In `Cu^(oplus)` ion, the number of electrons with the magnetic quantum numbers m = 0 and 1 are, respectively

Options

A. 12,6
B. 13,6
C. 12,4
D. 12,8

Explanation

To determine the number of electrons with magnetic quantum numbers \( m = 0 \) and \( m = 1 \) in the \( \text{Cu}^+ \) ion, we will follow these steps:

### Step 1: Determine the Electron Configuration of Copper
Copper (Cu) has an atomic number of 29, which means it has 29 electrons in its neutral state. The electron configuration of neutral copper is:
\[ \text{Cu}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^{10} \]
However, due to the stability of fully filled d-orbitals, the configuration is often written as:
\[ \text{Cu}: [\text{Ar}] \, 3d^{10} \, 4s^1 \]

### Step 2: Adjust the Configuration for the \( \text{Cu}^+ \) Ion
When copper loses one electron to form the \( \text{Cu}^+ \) ion, the electron is removed from the 4s orbital, resulting in:
\[ \text{Cu}^+: [\text{Ar}] \, 3d^{10} \]

### Step 3: Identify the Orbitals and Their Magnetic Quantum Numbers
In the \( 3d \) subshell, there are five orbitals corresponding to the magnetic quantum numbers:
- \( m = -2 \)
- \( m = -1 \)
- \( m = 0 \)
- \( m = +1 \)
- \( m = +2 \)

### Step 4: Count the Electrons in Each Magnetic Quantum State
Since the \( 3d \) subshell is fully filled with 10 electrons, the distribution of electrons in the \( 3d \) orbitals is as follows:
- Each orbital can hold 2 electrons (with opposite spins).
- Therefore, the distribution of electrons in the \( 3d \) orbitals is:
- \( m = -2 \): 2 electrons
- \( m = -1 \): 2 electrons
- \( m = 0 \): 2 electrons
- \( m = +1 \): 2 electrons
- \( m = +2 \): 2 electrons

### Step 5: Summarize the Results
- The number of electrons with \( m = 0 \) is **2**.
- The number of electrons with \( m = +1 \) is **2**.

### Final Answer
The number of electrons with magnetic quantum numbers \( m = 0 \) and \( m = 1 \) in the \( \text{Cu}^+ \) ion are **2** and **2**, respectively.

---