  It is possible that the proton is stable while atomic hydrogen is not. This
is the case in models with new particles carrying baryon number which are light
enough to be stable themselves but heavy enough so that proton decay is
kinematically blocked. Models of new physics that explain the neutron lifetime
anomaly generically have this feature, allowing for atomic hydrogen to decay
through electron capture on a proton. We calculate the radiative hydrogen decay
rate involving the emission of a few hundred keV photon, which makes this
process detectable in experiment. In particular, we show that the low energy
part of the Borexino spectrum is sensitive to radiative hydrogen decay, and
turn this into a limit on the hydrogen lifetime of order $10^{30}~\rm s$ or
stronger. For models where the neutron mixes with a dark baryon, $\chi$, this
limits the mixing angle to roughly $10^{-11}$, restricting the $n\to\chi\gamma$
branching to $10^{-4}$, over a wide range of parameter space.
