For the same metal, the stabiliing energies of tetrahedral and octahedral complex are related as

Options

A. `Delta_(t) = Delta_(0)`
B. `Delta_(t)xx4 = Delta_(0)xx6`
C. `Delta_(t)xx9 = Delta_(0)xx4`
D. `Delta_(t)xx6 = Delta_(0)xx4`

Explanation

To find the relationship between the stabilizing energies of tetrahedral and octahedral complexes for the same metal, we can follow these steps:

### Step 1: Understand the Definitions
- **Tetrahedral Complex**: A coordination complex where the central metal atom is surrounded by four ligands.
- **Octahedral Complex**: A coordination complex where the central metal atom is surrounded by six ligands.
- **Stabilizing Energy**: The energy associated with the formation of the complex, often denoted as Δt for tetrahedral and Δo for octahedral complexes.

### Step 2: Compare Stabilizing Energies
It is known that the stabilizing energy of octahedral complexes is generally greater than that of tetrahedral complexes. This can be expressed as:
\[ \Delta o > \Delta t \]

### Step 3: Establish the Relationship
The relationship between the stabilizing energies of tetrahedral and octahedral complexes can be derived from crystal field theory. It is established that:
\[ \Delta t = \frac{4}{9} \Delta o \]
This means that the stabilizing energy of a tetrahedral complex is \( \frac{4}{9} \) of that of an octahedral complex.

### Step 4: Rearranging the Equation
To express this relationship in a different form, we can rearrange the equation:
\[ \Delta t \times 9 = 4 \times \Delta o \]

### Step 5: Conclusion
Thus, we conclude that the relationship between the stabilizing energies of tetrahedral and octahedral complexes for the same metal is:
\[ \Delta t \times 9 = 4 \times \Delta o \]

### Final Answer
The correct relationship is given by the equation:
\[ \Delta t \times 9 = 4 \times \Delta o \]