  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.
