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 a spin quantum number of `+1/2`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number of Copper (Cu)**:
- The atomic number (Z) of copper is 29.

2. **Write the Electronic Configuration of Neutral Copper (Cu)**:
- According to the Aufbau principle, the electronic configuration of copper is:
\[ \text{Cu: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \]
- However, the actual configuration is:
\[ \text{Cu: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^{10} \]
- This is because a fully filled d subshell (3d) provides extra stability.

3. **Determine the Configuration of the Copper Ion (Cu⁺)**:
- The `Cu⁺` ion means that one electron is removed from the neutral copper atom. The electron is removed from the 4s subshell (the outermost shell).
- Therefore, the electronic configuration of `Cu⁺` is:
\[ \text{Cu}^+: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^0 \, 3d^{10} \]

4. **Count the d Electrons**:
- In the `Cu⁺` ion, there are 10 electrons in the 3d subshell.

5. **Determine the Spin Quantum Number**:
- Each electron can have a spin quantum number of either `+1/2` or `-1/2`.
- According to Hund's rule, electrons will fill degenerate orbitals singly before pairing up. In a completely filled d subshell (3d¹⁰), the distribution of spins will be:
- 5 electrons with spin `+1/2`
- 5 electrons with spin `-1/2`

6. **Conclusion**:
- Therefore, the number of d electrons in `Cu⁺` that can have a spin quantum number of `+1/2` is **5**.

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