In the solid state, `N_(2)O_(5)` exists as `[NO_(2)]^(+)[NO_(3)]^(-)` . The hybridizations around the N atoms in `NO_(2)^(+)` and `NO_(3)^(-)` are, respectively :

Options

A. `sp and sp^(2)`
B. `sp and sp^(3)`
C. `sp^(2)` and `sp^(3)`
D. sp and sp

Explanation

To determine the hybridization around the nitrogen atoms in \( NO_2^+ \) and \( NO_3^- \), we will follow these steps:

### Step 1: Identify the central atom and its valence electrons
The central atom in both \( NO_2^+ \) and \( NO_3^- \) is nitrogen (N). Nitrogen has 5 valence electrons.

### Step 2: Determine the number of surrounding atoms
- In \( NO_2^+ \), there are 2 oxygen atoms surrounding the nitrogen.
- In \( NO_3^- \), there are 3 oxygen atoms surrounding the nitrogen.

### Step 3: Calculate the value of \( x \) for \( NO_2^+ \)
Using the formula:
\[ x = \frac{1}{2} \left( \text{Number of valence electrons on central atom} + \text{Number of monovalent atoms} - \text{Charge on cation} + \text{Charge on anion} \right) \]
For \( NO_2^+ \):
- Valence electrons on nitrogen = 5
- Number of monovalent atoms (Oxygen is bivalent, so it counts as 0) = 0
- Charge on cation = +1
- Charge on anion = 0

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

### Step 4: Determine the hybridization for \( NO_2^+ \)
Since \( x = 2 \), the hybridization is \( sp \).

### Step 5: Calculate the value of \( x \) for \( NO_3^- \)
For \( NO_3^- \):
- Valence electrons on nitrogen = 5
- Number of monovalent atoms = 0
- Charge on cation = 0
- Charge on anion = -1

Substituting the values:
\[ x = \frac{1}{2} \left( 5 + 0 - 0 - 1 \right) = \frac{1}{2} \times 6 = 3 \]

### Step 6: Determine the hybridization for \( NO_3^- \)
Since \( x = 3 \), the hybridization is \( sp^2 \).

### Conclusion
The hybridizations around the nitrogen atoms in \( NO_2^+ \) and \( NO_3^- \) are, respectively:
- \( NO_2^+ \): \( sp \)
- \( NO_3^- \): \( sp^2 \)

### Final Answer
The hybridizations around the nitrogen atoms in \( NO_2^+ \) and \( NO_3^- \) are \( sp \) and \( sp^2 \), respectively.

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