There are numerous valid reasons why commercial nuclear energy is a questionable option for a safe and sustainable economy-- accidents, waste disposal problems, high cost, stock-limited fuels, etc.
Let's examine the risk of major nuclear accidents by looking at nuclear energy's record. The historical record is not an endorsement by nuclear proponents nor a condemnation by anti-nuclear activists. This is history speaking. In the past 50 years of global commercial electricity generation we have logged nearly 10,500 reactor-years. (A reactor-year is one reactor operating for one year.)
During this time we have experienced three major nuclear accidents: Three-Mile Island in 1979, Chernobyl in 1986, and Fukushimo Daiichi in 2011. We are not counting hundreds of lesser incidents at nuclear power stations. The causes of all of these accidents are failures of technology, human error, natural disasters, or combinations of these.
Nuclear power's 50-year record suggests an accident rate of one major peacetime nuclear disaster every 3,500 reactor-years. We are currently operating 430 reactors worldwide (430 reactor-years per year), and we should expect a major accident about every 8 years.
If we try to increase nuclear energy's share of commercial energy generation by building more plants, we should expect more frequent accidents.
Since nuclear energy currently provides 15% of the world's electricity (with 433 grid-connected reactors), in order to provide (hypothetically) 100% of the world's electricity we would need a total of 2,866 reactors. This changes the accident frequency, based on our calculations, to one major accident every 15 months.
Not much has changed, statistically, since I published this FoxSense graphic in 1992.