1 mole of HNO3 gains 4 moles of electrons to form

Oxidation state of 'N' in HNO3 = +5No. of electrons gained = 4∴Ox. state of 'N' in the product = +1So the product must be N2OTotal Ox. state of 'N' in product must be +11/2 mole of N2O is correctIn N2O , Ox. state of 'N' is +1Total Ox. state in 1mole of N2O =2(+1) = +2where as in 1/2 mole of N2O it will be  1/2(+2) = +1