Any distribution with a sufficient amount of entropy can be turned into "cryptographic-grade" randomness source using randomness extractors [1]. These work independently of any outside factors that might be trying to sneak signal (e.g. periodicity) into the noise -- as long as you can prove there's sufficient entropy to start with, you're good to go.
Low-intensity radiation is random enough, but it's slow: your device is necessarily twiddling thumbs between a detected event and the next, and entropy is mostly proportional to the number of events (for example, almost n bits from what of 2^n identical units is hit by the next particle).
[1] https://en.wikipedia.org/wiki/Randomness_extractor