The effects of radiation on the human body are different depending on the type of radiation, whether the radiation is coming from inside or outside the body, and what part of the body is irradiated.
All three types of radiation cause damage when they smash into atoms in our body and ionize those atoms, creating free radicals inside the cell. These free radicals are the same as any other kind of free radical – there’s nothing special or extra toxic about the ones created by radioactivity: if the rate of damage is small, the cell can repair it just like it does with free radical damage from any other source. However, if the radiation causes ionization faster than the cell can repair the damage, the cell may die or become cancerous.
Cells are especially vulnerable to damage by free radicals when they are dividing, which means that cell types that are constantly dividing are more prone to damage by radiation. Bone marrow – which is constantly dividing to replenish our supply of red blood cells – is a type of tissue that is heavily affected by radiation. This is why leukemia is so often a consequence of radiation damage, and why radionuclides that accumulate in your bones (like plutonium, uranium, and strontium) are especially dangerous. Other highly vulnerable types of cells include the gonads, and the villi that line the small intestine.
Alpha particles, being the largest, cause the most damage since they smash into (and ionize) the most atoms. That said, they smash into things so much that they slow noticeably in air (due to their collisions with air molecules) and they are stopped completely by clothing or a sheet of paper. Should they impact the body from the outside, they don’t penetrate more deeply than the skin.
This means that damage from alpha-emitters like uranium and plutonium is significantly enhanced when they are ingested, either by eating contaminated food or inhaling dust contaminated by those elements: not only are you suddenly getting irradiated from the inside by highly damaging alpha that wouldn’t even penetrate your skin from the outside, both of these metal tend to accumulate in your bones, where they irradiate the extremely vulnerable bone marrow. As if that weren’t enough, both uranium and plutonium are toxic metals, like lead or arsenic, so you get poisoned also. In fact, the chemical poisoning effect is usually more harmful than the radiation.
Beta particles come in a variety of energies. They are much, much smaller than alpha particles, so they penetrate further into your body; but they also do much less damage along the way. Higher-energy beta does more damage, but is otherwise the same.
Gamma rays generally go right through you, like x-rays. However, your bones stop more gamma rays than the rest of you, which of course is how x-ray imaging works. This means that your bones (and your bone marrow) accrue more damage, because they’re absorbing more of the gamma instead of letting it pass through. Gamma is about as damaging as beta, but all your vulnerable areas get irradiated with gamma, because it goes all the way through you. With gamma, every dose is a full-body dose.