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

### Step 1: Understand the Concept of Atomic Orbitals
Atomic orbitals are regions in an atom where there is a high probability of finding electrons. When these orbitals from different atoms overlap, they can combine to form new orbitals, known as molecular orbitals.

### Step 2: Apply the Linear Combination of Atomic Orbitals (LCAO) Principle
According to the Linear Combination of Atomic Orbitals (LCAO) principle, when 'n' atomic orbitals combine, they form 'n' molecular orbitals. These molecular orbitals can be either bonding or antibonding.

### Step 3: Determine the Number of Energy Bands
When 'n' valence atomic orbitals of the same element overlap, the number of occupied energy bands formed is equal to the number of atomic orbitals involved in the overlap. Therefore, if 'n' atomic orbitals overlap, they will create 'n' molecular orbitals.

### Step 4: Identify the Occupied Energy Bands
Out of the 'n' molecular orbitals formed, the number of occupied energy bands will depend on the number of electrons available to fill these orbitals. Each molecular orbital can hold a maximum of two electrons (with opposite spins).

### Conclusion
Thus, when 'n' valence atomic orbitals of the same element overlap, the number of occupied energy bands formed is equal to 'n', assuming that all the molecular orbitals formed are filled with electrons.

### Final Answer
The number of occupied energy bands formed is **n**.

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