In Radiometric Dating: A Christian Perspective, the author argues (persuasively, I think) in favor of the mainstream interpretation of radiometric dating (as opposed to the claims of young earth creationists). He says the fact that short-lives isotopes are generally not found on Earth is evidence showing that the Earth is billions of years old.
Just about the only radioisotopes found naturally are those with very long half-lives of close to a billion years or longer.... The only isotopes present with shorter half-lives are those that have a source constantly replenishing them...
The Earth is old enough that radioactive isotopes with half-lives less than half a billion years decayed away, but not so old that radioactive isotopes with longer half-lives are gone.
I would guess that some of these shorter-lived elements still exist in minute amounts because a decay curve has a long tail, but is the basic statement correct - that shorter-lived, non-replenished radioactive isotopes are absent (or nearly so) from Earth?
Where can I read more about this?
Clarification: I didn't make it clear enough, but I'm specifically asking about the relative abundance of non-replenished radioisotopes - those that are not produced on Earth by natural processes. Eg, excluding carbon-14 (produced in the atmosphere by cosmic rays), excluding thorium-230 (produced by the decay of uranium-234), etc.