how and why the decay of Uranium 238 and Technetium–99m are both considered spontaneous even though the time and rate of decay are different.
A spontaneous process is one that occurs naturally under certain conditions.
The spontaneity of a process is not correlated to the speed of the process. A spontaneous change may be so rapid that it is essentially instantaneous or so slow that it cannot be observed over any practical period of time.
Radioactive decay is by definition a spontaneous process in which the nuclei of unstable isotopes emit radiation as they are converted to more stable nuclei. All the decay processes occur spontaneously, but the rates at which different isotopes decay vary widely.
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