Generally speaking, no. Only very extreme radiation fields (around 1000 Roentgen/hr or a lethal dose in 30 minutes) can sometimes ionize the air to an extent that a smell of ozone is created. Accidents with an X-Ray machine on the fritz also suggest that dose rates tens or hundreds of times higher than that may cause a burning sensation in the flesh. Ionizing radiation of sufficient intensity can also create a blue glow or flash in water and to a lesser extent air.
Practically speaking, though, radiation will usually kill you and you don’t even know what happened for another hour or two.
Most commonly of course, the result is a theoretical increase in cancer risk that never actually manifests at all.
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