How many electrons with l=2 are there in an atom having atomic number 28 ?

Options

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

Answer

To determine how many electrons with azimuthal quantum number \( l = 2 \) are present in an atom with atomic number 28, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Atomic Number**: The atomic number given is 28. This indicates that the atom has 28 electrons.

2. **Write the Electronic Configuration**: We need to write the electronic configuration of the element with atomic number 28. The element with atomic number 28 is Nickel (Ni). The electronic configuration can be derived as follows:
- The first 18 electrons fill up to Argon (Ar): \( 1s^2 2s^2 2p^6 3s^2 3p^6 \) (which accounts for 18 electrons).
- The next electrons fill the 4s and 3d orbitals:
- 4s: \( 4s^2 \) (2 electrons)
- 3d: \( 3d^8 \) (8 electrons)
- Therefore, the complete electronic configuration for Nickel is:
\[ \text{Ni: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^8 \]

3. **Identify the Electrons in the d-Orbital**: The azimuthal quantum number \( l = 2 \) corresponds to the d-orbitals. From the electronic configuration, we see that the 3d subshell contains 8 electrons.

4. **Conclusion**: Thus, the number of electrons with \( l = 2 \) (in the d-orbital) in an atom with atomic number 28 is 8.

### Final Answer:
The number of electrons with \( l = 2 \) in an atom with atomic number 28 is **8**.

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