Re: You join an expedition to retrieve data tapes deep within the Chernobyl catacombs
It all depends on the energy levels and radiation types. At work I use radiation that is blocked by paper (40 millicurie Beta source). I've done work with more-intense sources that sit in lead-brick enclosures. The power (Electron volt?) level matters for penetration, and scattering radiation, and so on. Cosmic rays, for instance, punch through metal and create X-rays that penetrate. X-rays can stop at bone or not, depending on the eV level. And ultraviolet, of course, is stopped by most things. For all radiation, more mass is the only sure shield. For specific radiation, shielding and circuit design matter more.
Chernobyl is an interesting case with scads of medium-energy radiation particles. The dosages that will affect circuitry are probably well above the acutely lethal doses of radiation. Your light probably won't blink until you're in radiation that puts you a few hours from noticing that you are dead.