 300 years.

So, when the materials are appropriate and one carefully avoids contamination and re setting radiometric clocks can be VERY ACCURATE.

: Suppose there is a set of variables whose individual values are probably different, and may be anything larger than zero. If there is a group of radioisotopes whose eventual decay is not predictable on the individual level, I do not understand how a decay constant is measurable.

This question is asked with the intention of understanding basically the decay constant of radiometric dating (although I know the above is not an entirely accurate representation).

Measuring the ratio of C14 to C12 and C13 therefore dates the organic matter for periods back to about eight half-lives of the isotope, 45,000 years.

After a long enough time the minority isotope is in an amount too small to be measured.