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Theoretical emission‐line ratios involving Fe  xi  transitions in the 257–407 Å wavelength range are derived using fully relativistic calculations of radiative rates and electron impact excitation cross‐sections. These are subsequently compared with both long wavelength channel Extreme‐Ultraviolet Imaging Spectrometer (EIS) spectra from the  Hinode  satellite (covering 245–291 Å) and first‐order observations (∼235–449 Å) obtained by the Solar Extreme‐ultraviolet Research Telescope and Spectrograph (SERTS). The 266.39, 266.60 and 276.36 Å lines of Fe  xi  are detected in two EIS spectra, confirming earlier identifications of these features, and 276.36 Å is found to provide an electron density ( N  e ) diagnostic when ratioed against the 257.55 Å transition. Agreement between theory and observation is found to be generally good for the SERTS data sets, with discrepancies normally being due to known line blends, while the 257.55 Å feature is detected for the first time in SERTS spectra. The most useful Fe  xi  electron density diagnostic is found to be the 308.54/352.67 intensity ratio, which varies by a factor of 8.4 between   N  e = 10 8   and 10 11  cm −3 , while showing little temperature sensitivity. However, the 349.04/352.67 ratio potentially provides a superior diagnostic, as it involves lines which are closer in wavelength, and varies by a factor of 14.7 between   N  e = 10 8   and 10 11  cm −3 . Unfortunately, the 349.04 Å line is relatively weak, and also blended with the second‐order Fe  x  174.52 Å feature, unless the first‐order instrument response is enhanced.

Emission lines of Fe xi in the 257–407 Å wavelength region observed in solar spectra from EIS/ Hinode and SERTS