Step 1: Understanding the Question:
The question asks for the formal charges on three different oxygen atoms within an ozone ($O_3$) molecule, based on its standard Lewis resonance structure. Formal charge is a concept used in Lewis structures to help determine the distribution of electrons among atoms, assuming that electrons in a bond are shared equally between the atoms.
Step 2: Key Formula or Approach:
The Formal Charge (FC) of an atom is calculated using the formula:
\[ FC = V - L - \frac{1}{2}B \]
Where:
$V$ = valence electrons in the free atom (for Oxygen, $V=6$).
$L$ = number of lone pair (non-bonding) electrons.
$B$ = number of bonding electrons (2 electrons per bond).
Step 3: Detailed Explanation:
Oxygen 1 (Central): It is attached to one double bond and one single bond. This equals 3 bonds (6 bonding electrons) and has 1 lone pair (2 electrons).
$FC = 6 - 2 - \frac{1}{2}(6) = 6 - 2 - 3 = +1$.
Oxygen 2 (Double-bonded): It is attached to one double bond (4 bonding electrons) and has 2 lone pairs (4 electrons).
$FC = 6 - 4 - \frac{1}{2}(4) = 6 - 4 - 2 = 0$.
Oxygen 3 (Single-bonded): It is attached to one single bond (2 bonding electrons) and has 3 lone pairs (6 electrons).
$FC = 6 - 6 - \frac{1}{2}(2) = 6 - 6 - 1 = -1$.
The question asks for the charges in the order 2, 1, 3. So the sequence is $0, +1, -1$.
Step 4: Final Answer:
The formal charges on oxygen atoms 2, 1, and 3 are $0, +1, \text{and } -1$, respectively. This matches option (B).