Step 1: Understanding the Concept:
Resonance is a method of describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis structure.
Step 2: Key Formula or Approach:
Apply the rules of resonance: atomic nuclei positions must remain fixed while only electrons (pi bonds and lone pairs) move, creating a hybrid structure.
Step 3: Detailed Explanation:
(a) Equivalent bonds: In the resonance hybrid of the carbonate ion, the double bond character is distributed equally among all three $C-O$ bonds. They all have a bond order of $1.33$. (Correct)
(b) Three structures: The Lewis structure has one double bond and two single bonds. The double bond can be placed on any one of the three oxygen atoms, resulting in three equivalent canonical forms. (Correct)
(c) Position of atoms: In resonance, only the arrangement of electrons changes. The spatial positions of the nuclei (atoms) must remain absolutely constant. (Incorrect)
(d) Formal charge: In the resonance hybrid, the net charge is $-2$. However, the calculated formal charge on the central carbon atom is exactly 0, while each oxygen carries an average formal charge of $-2/3$. (Incorrect)
Step 4: Final Answer:
Statements (a) and (b) are correct.