  The standard model predicts that, in addition to a proton, an electron, and
an antineutrino, a continuous spectrum of photons is emitted in the $\beta$
decay of the free neutron. We report on the RDK II experiment which measured
the photon spectrum using two different detector arrays. An annular array of
bismuth germanium oxide scintillators detected photons from 14 to 782~keV. The
spectral shape was consistent with theory, and we determined a branching ratio
of 0.00335 $\pm$ 0.00005 [stat] $\pm$ 0.00015 [syst]. A second detector array
of large area avalanche photodiodes directly detected photons from 0.4 to
14~keV. For this array, the spectral shape was consistent with theory, and the
branching ratio was determined to be 0.00582 $\pm$ 0.00023 [stat] $\pm$ 0.00062
[syst]. We report the first precision test of the shape of the photon energy
spectrum from neutron radiative decay and a substantially improved
determination of the branching ratio over a broad range of photon energies.
