If the OP was either Japanese, or lived in Japan during the 2011 Tōhoku earthquake and tsunami, I could well understand the concern.
Before the tsunami, approx. 30% of Japan's electric power generation was nuclear - now it's only a few percent. The exclusion zone around the damaged Fukushima I Nuclear Power Plant (melt-down, containment breaches) reaches out some 15 miles, or roughly the size of Wake county:
If a similar severity event (however unlikely) occurred at Shearon Harris, the initial 50 mile evacuation zone would encompass Greensboro, Wake Forest and Fayetteville - a LOT of people.
The current exclusion zone for the Chernobyl area is currently 1,000 square mile, I believe.
Is it likely that Shearon Harris could suffer the same fate as the similarly designed Fukushima units, no, and it appears the U.S. Nuclear Regulatory Commission (NRC) has taken steps to learn (and adapt) from the Fukushima event(s) (generator fail-over, etc.)
There are places one can live "away" from nuclear power plants (central western U.S., for example), but on the east coast, we're pretty much downwind (blowing NE) from a plant everywhere ... especially North Carolina.
Some reading:
How Safe Are U.S. Nuclear Reactors? Lessons from Fukushima - Scientific American
After Fukushima, a tour of the Shearon Harris nuclear power facility | Casual Observer | Indy Week
P.S. I'm not an expert in this subject - just trying to express a view.