Calculate the number of exchange pairs of electrons present in configuration of Cu according to Aufbau principle. Considering 3d orbitals.

Explanation

To calculate the number of exchange pairs of electrons in the electronic configuration of copper (Cu) according to the Aufbau principle, we will follow these steps:

### Step 1: Determine the Electronic Configuration of Copper
Copper has an atomic number of 29. According to the Aufbau principle, the electronic configuration of copper is:
- \( \text{Cu: } [\text{Ar}] 4s^2 3d^9 \)

### Step 2: Identify the Electrons in the 3d Orbital
In the configuration \( 3d^9 \), there are 9 electrons in the 3d subshell.

### Step 3: Draw the Orbital Diagram for 3d Electrons
The 3d subshell has 5 orbitals. According to Hund's rule, we fill each orbital singly before pairing:
- The first 5 electrons will occupy each of the 5 d orbitals (each with the same spin).
- The remaining 4 electrons will then pair up in the orbitals.

The distribution of electrons in the 3d orbitals will look like this:
- \( \uparrow \) \( \uparrow \) \( \uparrow \) \( \uparrow \) \( \uparrow \) (5 electrons in separate orbitals)
- Then, the next 4 electrons will pair up:
- \( \uparrow\downarrow \) \( \uparrow\downarrow \) \( \uparrow\downarrow \) \( \uparrow\downarrow \) \( \uparrow \)

### Step 4: Count the Exchange Pairs of Electrons
Exchange pairs can be formed from electrons with the same spin. In our case:
- There are 5 electrons with the same spin (unpaired).
- There are 4 paired electrons (with opposite spins).

#### Calculation of Exchange Pairs:
1. **For the 5 unpaired electrons**:
The number of ways to choose 2 electrons from 5 is given by the combination formula \( nC2 \):
\[ 5C2 = \frac{5 \times (5 - 1)}{2} = \frac{5 \times 4}{2} = 10 \]

2. **For the 4 paired electrons**:
The number of ways to choose 2 electrons from 4 is:
\[ 4C2 = \frac{4 \times (4 - 1)}{2} = \frac{4 \times 3}{2} = 6 \]

### Step 5: Total Number of Exchange Pairs
Now, we add the exchange pairs from both groups:
\[ \text{Total exchange pairs} = 10 + 6 = 16 \]

### Final Answer
Thus, the number of exchange pairs of electrons in the 3d configuration of copper is **16**.

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