Question

Effective nuclear charge, Zeff, is defined as:

Zeff=Z−S
where Z is true nuclear charge and S is the amount of shielding.
In 1930, John C. Slater devised the following set of empirical rules to estimate S for a designated ns or np electron:
1. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on.
2. Electrons in groups to the right of the (ns, np) group contribute nothing to the shielding constant for the designated electron.
3. All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each.
4. All electrons in the n−1 shell shield to the extent of 0.85 each.
5. All electrons in the n−2 shell, or lower, shield completely—their contributions to the shielding constant are 1.00 each.
When the designated electron is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following: Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant. These rules are a simplified generalization based on the average behavior of different types of electrons.
Part A) Calculate Zeff for a valence electron in an oxygen atom.

Answer 1

The effective nuclear charge for a valence electron in oxygen atom:
`Z_(eff) = 4.55`

Step-by-step explanation:

Effective nuclear charge
`[Z_(eff)]` is the net nuclear charge experienced by the electron in a given atom. It is always less than the actual charge of the nucleus [Z], due to shielding by electrons in the inner shells.

It is equal to the difference between the actual nuclear charge or the atomic number (Z) and the shielding constant (s).

`\Rightarrow Z_(eff) = Z - s`

For an oxygen atom-

Electron configuration: (1s²) (2s² 2p⁴)

The atomic number (actual nuclear charge): Z = 8

The shielding constant (s) for a valence electron can be calculated by using the Slater's rules:

⇒ s = 5 × 0.35 + 2 × 0.85 = 1.75 + 1.7 = 3.45

Therefore, the effective nuclear charge for a valence electron in oxygen atom is:

`Z_(eff) = Z - s = 8 - 3.45 = 4.55`

Therefore, the effective nuclear charge for a valence electron in oxygen atom:
`Z_(eff) = 4.55`