Answer
See answers for a list of the observations that support radioactivity being a nuclear process.
Work Step by Step
See section 30–3. Experiments have been performed to see if radioactivity is affected by physical (heating, cooling, humidifying) or chemical (e.g., strong reagents) treatments. It is found that the radioactivity is unaffected. Since we know that chemical reactions occur via electron interactions, this null result provides evidence that radioactivity is due to nuclear processes.
In the case of $\beta$ radiation, the emerging electrons or positrons typically have energies that are much higher than the energy of electrons in orbits, so these energies cannot be explained by them making transitions between orbits. The nucleus must be involved.
Furthermore, in the case of $\alpha$ particle emission, the particle is much heavier than an electron and has a charge of +2e. By mass and charge conservation, alpha radiation cannot be composed of electrons – so $\alpha$ particles must originate from the nucleus.