Dielectric‐barrier discharges (DBDs) in Ar–N2 mixtures, with N2 fractions in 0.1–1% range, would be attractive alternatives to DBDs in pure N2 if energy‐transfer reactions between Ar(1s) atoms and N2 molecules were an efficient source of N atoms. Attempts to functionalize polyolefins in flowing postdischarges fed by such DBDs, as well as the search for the First Positive System in the emission spectrum, however, failed. Evidently, the energy‐transfer reactions do not produce N atoms. For Ar(1s3) and Ar(1s5) metastable states, this fact has already been reported in the literature. For Ar(1s2) and Ar(1s4) resonant states, a quantitative argument is derived in this paper: energy transfer from Ar(1s) atoms to N2 molecules is not an efficient source of N atoms. Dielectric‐barrier discharges (DBDs) in Ar–N2 mixtures, with molar N2 fractions below 1%, would be attractive alternatives to DBDs in pure N2 if energy‐transfer reactions between Ar(1s) atoms and N2 molecules were an efficient source of N atoms. The failure of attempts to functionalize polyolefins in flowing postdischarges fed by such DBDs, however, showed that this energy transfer does not produce significant amounts of N atoms. For Ar(1s3) and Ar(1s5) metastable states, this had already been reported in literature. As shown here, the sum of rate coefficients for N2 dissociation by Ar(1s2) and Ar(1s4) resonant states is less than 2 × 10–13 cm3/s, nearly two orders of magnitude below the total quenching rates.