Final answer:
The best Lewis structure for the free radical NO₂ indicates that nitrogen has a formal charge of +1 after accounting for its bonds and unpaired electron.
Step-by-step explanation:
The best Lewis structure for the free radical NO₂ starts with determining the total number of valence electrons, which is 5 (from N) + 6*2 (from each O) + 1 (for the free radical) = 18. We initially draw a skeleton with an N-O single bond for each oxygen: N-O. Each oxygen atom gets six electrons to fulfill the octet rule, while nitrogen gets one of its electrons as an unpaired electron, representing the free radical character of the molecule. When calculating the formal charge on nitrogen, it originally has five valence electrons. In the structure with the free radical, nitrogen has one unpaired electron, participates in one single bond and one double bond, giving it a formal charge of +1.