A cobalt coincidence radioactivity detector is used to separate radioactive concrete dust from uncontaminated dust resulting from dismantling a nuclear power plant. A suction air stream carries the dust through a vacuum line to a cyclone segregator. The dust falls into a smaller first container from the segregator, and the detector detects radioactivity in the filled first container. The dust is transferred from the first container to a second container if the detected radioactivity exceeds a predetermined threshold. The dust is transferred from the first container to a third container if the detected radioactivity does not exceed the predetermined threshold. A filter collects the dust carried past the segregator by the suction air stream. If the radioactivity detected in the dust that collects on the filter exceeds the predetermined threshold, the dust in the first container is transferred to the second container before the first container is allowed to fill.