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There are a number of implausible assumptions involved in radiometric dating with respect to long time periods.One key assumption is that the initial quantity of the parent element can be determined.With uranium-lead dating, for example, the process assumes the original proportion of uranium in the sample.
Another assumption is that the rate of decay is constant over long periods of time.In the case of carbon dating, it is not the initial quantity that is important, but the initial ratio of C, but the same principle otherwise applies.Recognizing this problem, scientists try to focus on rocks that do not contain the decay product originally.Radiometric dating requires that the decay rates of the isotopes involved be accurately known, and that there is confidence that these decay rates are constant. The physical constants (nucleon masses, fine structure constant) involved in radioactive decay are well characterized, and the processes are well understood.
Careful astronomical observations show that the constants have not changed significantly in billions of years—spectral lines from distant galaxies would have shifted perceptibly if these constants had changed.
The effect of this on alpha decay, which is the most common decay mode in radiometric dating, is utterly insignificant.