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The 133.5 nm lines are important observables for the NASA/SMEX missionInterface Region Imaging Spectrograph (IRIS). To make 3D non-LTE radiativetransfer computationally feasible it is crucial to have a model atom with asfew levels as possible while retaining the main physical processes. We heredevelop such a model atom and we study the general formation properties of theC II lines. We find that a nine-level model atom of C I-C III with thetransitions treated assuming complete frequency redistribution (CRD) sufficesto describe the 133.5 nm lines. 3D scattering effects are important for theintensity in the core of the line. The lines are formed in the optically thickregime. The core intensity is formed in layers where the temperature is about10kK at the base of the transition region. The lines are 1.2-4 times wider thanthe atomic absorption profile due to the formation in the optically thickregime. The smaller opacity broadening happens for single peak intensityprofiles where the chromospheric temperature is low with a steep sourcefunction increase into the transition region, the larger broadening happenswhen there is a temperature increase from the photosphere to the lowchromosphere leading to a local source function maximum and a double peakintensity profile with a central reversal. Assuming optically thin formationwith the standard coronal approximation leads to several errors: Neglectingphotoionization severly underestimates the amount of C II at temperatures below16kK, erroneously shifts the formation from 10kK to 25kK and leads to too lowintensities.

The formation of IRIS diagnostics V. A quintessential model atom of C II and general formation properties of the C II lines at 133.5 nm