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This is incorrect. The Lamb shift makes the $2\,{}^2 P_{1/2}$ state lower than the $2\,{}^2 S_{1/2}$; as such, the former will not spontaneously decay into the latter. In any case, these are states within the $n=2$ shell, so that their main decay channel is to the ground state, $1\,{}^2S_{1/2}$; this can and will happen on a ~nanosecond timescale (i.e. slow ...



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