When 'n' valence atomic orbitals of the same elements overlap, then the number of occupied energy bands formed are

Options

A. n
B. n/2
C. 2n
D. n/4

Answer

To determine the number of occupied energy bands formed when 'n' valence atomic orbitals of the same element overlap, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Atomic Orbitals**:
- Valence atomic orbitals are the outermost orbitals of an atom that can participate in bonding. When these orbitals overlap, they can form molecular orbitals.

2. **Linear Combination of Atomic Orbitals (LCAO)**:
- The principle of LCAO states that when 'n' atomic orbitals combine, they form 'n' molecular orbitals. These molecular orbitals can be classified into bonding and anti-bonding orbitals.

3. **Distribution of Molecular Orbitals**:
- Out of the 'n' molecular orbitals formed, half will be bonding orbitals and half will be anti-bonding orbitals. This is because each atomic orbital can contribute to one bonding and one anti-bonding molecular orbital.

4. **Calculating the Number of Occupied Energy Bands**:
- Since bonding orbitals are lower in energy and are filled first, the number of occupied energy bands will be equal to the number of bonding orbitals formed.
- Therefore, if 'n' atomic orbitals overlap, the number of occupied energy bands formed will be \( \frac{n}{2} \).

5. **Conclusion**:
- The final answer to the question is that the number of occupied energy bands formed is \( \frac{n}{2} \).

### Final Answer:
The number of occupied energy bands formed when 'n' valence atomic orbitals of the same element overlap is \( \frac{n}{2} \).