Step 1: Basic Principle
The number of unpaired electrons can be determined from the molecular orbital (MO) electronic configuration.
Step 2: Solution Procedure:
(A) NO: 15 electrons. MO configuration: \(KK (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2px})^2 (\pi_{2py})^2 (\sigma_{2pz})^2 (\pi_{2px}^*)^1\). One unpaired electron.
(B) CO: 14 electrons. MO configuration: \(KK (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\pi_{2px})^2 (\pi_{2py})^2 (\sigma_{2pz})^2\). No unpaired electrons.
(C) CN\(^-\): 14 electrons (C has 6, N has 7, plus 1 extra = 14). Same as CO, no unpaired electrons.
(D) O\(_2\): 16 electrons. MO configuration: \(KK (\sigma_{2s})^2 (\sigma_{2s}^*)^2 (\sigma_{2pz})^2 (\pi_{2px})^2 (\pi_{2py})^2 (\pi_{2px}^*)^1 (\pi_{2py}^*)^1\). Two unpaired electrons.
Step 3: Required Answer:
NO has one unpaired electron, option (A).