A radioactivity analyzing apparatus for analyzing a radionuclide contained in a sample material. The apparatus includes a radiation detector that detects a radiation to be detected emitted from the sample material and a radiation analyzer configured to analyze the radiation based on an output from the radiation detector. The radiation analyzer includes a pulse-height analyzer configured to extract a pulse-height distribution from a pulse signal being output from the radiation detector and depending on the radiation, an inverse-problem operator configured to perform an inverse-problem solution of the pulse-height distribution to extract an energy spectrum of the radiation, and a deterioration detector configured to determine a deterioration state of the radiation detector based on the extracted energy spectrum.