Halobacterium has a photosynthetic membrane that appears purple. its photosynthetic action spectrum is the inverse of the action spectrum for green plants. (that is, the halobacterium action spectrum has a peak where the green plant action spectrum has a trough.) what wavelengths of light do the halobacterium photosynthetic pigments absorb?

I believe the wavelength of lights absorbed by the Halobacterium photosynthetic pigments is Green and Yellow.
Halobacterium are in the domain of Archea, a group of single-celled micro-organisms and therefore not bacteria. They can live in extreme environments. Even though they are prokaryotic, halobacteria act as a good model for eukaryotic processes, including DNA replication.