We present joint observations of the Sun by the Atacama Large Millimeter/submillimeter Array (ALMA) and the Interface Region Imaging Spectrograph (IRIS). The observations were made of a solar active region on 2015 December 18 as part of the ALMA science verification effort. A map of the Suns continuum emission of size $2.4 times 2.3$ was obtained by ALMA at a wavelength of 1.25 mm (239 GHz) using mosaicing techniques. A contemporaneous map of size $1.9times 2.9$ was obtained in the Mg II h doublet line at 2803.5AA by IRIS. Both mm/submm$-lambda$ continuum emission and ultraviolet (UV) line emission are believed to originate from the solar chromosphere and both have the potential to serve as powerful and complementary diagnostics of physical conditions in this poorly understood layer of the solar atmosphere. While a clear correlation between mm-$lambda$ brightness temperature $T_B$ and the Mg II h line radiation temperature $T_{rad}$ is observed the slope is $<1$, perhaps as a result of the fact that these diagnostics are sensitive to different parts of the chromosphere and/or the Mg II h line source function includes a scattering component. There is a significant offset between the mean $T_B$(1.25 mm) and mean $T_{rad}$(Mg II), the former being $approx 35%$ greater than the latter. Partitioning the maps into sunspot, quiet regions, and plage regions we find that the slope of the scatter plots between the IRIS Mg II h line $T_{rad}$ and the ALMA brightness temperature $T_B$ is 0.4 (sunspot), 0.56 (quiet regions), and 0.66 (plage regions). We suggest that this change may be caused by the regional dependence of the formation heights of the IRIS and ALMA diagnostics, and/or the increased degree of coupling between the UV source function and the local gas temperature in the hotter, denser gas in plage regions.
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