To determine the correct set of quantum numbers for 4d-electrons, we need to understand the four quantum numbers involved:
1. **Principal Quantum Number (n)**: This indicates the main energy level of the electron. For 4d electrons, the principal quantum number is **n = 4**.
2. **Azimuthal Quantum Number (l)**: This quantum number defines the shape of the orbital. For d-orbitals, the azimuthal quantum number is **l = 2**.
3. **Magnetic Quantum Number (m)**: This quantum number specifies the orientation of the orbital in space. For d-orbitals (where l = 2), the possible values of m are **-2, -1, 0, +1, +2**.
4. **Spin Quantum Number (s)**: This quantum number indicates the spin of the electron. The possible values for the spin quantum number are **+1/2 or -1/2**.
Now, let's summarize the quantum numbers for 4d-electrons:
- **n = 4**
- **l = 2**
- **m = -2, -1, 0, +1, +2** (we can choose any of these values)
- **s = +1/2 or -1/2** (we can choose either of these values)
### Step-by-step Solution:
1. **Identify the Principal Quantum Number (n)**:
- For 4d electrons, **n = 4**.
2. **Identify the Azimuthal Quantum Number (l)**:
- For d-orbitals, **l = 2**.
3. **Determine the Magnetic Quantum Number (m)**:
- The possible values for m when l = 2 are **-2, -1, 0, +1, +2**. We can choose any of these.
4. **Determine the Spin Quantum Number (s)**:
- The possible values for the spin quantum number are **+1/2 or -1/2**. We can choose either of these.
5. **Evaluate the Options**:
- We check the options given in the question. The correct set of quantum numbers must have:
- n = 4
- l = 2
- m = one of the values from -2 to +2
- s = either +1/2 or -1/2
6. **Select the Correct Option**:
- After evaluating the options, we find that the correct set of quantum numbers for 4d electrons is **n = 4, l = 2, m = +1, s = -1/2** (for example).
### Final Answer:
The correct set of quantum numbers for 4d-electrons is:
- **n = 4, l = 2, m = +1, s = -1/2**.
