Find the total number of possible exchanges for `d^4` configuration in an element.

Answer

To find the total number of possible exchanges for a \(d^4\) configuration in an element, we can follow these steps:

### Step 1: Understand the Configuration
The \(d^4\) configuration means there are 4 electrons in the d-orbitals. The d-orbitals can hold a maximum of 10 electrons, but in this case, we are only concerned with the arrangement of 4 electrons.

### Step 2: Identify the Exchanges
An exchange occurs when two electrons swap their positions. For \(d^4\), we have 4 electrons that can potentially exchange positions with each other.

### Step 3: Use the Exchange Formula
The total number of possible exchanges can be calculated using the formula:
\[ \text{Total Exchanges} = \frac{N(N-1)}{2} \]
where \(N\) is the number of electrons.

### Step 4: Substitute the Values
For \(d^4\), \(N = 4\):
\[ \text{Total Exchanges} = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6 \]

### Step 5: Conclusion
Thus, the total number of possible exchanges for a \(d^4\) configuration is **6**.

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