Is nuclear power safe??

This is a real problem. A couple of years ago I got a couple of MRI's and was talking with my neurologist and mentioned that in the oil and gas industry we had a borehole geophysical log called the Nuclear Magnetic Resonance Log which worked on the same principle as an MRI.He had worked with the first MRI machines and said they also at the time called it Nuclear Magnetic Resonance Imaging but no one wanted to get near it or have it done so they changed the name to MRI (no one is afraid of magnets and resonance sounds like a nice thing from music).Maybe the name should be changed to Natural Fission Power Plant and everyone told these are designed completely different than old Nuclear Power Plants (not completely untrue).