Hoppe studied chemistry at the Christian-Albrechts-University of Kiel and was awarded his doctorate at the Westfälische Wilhelms-University of Münster in 1954 under the supervision of Wilhelm Klemm.

In 1965, Hoppe accepted an offer for the chair of inorganic and analytic chemistry at the Justus Liebig University Giessen, which he kept until his retirement in 1991.

His work followed the previous synthesis of by xenon hexafluoroplatinate by Neil Bartlett, in an experiment run on March 23, 1962 and reported in June of that year.

In Gießen, Hoppe continued his extensive research in the field of solid state chemistry with a focus on the synthesis and characterization of oxo- and fluorometalates of the alkali metals.

In addition, he had been the scientific editor for the German Journal of Inorganic and General Chemistry (Zeitschrift für Anorganische und Allgemeine Chemie).