How many electrons with l=2 are there in an atom having atomic number 26 ?

Options

A. 2
B. 4
C. 6
D. 8

Explanation

To determine how many electrons with azimuthal quantum number \( l = 2 \) are present in an atom with atomic number 26, we can follow these steps:

### Step 1: Understand the Quantum Numbers
The azimuthal quantum number \( l \) indicates the shape of the orbital:
- \( l = 0 \): s orbital
- \( l = 1 \): p orbital
- \( l = 2 \): d orbital
- \( l = 3 \): f orbital

Since we are interested in \( l = 2 \), we are looking at the d orbitals.

### Step 2: Determine the Electronic Configuration
The atomic number 26 corresponds to the element iron (Fe). To find the electronic configuration, we fill the orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

1. The first 18 electrons fill the orbitals up to argon (Ar):
- \( 1s^2 \)
- \( 2s^2 \)
- \( 2p^6 \)
- \( 3s^2 \)
- \( 3p^6 \)

2. After argon, we have 8 more electrons to place:
- The next orbitals to fill are \( 4s \) and \( 3d \).
- We fill \( 4s^2 \) first (2 electrons).
- Then we fill \( 3d \) with the remaining 6 electrons.

Thus, the electronic configuration of iron (atomic number 26) is:
\[ \text{Ar} \, 4s^2 \, 3d^6 \]

### Step 3: Identify the Electrons in the d Orbital
From the electronic configuration \( 4s^2 \, 3d^6 \), we see that there are 6 electrons in the \( 3d \) orbital.

### Conclusion
The number of electrons with \( l = 2 \) (which corresponds to the d orbitals) in an atom with atomic number 26 is **6**.