Calculate the effective nuclear charge on a valence electron in an aluminum atom

Calculate the effective nuclear charge on a valence electron in an aluminum atom.

Calculate the effective nuclear charge on a valence electron in an oxygen atom.

The Correct Answer and Explanation is :

Calculating Effective Nuclear Charge (Z_eff)

The effective nuclear charge ((Z_{eff})) is the net positive charge experienced by a valence electron in an atom. It accounts for the shielding effects of inner electrons that reduce the full nuclear charge felt by the valence electrons.

The formula for (Z_{eff}) is:

[
Z_{eff} = Z – S
]

Where:

• (Z) is the atomic number (total protons in the nucleus),
• (S) is the shielding constant, which represents the extent to which the inner electrons shield the outer electrons from the nuclear charge.

1. Aluminum (Al) Atom

• Atomic Number (Z): 13 (Aluminum has 13 protons).
• Electron Configuration: [Ne] (3s^2 3p^1). The valence electron is in the 3p orbital.

Shielding (S):

• The inner electrons are in the 1s, 2s, and 2p orbitals (10 electrons).
• The shielding constant (S) can be approximated using Slater’s rules. For a 3p electron, the shielding constant is calculated to be around 10 (full shielding from the inner electrons).

Thus, the effective nuclear charge for aluminum is:

[
Z_{eff} = 13 – 10 = 3
]

So, the effective nuclear charge on a valence electron in aluminum is +3.

2. Oxygen (O) Atom

• Atomic Number (Z): 8 (Oxygen has 8 protons).
• Electron Configuration: [He] (2s^2 2p^4). The valence electron is in the 2p orbital.

Shielding (S):

• The inner electrons are in the 1s orbital (2 electrons).
• The shielding constant (S) for a 2p electron is around 2.

Thus, the effective nuclear charge for oxygen is:

[
Z_{eff} = 8 – 2 = 6
]

So, the effective nuclear charge on a valence electron in oxygen is +6.

Explanation:

In both cases, the effective nuclear charge increases as the atomic number increases, reflecting the greater pull from the nucleus felt by the valence electrons. However, the number of shielding electrons plays a key role in determining how much of the nuclear charge is actually felt by the outer electrons. Aluminum experiences more shielding from its inner electrons than oxygen, resulting in a lower effective nuclear charge on the valence electron in aluminum compared to oxygen.

Now, I’ll generate an image to illustrate this concept.

Here is the diagram illustrating the concept of effective nuclear charge for both aluminum and oxygen atoms. You can see how the shielding by inner electrons affects the effective nuclear charge felt by the valence electron. Let me know if you need any further explanation!