The title says it all.
For example why is plutonium considered more dangerous than radioactive iodine?
Answer
A more balanced approach might be to recognize that both short and long half-live materials can be serious hazards, but usually for somewhat different reasons. Also, the devil is very much in the details here, because issues such as how your body absorbs the isotopes is also very, very important.
Radioisotopes with short half-lives are dangerous for the straightforward reason that they can dose you very heavily (and fatally) in a short time. Such isotopes have been the main causes of radiation poisoning and death after above-ground explosions of nuclear weapons.
Iodine is an example where preferential absorption by the human body can further aggravate the dangers of short-lived isotopes.
Long-term isotopes are more complicated. They don't dose as heavily, but there are a lot more issues than just that. Plutonium for example is comparatively long-lived, but some of its decay products can be quite nasty. Also, plutonium happens to be particularly toxic due to its chemistry, which aggravates the damage it can do.
The biggest danger from radioisotopes with mid-to-long half lives is that they can keep an entire region of earth nastily radioactive for a very long time, e.g. hundreds or thousands or even tens of thousand of years. That's the main reason why disposing of reactor wastes, which often contain just such isotopes, is such a contentious issue.
At the extreme end are isotopes that are so long-lived that their hazard levels are close to zero. Uranium-238, the kind left after the fissile 235 is removed, pretty well falls into this category. Bismuth (as in the main ingredient in a popular pink stomach relief aid) is ironically in this category, with a half-life so long it's hard even to tell that it is radioactive.
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