if the valency of nitrogen is 3 then how is the formula of nitrogen oxide NO2 and not N2O3??

Nitrogen has 5 valence electrons and hence shows the valency of 3 and also 5. In case of N2O3 its valency has been satisfied so it forms respective oxide but in case of NO2 its valency is not satisfied and hence it exists as dimer i.e. N2O4

From the structure the satisfied valencies of Nitrogen can be seen, which are found in its oxides.  

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formula of nitrogen oxide is (NO)

(NO2) is nitrogen dioxide.

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