How many electrons with `l=2` are there in an atom having atomic number 54 ?

Options

A. 3
B. 10
C. 14
D. 20

Answer

To determine how many electrons with \( l = 2 \) are present in an atom with an atomic number of 54, we can follow these steps:

### Step 1: Identify the Element
The atomic number 54 corresponds to the element Xenon (Xe).

### Step 2: Write the Electron Configuration
Next, we need to write the electron configuration for Xenon. The electron configuration is as follows:
1. \( 1s^2 \)
2. \( 2s^2 \)
3. \( 2p^6 \)
4. \( 3s^2 \)
5. \( 3p^6 \)
6. \( 4s^2 \)
7. \( 3d^{10} \)
8. \( 4p^6 \)

Combining these, the complete electron configuration for Xenon is:
\[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \]

### Step 3: Identify the Subshells Corresponding to \( l = 2 \)
The azimuthal quantum number \( l \) indicates the subshell:
- \( l = 0 \) corresponds to the s subshell
- \( l = 1 \) corresponds to the p subshell
- \( l = 2 \) corresponds to the d subshell

### Step 4: Count the Electrons in the d Subshells
For \( l = 2 \) (d subshell), we need to find the total number of electrons in the d orbitals:
- The electron configuration shows \( 3d^{10} \) and \( 4d^{10} \).

### Step 5: Calculate the Total Number of Electrons in the d Orbitals
From the configuration:
- \( 3d^{10} \) contributes 10 electrons.
- \( 4d^{10} \) also contributes 10 electrons.

Thus, the total number of electrons in the d orbitals is:
\[ 10 + 10 = 20 \]

### Conclusion
Therefore, the total number of electrons with \( l = 2 \) in an atom with atomic number 54 is **20**.