The isotopes which are radioactive in nature is said to be radioisotopes. Radioisotope has unstable atomic nucleus and to attain a stable form, they emit particles and energy.
Since, radioisotopes are very reactive in nature as they are unstable and hence, they decay to form other particles. Energy may be released in the form of alpha particles (helium nuclei), beta particles, (electrons or positrons), or gamma particles (electromagnetic energy).
Hence, incorrect statement is: radioisotope is stable.