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Argons outer shell is full it doesnt have any gaps either loose or gain electrons.so its reactivity is less and it is last group which means all the elements doesnt take part in any chemical reaction. hence its valency is zero.
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According to formula 2n², M shell should have 18 electrons;but this only theoretical. Talking about Argon,have 8 electrons in its outer most shell making its octave complete ,has valency=0.
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