Here it says draw the Lewis dot structure for the radical of nitrogen dioxide. So nitrogen dioxide is a very common example used to talk about radicals. If we look at the total number of valence, we have 5 from nitrogen since it's in Group 5, a 6 * 2 oxygens in Group 6A, so it has six, and there's two of them. So this has a total of 17 total valence electrons. It's an odd number of valence electrons, so that's a strong indication we're dealing with a radical.
We place nitrogen in the center. It forms single bonds to the oxygens initially. Make sure that your surrounding elements follow the octet rule. Right now we have a total of 16 electrons being depicted, leaving us with one electron left. The issue now is that nitrogen is not fulfilling the octet rule. It has 235 electrons around it. So remember, when an element is not fulfilling the octet rule, what we can do is make double or triple bonds.
Here we can't make a triple bond because then that would be too many electrons around nitrogen. It can only go up to 8 for the octet rule. So we're just going to use one of the lone pairs on oxygen, either one to make a double bond and in that way nitrogen has 7 electrons around it and that's the best that we can do. This year depicts what the nitrogen dioxide molecule would look like. It is a radical because we have that one lone electron on top of nitrogen.