How many d electrons in `Cu^(+)` ion can have the value of spin quantum number to be `1//2`

Options

A. 3
B. 7
C. 5
D. 9

Answer

To determine how many d electrons in the `Cu^(+)` ion can have the value of the spin quantum number equal to `1/2`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Electronic Configuration of Copper (Cu)**:
- The atomic number of copper (Cu) is 29. The electronic configuration of neutral copper is:
\[ \text{Cu: } [\text{Ar}] \, 4s^1 \, 3d^{10} \]

2. **Determine the Electronic Configuration of `Cu^(+)`**:
- The `Cu^(+)` ion is formed by removing one electron from the neutral copper atom. The electron is removed from the 4s orbital first:
\[ \text{Cu}^{+}: [\text{Ar}] \, 4s^0 \, 3d^{10} \]

3. **Identify the d Electrons**:
- In the `Cu^(+)` ion, we have 10 electrons in the 3d subshell:
\[ 3d^{10} \]

4. **Determine the Spin Quantum Number**:
- Each d orbital can hold a maximum of 2 electrons, and there are 5 d orbitals. The 10 electrons in the 3d subshell will fill the orbitals according to Hund's rule, which states that electrons will fill degenerate orbitals singly first before pairing up.
- The filling of the d orbitals will be as follows:
- 1 electron in each of the 5 orbitals (with spin +1/2) before pairing occurs.
- After the first 5 electrons fill the orbitals, the next 5 electrons will pair with the first 5, resulting in:
- 5 electrons with spin +1/2 (clockwise rotation)
- 5 electrons with spin -1/2 (counterclockwise rotation)

5. **Count the Electrons with Spin Quantum Number +1/2**:
- From the above distribution, we can see that there are **5 electrons** in the 3d subshell of `Cu^(+)` that have a spin quantum number of +1/2.

### Final Answer:
The number of d electrons in `Cu^(+)` that can have the value of the spin quantum number equal to +1/2 is **5**.