The Mid-Infrared Instrument (MIRI) on-board JWST will provide imaging, coronagraphy, low-resolution spectroscopy and medium-resolution spectroscopy at unprecedented sensitivity levels in the mid-infrared wavelength range. The Medium-Resolution Spectrometer (MRS) of MIRI is an integral field spectrograph that provides diffraction-limited spectroscopy between 4.9 and 28.3 um, within a FOV varying from 13 to 56 square. From ground testing, we calculate the physical parameters essential to general observers and calibrating the wavelength solution and resolving power of the MRS is critical for maximising the scientific performance of the instrument. We have used ground-based observations of discrete spectral features in combination with Fabry-Perot etalon spectra to characterize the wavelength solution and spectral resolving power of the MRS. We present the methodology used to derive the MRS spectral characterisation, which includes the precise wavelength coverage of each MRS sub-band, computation of the resolving power as a function of wavelength, and measuring slice-dependent spectral distortions. The resolving power varies from R3500 in channel 1 to R1500 in channel 4. Based on the ground test data, the wavelength calibration accuracy is estimated to be below one tenth of a pixel, with small systematic shifts due to the target position within a slice for unresolved sources, that have a maximum amplitude of about 0.25 spectral resolution elements. Based on ground test data, the MRS complies with the spectral requirements for both the R and wavelength accuracy for which it was designed. We also present the commissioning strategies and targets that will be followed to update the spectral characterisation of the MRS.
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