In which of the following species, S-atom assumes `sp^3` hybrid state ?
(I) `(SO_3)` ,
(II) `(SO_2)` ,
(III) `(H_2 S)` ,
(IV) `(S_8)`.

Options

A. `I, II`
B. `II, III`
C. `II, IV`
D. `III,IV`

Explanation

To determine in which of the following species the sulfur atom assumes an `sp^3` hybrid state, we need to analyze each species one by one using the concept of hybridization and steric number.

### Step-by-Step Solution:

1. **Identify the Species**: We have four species to analyze:
- (I) SO₃
- (II) SO₂
- (III) H₂S
- (IV) S₈

2. **Calculate the Steric Number**: The steric number can be calculated using the formula:
\[ \text{Steric Number} = \frac{1}{2} \left( V + M + C - A \right) \]
where:
- \( V \) = number of valence electrons of the central atom (sulfur in this case)
- \( M \) = number of monovalent atoms bonded to the central atom
- \( C \) = charge on the molecule (if any)
- \( A \) = charge on the cation (if any)

3. **Analyze Each Species**:
- **(I) SO₃**:
- Sulfur (S) has 6 valence electrons.
- It is bonded to 3 oxygen atoms (considered divalent).
- Using the formula:
\[ \text{Steric Number} = \frac{1}{2} (6 + 0) = 3 \]
- Hybridization: `sp²` (not `sp³`).

- **(II) SO₂**:
- Sulfur (S) has 6 valence electrons.
- It is bonded to 2 oxygen atoms.
- Using the formula:
\[ \text{Steric Number} = \frac{1}{2} (6 + 0) = 3 \]
- Hybridization: `sp²` (not `sp³`).

- **(III) H₂S**:
- Sulfur (S) has 6 valence electrons.
- It is bonded to 2 hydrogen atoms (monovalent).
- Using the formula:
\[ \text{Steric Number} = \frac{1}{2} (6 + 2) = 4 \]
- Hybridization: `sp³` (this is correct).

- **(IV) S₈**:
- Each sulfur atom has 6 valence electrons.
- In S₈, each sulfur forms 2 bonds with neighboring sulfur atoms.
- Using the formula for one sulfur atom:
\[ \text{Steric Number} = \frac{1}{2} (6 + 2) = 4 \]
- Hybridization: `sp³` (this is also correct).

4. **Conclusion**: The sulfur atom assumes `sp³` hybrid state in:
- (III) H₂S
- (IV) S₈

### Final Answer:
The species in which the sulfur atom assumes `sp³` hybrid state are **(III) H₂S and (IV) S₈**.