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

Explanation

To solve the problem of calculating 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 Atomic Number and Electronic Configuration
- The atomic number of copper (Cu) is 29.
- The electronic configuration of copper is written as:
\[ \text{Cu: } [\text{Ar}] \, 4s^2 \, 3d^9 \]
Here, \([\text{Ar}]\) represents the electron configuration of argon, which accounts for 18 electrons.

### Step 2: Focus on the 3d Orbital
- We need to consider only the 3d orbitals for calculating the exchange pairs.
- The 3d subshell can hold a maximum of 10 electrons, but in the case of copper, it has 9 electrons.

### Step 3: Fill the 3d Orbital According to Hund's Rule
- According to Hund's rule, we first fill each of the five d orbitals singly before pairing up electrons.
- We distribute the 9 electrons in the 3d orbitals as follows:
- Place 1 electron in each of the 5 orbitals: \( \uparrow \, \uparrow \, \uparrow \, \uparrow \, \uparrow \) (5 electrons)
- Then, we pair the remaining 4 electrons: \( \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \, \uparrow \) (4 paired electrons)

### Step 4: Identify the Number of Electrons with the Same Spin
- In the configuration:
- There are 5 electrons with the same spin (unpaired).
- There are 4 electrons that are paired (but they can also be considered as having the same spin).

### Step 5: Calculate the Number of Exchange Pairs
- The number of exchange pairs can be calculated using the combination formula:
\[ \text{Number of exchange pairs} = \binom{n}{2} \]
where \( n \) is the number of electrons with the same spin.

- For the 5 unpaired electrons:
\[ \text{Exchange pairs from 5 electrons} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10 \]

- For the 4 paired electrons:
\[ \text{Exchange pairs from 4 electrons} = \binom{4}{2} = \frac{4 \times 3}{2 \times 1} = 6 \]

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

Thus, the total number of exchange pairs of electrons present in the configuration of copper according to the Aufbau principle is **16**.