Question:
What isotope has the shortest half life?
Answer
The question is ill-posed.
To begin it should be "*What isotope has the..." and even then the answer is "We don't really know, as there are some we have produced too few times to have an accurate measure for but they sure don't live long." Looking at the low-mass end of the periodic table I find some described in terms of the linewidth---which means really short.
Isotopes with halflives measured in 10s of seconds have been put to use from time to time. And the shortlived low-mass isotopes are useful in calibrating underground neutrino detectors.
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