Which of the following attain the linear structure ?

Options

A. `BeCl_(2)`
B. `NCO^(+)`
C. `NO_(2)`
D. `CS_(2)`

Explanation

To determine which of the given compounds attain a linear structure, we will analyze each compound one by one using the concept of steric number and hybridization.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds given are BeCl2, NCO+, NO2, and CS2.

2. **Calculate the Steric Number for BeCl2**:
- Beryllium (Be) has 2 valence electrons.
- It forms 2 single bonds with chlorine (Cl).
- There are no charges (cation or anion).
- Using the formula:
\[ \text{Steric Number} = \frac{(V + M - \text{charge of cation} + \text{charge of anion})}{2} \]
\[ = \frac{(2 + 2 - 0 + 0)}{2} = \frac{4}{2} = 2 \]
- For a steric number of 2, the hybridization is sp, which corresponds to a linear structure.

3. **Calculate the Steric Number for NCO+**:
- Nitrogen (N) has 5 valence electrons.
- The carbon (C) has 4 valence electrons, and oxygen (O) has 6 valence electrons.
- In NCO+, the total valence electrons are 5 (N) + 4 (C) + 6 (O) - 1 (due to positive charge) = 14.
- The central atom (C) forms 2 bonds (N and O).
- Using the formula:
\[ \text{Steric Number} = \frac{(5 + 2 - 1 + 0)}{2} = \frac{6}{2} = 3 \]
- For a steric number of 3, the hybridization is sp2, which does not correspond to a linear structure (it is bent).

4. **Calculate the Steric Number for NO2**:
- Nitrogen has 5 valence electrons.
- Oxygen has 6 valence electrons, and there are 2 O atoms.
- Total valence electrons = 5 + 2(6) = 17.
- The central atom (N) forms 2 bonds with O.
- Using the formula:
\[ \text{Steric Number} = \frac{(5 + 2 - 0 + 0)}{2} = \frac{7}{2} = 3.5 \]
- This indicates a bent structure (not linear).

5. **Calculate the Steric Number for CS2**:
- Carbon (C) has 4 valence electrons.
- Sulfur (S) has 6 valence electrons, and there are 2 S atoms.
- Total valence electrons = 4 + 2(6) = 16.
- The central atom (C) forms 2 double bonds with S.
- Using the formula:
\[ \text{Steric Number} = \frac{(4 + 4 - 0 + 0)}{2} = \frac{8}{2} = 4 \]
- For a steric number of 4, the hybridization is sp3, but since it forms 2 double bonds, it is linear with a bond angle of 180 degrees.

6. **Conclusion**: The compounds that attain a linear structure are BeCl2 and CS2.

### Final Answer:
The compounds that attain a linear structure are **BeCl2** and **CS2**.