The quantum number which is equal for all the d-electrons in an atom is

Options

A. l
B. m
C. s
D. n

Answer

To solve the question, "The quantum number which is equal for all the d-electrons in an atom is," we need to analyze the different types of quantum numbers associated with the d-electrons.

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
There are four types of quantum numbers:
- Principal Quantum Number (n)
- Azimuthal Quantum Number (l)
- Magnetic Quantum Number (m_l)
- Spin Quantum Number (m_s)

2. **Principal Quantum Number (n)**:
The principal quantum number (n) indicates the energy level of an electron. For d-electrons, n can vary (e.g., 3 for 3d, 4 for 4d, etc.). Therefore, it is not the same for all d-electrons.

3. **Azimuthal Quantum Number (l)**:
The azimuthal quantum number (l) defines the shape of the orbital. For d-orbitals, l is always equal to 2, regardless of the principal quantum number (n). Thus, this quantum number is constant for all d-electrons.

4. **Magnetic Quantum Number (m_l)**:
The magnetic quantum number (m_l) determines the orientation of the orbital in space. For d-orbitals, m_l can take values of -2, -1, 0, +1, and +2. Hence, this number varies among d-electrons.

5. **Spin Quantum Number (m_s)**:
The spin quantum number (m_s) indicates the spin of the electron, which can be either +1/2 or -1/2. This also varies among d-electrons depending on their individual spins.

6. **Conclusion**:
The only quantum number that is the same for all d-electrons is the **azimuthal quantum number (l)**, which is equal to 2 for all d-electrons.

### Final Answer:
The quantum number which is equal for all the d-electrons in an atom is **2 (Azimuthal Quantum Number, l)**.

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