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Yes, in theory it is a similar or the same kind of nanoparticle but carbon dots are not toxic or less than the traditional quantum dots made of Se, Cd, etc. And that why this kind of nanomaterial is used for bioimaging.

Its definitely not heavy metal, but is that the toxicity of nanoparticles (in general) is still somehow not fully investigated?

Well that is a good question, but definitely the toxicity is because of the heavy metal.