The invention is directed to an apparatus vitrifying radioactive fission ducts in liquid solution. The liquid solution is pumped in metered quantities from a feed container to a vitrifying oven. The offgas occurring during vitrification is scrubbed of entrained radioactive dust particles and the like by a scrubbing liquid in a scrubber. In order to obtain a simplified sequence of method steps for metering the liquid solution and for scrubbing the offgas, the radioactive fission product solution from the feed container itself is used as the scrubbing liquid. This fission product solution is taken from the feed container and conducted to the counterflow scrubber through which it is passed in a direction opposite to the flow of the offgas. The fission product solution used as a scrubbing liquid is returned to the feed container after passing through the counterflow scrubber.