To determine which type of radiation is most harmful, we must first determine how far each one can travel. The distance that radiation travels is important for two reasons:
1.The further it travels the more easily it will get to your body. 2.The distance it travels in your body, affects how much damage it does.
There are various things to consider when determining how far radiation will travel. For a discussion on this, see How does radiation get stopped?
Alpha particles can not even penetrate a piece of ordinary paper, beta particles are stopped by a thin sheet of aluminum, while it takes an inch of lead (at least) to stop gamma rays. Thus, alpha and beta particles can not even penetrate through a person's skin, while gamma rays can get into the body and cause damage. For external radiation, GAMMA RAYS ARE THE MOST HARMFUL
Of course, to every rule, there is at least one exception. If you eat or inhale an isotope that is an alpha emitter, it doesn't have to penetrate your skin anymore to get into the body. Some alpha emitters, when inhaled, can even pass into your blood and irradiate your whole body that way. In these situations, the alphas are most harmful because the side effect of slowing down quickly is that they deposit all their energy in a short distance, thus concentrating their effect.
It is because of this effect that smokers receive a much higher annual dose of radiation than non-smokers. Radioactive polonium (from the radon decay chain) gets deposited from the air onto tobacco leaves when they are dried. When the smoker inhales the smoke, they are also inhaling polonium and other isotopes in the decay chain, all of which are alpha and beta emitters. This radiation is harmful once it gets into the lungs.
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