On of the interesting facts associated with the debate over nuclear power is the amount of radiation emitted by burning coal. Typically a coal-fired power plant emits about 3.3 times the amount of radioactive material into the environment that a nuclear plant does for a similar amount of power produced.
This is due to the fact that coal contains radioactive material, mostly uranium and thorium, at about 4 parts per million. Now this does not seem like a lot until the quantity of coal a 1000 megawatt plant will burn in a day, around 11,000 tons, is considered. This works out to be roughly 40 kilos of radioactive material (88 pounds) each day. About 10% of this will be released to the atmosphere and the rest will end up in the ash pile and subject to weathering. If proper scrubbers are in place as little as 1% could reach the atmosphere, but this is still rather significant given the tonnage of coal burned for electric generation.
Additionally there is the radon present in coal that is directly vented to the atmosphere by mining operations and the smaller amounts of more dangerous radioactive elements like radioactive potassium or phosphorous.
But on the other side is the fact that occasionally things go wrong at nuclear power plants and unless the waste is properly disposed of it could pose a significant threat to public health. Though it should be noted that much of the danger is exaggerated a great deal. The Chernobyl Disaster has resulted in a maximum of 300 deaths, and more likely to be 34 or less according to the UN Scientific Committee on the Effects of Atomic Radiation. With this information it would seem that if the glassification (a.k.a. vitrification) of wastes and permanent storage in facilities like the one at Yucca Mountain were carried out it would provide for storage of a safety equal to that of coal plants. | 
