  We extend results of Colliot-Th\'el\`ene and Raskind on the
$\mathcal{K}_2$-cohomology of smooth projective varieties over a separably
closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily
projective, varieties over $k$. Some consequences are drawn, such as the
degeneration of the Bloch-Lichtenbaum spectral sequence for any field
containing $k$.
