When two `AO` s combine energy of bonding `MO` is lowered by x while of antibonding `MO` is raised by y Then .

Options

A. `x =y`
B. `x lt y`
C. `x gt y`
D. Can be any of these

Answer

To solve the problem, we need to analyze the changes in energy when two atomic orbitals combine to form molecular orbitals.

### Step-by-Step Solution:

1. **Understanding Molecular Orbital Theory**:
- When two atomic orbitals (AOs) combine, they form two types of molecular orbitals (MOs): bonding and antibonding. The bonding molecular orbital (MO) is lower in energy than the original atomic orbitals, while the antibonding MO is higher in energy.

2. **Energy Changes**:
- According to the problem, the energy of the bonding MO is lowered by a value \(X\).
- Simultaneously, the energy of the antibonding MO is raised by a value \(Y\).

3. **Conservation of Energy Principle**:
- The principle of conservation of energy states that the total energy of a closed system remains constant. Therefore, any decrease in energy in one part of the system must be balanced by an equal increase in energy in another part.

4. **Setting Up the Equation**:
- Since the bonding MO's energy decreases by \(X\) and the antibonding MO's energy increases by \(Y\), we can express this relationship as:
\[ \text{Total Energy Change} = \text{Change in Bonding MO} + \text{Change in Antibonding MO} \]
- This can be written as:
\[ -X + Y = 0 \]
- Rearranging gives us:
\[ Y = X \]

5. **Conclusion**:
- From the above analysis, we conclude that the decrease in energy of the bonding MO (\(X\)) is equal to the increase in energy of the antibonding MO (\(Y\)). Therefore, the correct answer is:
\[ X = Y \]

### Final Answer:
- \(X\) is equal to \(Y\).