Approx. 2 500 years ago.
However, let's get our terminology straight: Leucippus didn't "discover" anything, except possibly that his fellow Greeks were willing to listen to any crazy idea you pulled out of your posterior. Leucippus and/or Democritus (his student) were the people who first talked about "atoms", but they had no idea what they were really like or even that they really existed.
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because the credit was given to Dylan Narvadez (buang)
Leucippus and Democritus were important Greek philosophers from the antiquity. Leucippus was the first to have the idea of an atomic structure of all kinds of matter, 2500 years ago. Democritus was his disciple.
Leucippus (450?-370? BC), was a Greek philosopher. He proposed the atomic theory of matter, that all matter is constituted of identical indivisible particles called atoms. This theory was further developed by his student, Democritus.
Moseley was the first to clear and scientifically justify in 1913 the atomic number studying X-ray spectra of chemical elements. But Moseley hadn't a personal atomic theory, he was not the discoverer of the atomic theory.
It depends. If you mean just any old atomic theory, credit usually goes to either Democritus or his mentor Leucippus. However, if you mean an atomic theory that wasn't totally blowing smoke out their nether regions, was backed up by actual experimental data, and at least resembled the truth in certain ways if you squinted hard enough, I'd say John Dalton is probably your guy.