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Regarding carbon-14, there is so little of it that it makes no sense to even think about it (about 1 in 10^12 atoms). In addition, all biological matter (including you and the food you eat) has carbon-14 present in it -- that's the basic principle behind carbon dating. In fact, ash from wood burning would probably have more carbon-14 if anything.

But yes, the article you linked talks about trace amounts of uranium and other materials that actually could be harmful.

The half life of C-14 is much shorter than geologic formation time for coal. Coal's radioactivity is due to primordial nuclides and their decay chains.

How does the radioactivity from coal compare with the radioactivity from bananas?