Changes

Since the rate at which radiation is admitted is proportional to the amount of the substance present, and the amount of substance remaining undergoes exponential decay, the rate of particle emission (e.g. Geiger counter clicks per second) also decays exponentially.

Since the rate at which radiation is admitted is proportional to the amount of the substance present, and the amount of substance remaining undergoes exponential decay, the rate of particle emission (e.g. Geiger counter clicks per second) also decays exponentially.

While the mechanisms for decay, and hence the half-lives of various isotopes, are well understood on theoretical grounds, the calculations are so complex that half-lives are measured experimentally.  The measured half-lives of the various isotopes of elements are known to be fixed quite accurately.  Careful astronomical observations show that half-lives have not changed significantly in billions of years—spectral lines from distant galaxies would have shifted perceptibly if the constants involved had changed.  In some cases radioactive decay itself can be observed and measured in distant galaxies when a supernova explodes and ejects radioactive nuclei.

While the mechanisms for decay, and hence the half-lives of various isotopes, are well understood on theoretical grounds, the calculations are so complex that half-lives are measured experimentally.  The measured half-lives of the various isotopes of elements are known to be fixed quite accurately.  Careful astronomical observations show that half-lives have not changed significantly in billions of years—spectral lines from distant galaxies would have shifted perceptibly if the constants involved had changed.  In some cases radioactive decay itself can be observed and measured in distant galaxies when a supernova explodes and ejects radioactive nuclei.