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The alpha particles cannot get through your skin but once the emitter ie plutonium, is inside your body you cannot get rid of it ie stays in your lungs, organs or bones..then the alpha particles can get you from the inside. plutonium is an abundant alpha particle emitter.

The same thing can happen with tritium & radium inside your body, tritium is used in nightsights on firearms and in the hands of some watches, radium was used in dials and older watch hands. Although I dont know of many people that try to ingest gun sights watch hands or old dials...

Another isotope close at hand is Americium. It is used in smoke detectors and can be used as a portable source of gamma rays. Americium moves rapidly through the body after uptake and is concentrated within the bones for a long period of time. During this storage americium will slowly decay and release radioactive particles and rays. These rays can cause alteration of genetic materials and bone cancers.

Scary stuff huh...