Wavenumbers, aka inverse centimeters, has dimensions of energy and thus should be easily convertible to joules. MMA clearly recognizes "Wavenumbers" at some level, since it autosuggests this unit when I begin to type it in the UnitConvert command (see last input at the bottom of the first screenshot below; MMA offers this autosuggestion even on a fresh kernel). Yet when I attempt to evaluate the command, it fails, incorrectly stating that "Wavenumbers and Joules are incompatible units" (see In(5) in first screenshot).
Perhaps correspondingly, I'm getting odd behavior from Wolfram Alpha when I attempt to use it to perform the conversion. Note that it fails in In(1). Yet I recalled a previous notebook in which it worked. If I copy that cell and paste it into this notebook, it works (see In(2)). But when I try copying and pasting just the text from In(2) into a new cell and then evaluating it, it fails (see In(3)). I.e., if I copy and paste the entire working cell, it evaluates successfully, but if I copy and paste its text only, it fails to evaluate.
I should further add that, when I subsequently clicked the "+" sign at the upper right of a failed Wolfram Alpha conversion (e.g., In), the expanded result did indeed provide the correct conversion (see second screenshot).