  We show that the X-ray line flux of the Mn Kalpha line at 5.9 keV from the
decay of 55Fe is a promising diagnostic to distinguish between Type Ia
supernova (SN Ia) explosion models. Using radiation transport calculations, we
compute the line flux for two 3D explosion models: a near-Chandrasekhar mass
delayed detonation and a violent merger of two white dwarfs. Both models are
based on solar metallicity zero-age main sequence progenitors. Due to explosive
nuclear burning at higher density, the delayed-detonation model synthesises 3.5
times more radioactive 55Fe than the merger model. As a result, we find that
the peak Mn Kalpha line flux of the delayed-detonation model exceeds that of
the merger model by a factor of 4.5. Since in both models the 5.9 keV X-ray
flux peaks five to six years after the explosion, a single measurement of the
X-ray line emission at this time can place a constraint on the explosion
physics that is complementary to those derived from earlier phase optical
spectra or light curves. We perform detector simulations of current and future
X-ray telescopes to investigate the possibilities of detecting the X-ray line
at 5.9 keV. For the delayed-detonation scenario, a line detection is feasible
with Chandra up to 3 Mpc for an exposure time of 10^6 s. We find that it should
be possible with currently existing X-ray instruments (with exposure times
5x10^5 s) to detect both of our models at sufficiently high S/N to distinguish
between them for hypothetical events within the Local Group. The prospects for
detection will be better with future missions. For example, the proposed
Athena/X-IFU instrument could detect our delayed-detonation model out to a
distance of 5 Mpc. This would make it possible to study future events occurring
during its operational life at distances comparable to those of the recent
supernovae SN 2011fe (6.4 Mpc) and SN 2014J (3.5 Mpc).
