`3d^4` configuration may have the exchange of s

Options

A. four electrons
B. three electrons
C. sixteen electrons
D. six electrons

Answer

To solve the question regarding the `3d^4` electron configuration and the maximum number of exchanges of electrons, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Electron Configuration**:
The configuration `3d^4` indicates that there are 4 electrons in the 3d subshell. The d subshell has 5 orbitals.

2. **Determine the Number of Orbitals**:
The d subshell has 5 orbitals (dxy, dyz, dzx, dx2-y2, dz2). Each orbital can hold a maximum of 2 electrons, giving a total capacity of 10 electrons.

3. **Understanding Electron Exchange**:
Electron exchange refers to the swapping of positions between electrons in the same subshell. We need to calculate how many unique exchanges can occur among the 4 electrons in the 3d subshell.

4. **Counting Possible Exchanges**:
- For the **1st electron** (let's label it as E1), it can exchange with 3 other electrons (E2, E3, E4). So, there are 3 possible exchanges.
- For the **2nd electron** (E2), it can exchange with 2 remaining electrons (E3, E4) since E1 has already been counted. Thus, there are 2 possible exchanges.
- For the **3rd electron** (E3), it can only exchange with the last electron (E4) which has not been counted yet. So, there is 1 possible exchange.
- The **4th electron** (E4) cannot exchange with any other since all possible exchanges have been counted.

5. **Total Exchanges Calculation**:
To find the total number of unique exchanges, we add the possible exchanges:
\[ 3 \text{ (for E1)} + 2 \text{ (for E2)} + 1 \text{ (for E3)} = 6 \]

6. **Conclusion**:
The maximum number of exchanges that can occur among the 4 electrons in the `3d^4` configuration is 6.

### Final Answer:
The maximum number of exchanges for the `3d^4` configuration is **6**.

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