The structure and hybridization of `NO_(2) ^(+)` is

Options

A. Linear, sp
B. Trigonal, `sp^(2)`
C. Octahedral, `sp^(3)d`
D. Tetrahedral,`sp^(3)`

Answer

To determine the structure and hybridization of the ion \( NO_2^+ \), we can follow these steps:

### Step 1: Identify the central atom and its valence electrons
The central atom in \( NO_2^+ \) is nitrogen (N). Nitrogen is in group 15 of the periodic table and has 5 valence electrons.

### Step 2: Count the number of monovalent atoms attached to the central atom
In \( NO_2^+ \), there are two oxygen (O) atoms attached to the nitrogen. Oxygen is not a monovalent atom, so we do not count it as a monovalent atom.

### Step 3: Determine the charge of the ion
The ion \( NO_2^+ \) has a positive charge of +1. Since this is a cation, we will subtract this charge in our calculations.

### Step 4: Calculate the steric number
Using the formula for steric number:
\[ \text{Steric Number} = \frac{1}{2} \left( V + M + \text{Charge} \right) \]
Where:
- \( V \) = number of valence electrons of the central atom (N = 5)
- \( M \) = number of monovalent atoms attached (0 in this case)
- Charge = +1 (since it's a cation)

Substituting the values:
\[ \text{Steric Number} = \frac{1}{2} \left( 5 + 0 - 1 \right) = \frac{1}{2} \left( 4 \right) = 2 \]

### Step 5: Determine the hybridization
A steric number of 2 corresponds to \( sp \) hybridization.

### Step 6: Determine the molecular geometry
For \( sp \) hybridization, the molecular geometry is linear.

### Final Answer
The structure of \( NO_2^+ \) is linear, and the hybridization is \( sp \).

---