By the time it needs recharging you will never remember where you left the adapter...
But seriously... aside from Chernobyl and other RBMKs, where are you going to get all of that graphite? Last I checked, PWRs and BWRs don't count that as a major component of their waste stream, and there can't be that much coming out of research reactors. More importantly, how much carbon-14 with its itty-bitty beta do you need to make electricity?
Would be cool if they can make it work, though.