Number of electron exchanges present in `d^(5) and d^(10)` configuration are

Options

A. `10,0`
B. 20, 10
C. 10, 20
D. 15, 20

Answer

To determine the number of electron exchanges in the `d^(5)` and `d^(10)` configurations, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electron Configuration**:
- The `d` subshell can hold a maximum of 10 electrons, with 5 orbitals available.
- Each orbital can hold 2 electrons (one with spin +1/2 and one with spin -1/2).

2. **Calculating for `d^(5)` Configuration**:
- In the `d^(5)` configuration, there are 5 electrons, all with positive spin (+1/2).
- Therefore, the number of electrons with spin +1/2 = 5.
- The number of electrons with spin -1/2 = 0.
- The formula for calculating the number of exchanges is given by:
\[ \text{Number of exchanges} = \frac{N(N-1)}{2} \]
- Here, \(N\) is the number of electrons with the same spin. For `d^(5)`, we only consider the +1/2 electrons:
\[ \text{Number of exchanges} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = 10 \]

3. **Calculating for `d^(10)` Configuration**:
- In the `d^(10)` configuration, all 5 orbitals are completely filled with 10 electrons (5 with spin +1/2 and 5 with spin -1/2).
- Therefore, the number of electrons with spin +1/2 = 5 and the number of electrons with spin -1/2 = 5.
- We calculate the exchanges for both spins:
- For +1/2:
\[ \text{Number of exchanges} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = 10 \]
- For -1/2:
\[ \text{Number of exchanges} = \frac{5(5-1)}{2} = \frac{5 \times 4}{2} = 10 \]
- Total exchanges for `d^(10)`:
\[ \text{Total exchanges} = 10 + 10 = 20 \]

4. **Final Result**:
- The number of electron exchanges for `d^(5)` is **10**.
- The number of electron exchanges for `d^(10)` is **20**.

### Summary:
- For `d^(5)`: 10 exchanges
- For `d^(10)`: 20 exchanges