Calculate Zeff for a valence electron in an oxygen atom
The Correct Answer and Explanation is :
The effective nuclear charge ((Z_{\text{eff}})) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for both the full charge of the nucleus ((Z)) and the shielding effects of other electrons.
For an oxygen atom, the atomic number (Z) is 8, which means it has 8 protons in the nucleus. The electron configuration of oxygen is (1s^2 2s^2 2p^4). The valence electrons are in the 2p orbital, and these are the electrons we’re interested in when calculating (Z_{\text{eff}}).
To calculate (Z_{\text{eff}}), we use the formula:
[
Z_{\text{eff}} = Z – S
]
Where:
- (Z) is the atomic number (number of protons),
- (S) is the shielding constant, which accounts for the shielding of the valence electrons by the inner electrons.
The inner electrons in oxygen are the 1s and 2s electrons. The 1s electrons shield the 2p electrons more effectively than the 2s electrons. The shielding constant is often determined experimentally, but a good estimation for oxygen gives (S \approx 4.9).
So, for oxygen:
[
Z_{\text{eff}} = 8 – 4.9 = 3.1
]
Thus, the effective nuclear charge ((Z_{\text{eff}})) for a valence electron in an oxygen atom is approximately 3.1.
Explanation:
In multi-electron atoms like oxygen, each electron feels the attraction of the positively charged nucleus, but also experiences repulsion from other electrons. The inner-shell electrons (like the 1s and 2s electrons) are closer to the nucleus and shield the outer electrons (like the 2p electrons) from the full effect of the nuclear charge. The valence electrons are farther from the nucleus and experience less attractive force due to the shielding effect of the inner electrons.
The (Z_{\text{eff}}) value reflects this reduced nuclear attraction and is crucial for understanding various properties of the atom, such as ionization energy, electronegativity, and atomic size. Higher (Z_{\text{eff}}) means the valence electrons are more tightly bound to the nucleus.
I will now generate an image to visually represent this concept.
Here is the visual representation of the oxygen atom with its effective nuclear charge (Zeff). The diagram illustrates the protons in the nucleus, the valence electrons in the 2p orbital, and the shielding effect of the inner electrons. It also shows the calculated value of (Z_{\text{eff}} = 3.1). Let me know if you need further details or clarification!
