Step 1: Recall the two zones of an atom. An atom has a tiny, massive, positively charged central core (the nucleus of protons and neutrons) surrounded by a comparatively vast cloud of orbiting electrons.
Step 2: Match radiation to its zone. Radioactive decay changes the identity of the nucleus (alpha decay removes 2 protons and 2 neutrons, beta decay converts a neutron to a proton, gamma decay releases nuclear excitation energy). All of these involve only the nucleons, so the electron cloud plays no part in producing \(\alpha\), \(\beta\) or \(\gamma\) radiation.
Step 3: State clearly. Hence radioactive radiation comes out of the nuclear core, not the electron shells.
\[\boxed{\text{Radioactive radiation is emitted from the atomic nucleus.}}\]