The average age of uranium miners who die of lung cancer is 46. As radioactive fuel and wastes are created and handled and transported and stored, many people are exposed a little. Inside the plant itself, a broken pipe spills a puddle of radioactive water, which someone mops up. Then the pipe is fixed or replaced. Each operation exposes workers a little more and creates a little more radioactive waste, which must be packaged and shipped somewhere by someone.
Exposures add up.
The unit of measurement for radioactivity is the rem. One person exposed to one rem of radiation creates an exposure of one person-rem. The size of a nuclear power plant is measured by the plant's capacity to produce electricity. A large plant is rated at 2 billion watts, or 2 gigawatts, meaning it could light 20 million 100-watt light bulbs continuously. Such a plant operating for one year will produce 2 gigawatt-years of electricity.