The relative risk to the human body from exposure to alpha, beta and gamma radiation, as emitted by fallout [ignoring the intense burst of electro-magnetic radiation from the actual detonation].

Alpha particles are relatively low power, even skin [unbroken] is an effective barrier, as are a very few inches of air.
Beta particles are more energetic but are stopped by a thin layer of metal ...
Gamma radiation is very energetic, requiring lead or greater thicknesses of other materials for protection. [cf X-rays]

However, all three are capable of much more serious damage to the human body if ingested [and that includes deposition in the lungs from breathing in contamination]

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