This is all oil disinformation.
1) If you take all the nuclear waste that has been produced since the dawn of nuclear energy, it would fit in an area smaller than a football field with 50 more years to spare, safely encased in lead and concrete.
2) Currently in the US we keep all of the waste in a seismically non eventful area, buried under a mountain. There is this misconception about nuclear waste that it will accumulate beyond our ability to safely deal with. Spent fuel rods are actually quite small. Even if they weren't, there are a number of nuclear reactors that can actually recycle spent fuel rods
3) Modern thorium reactor designs can actually be shut down with no risk of meltdown. The Fukishima disaster would not have happened if they were using thorium reactors. A counter attack to this argument is the environmental disaster that a major oil spill can and has caused. Look at what happened to the Gulf of Mexico. Lets also not forget fracking leaks and poisoning of water tables. Oil and natural gas dont exactly hsve a great track record either.
4) Cost is brought up as a common argument against nuclear power. Fair enough, but if you remove the subsidies that oil and natural gas receive as well then that alternative becomes a lot more expensive as well. My final thought on this is about cost externalities. When the affordable cost of fossil fuels is brought up, this argument only holds true when burners of these fuels are not held liable for cleaning up the environmental damage and pollution that these cause. For the lead and carbon in the atmosphere that must be cleaned up, the health issues caused by those subject to this pollution, the oil spills to be cleaned up. The poisoned water supplys from fracking activities, these are all hidden costs that oil, natural gas and coal have put on society at large to deal with. The damage has been estimated to be in the trillions and the future generations are picking up the tab. Cost average this to the price per MCF of natural gas or a barrell of oil and the true cost of fossil fuels will likely make it extremely unattractive compared to not just nuclear, but most other types of renewable power generation.