How many electrons with l=2 are there in an atom having atomic number 23 ?

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine how many electrons with azimuthal quantum number \( l = 2 \) are present in an atom with atomic number 23, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Azimuthal Quantum Number**:
The azimuthal quantum number \( l \) indicates the subshell of the electron. For \( l = 2 \), the corresponding subshell is the d subshell.

2. **Identify the Atomic Number**:
The atomic number (Z) of the atom is given as 23. This means the atom has 23 electrons.

3. **Write the Electronic Configuration**:
We need to write the electronic configuration for an atom with 23 electrons. The order of filling the orbitals follows the Aufbau principle:
- 1s can hold 2 electrons
- 2s can hold 2 electrons
- 2p can hold 6 electrons
- 3s can hold 2 electrons
- 3p can hold 6 electrons
- 4s can hold 2 electrons
- 3d can hold 10 electrons

Filling these orbitals according to the number of electrons:
- 1s² (2 electrons)
- 2s² (2 electrons)
- 2p⁶ (6 electrons)
- 3s² (2 electrons)
- 3p⁶ (6 electrons)
- 4s² (2 electrons)
- 3d³ (3 electrons)

Thus, the electronic configuration for atomic number 23 (Vanadium) is:
\[ \text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^3 \]

4. **Count the Electrons in the d Orbital**:
From the electronic configuration, we see that the 3d subshell has 3 electrons.

5. **Conclusion**:
Therefore, the number of electrons with \( l = 2 \) (which corresponds to the d orbital) in an atom with atomic number 23 is **3**.

### Final Answer:
The number of electrons with \( l = 2 \) in an atom with atomic number 23 is **3**.