Z effective (Zeff), or effective nuclear charge, is the net positive charge experienced by an electron in a multi-electron atom. It is defined as the net positive charge pulling these electrons towards the nucleus. The stronger the pull on the outermost electrons (valence electrons) towards the nucleus, the higher the effective nuclear charge. This fundamental concept in chemistry helps explain many periodic trends of elements.
The Concept of Shielding
In an atom with multiple electrons, not all electrons experience the full attractive force of the nucleus. Inner-shell electrons, positioned closer to the nucleus, effectively shield or screen the outer-shell (valence) electrons from the full nuclear charge. This shielding effect reduces the positive charge that the valence electrons 'feel' from the nucleus.
- Inner Electron Shielding: Electrons in core shells block a significant portion of the nuclear charge from reaching the valence electrons.
- Inter-electron Repulsion: Even electrons within the same shell repel each other, contributing to a lesser degree of shielding.
- Distance from Nucleus: Electrons further from the nucleus are more effectively shielded than those closer to it.
Calculating Z Effective (Slater's Rules)
The effective nuclear charge can be estimated using the following formula:
$Z_{eff} = Z - S$
Where:
- $Z_{eff}$ is the effective nuclear charge.
- $Z$ is the atomic number (the actual number of protons in the nucleus).
- $S$ is the shielding constant (also known as the screening constant), which accounts for the shielding effect of other electrons.
A common method for estimating the shielding constant ($S$) is through Slater's Rules, which involve a set of empirical rules for assigning shielding contributions based on electron configurations. These rules group electrons into specific "shells" and "subshells" for calculation.
Steps for Applying Slater's Rules:
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Write the electron configuration of the atom and group electrons as follows:
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc. -
Identify the electron of interest. This is the electron for which you want to calculate Zeff. All electrons in groups to the right of this electron contribute 0 to S.
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Calculate the shielding constant (S) using the following contributions:
Electron Group of Interest Electrons in the same (n) group (e.g., ns, np) Electrons in the (n-1) group Electrons in the (n-2) or lower groups ns or np electron 0.35 for each other electron in the same group 0.85 for each electron 1.00 for each electron nd or nf electron 0.35 for each other electron in the same group 1.00 for each electron 1.00 for each electron - Note: The 1s electrons contribute 0.30 to S if there is only one other 1s electron.
Example: Calculating Zeff for a Valence Electron in Oxygen (O)
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Atomic Number (Z) for Oxygen: 8
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Electron Configuration: $1s^2 2s^2 2p^4$. Grouped as $(1s^2) (2s^2 2p^4)$.
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Electron of Interest: A valence electron in the (2s, 2p) group.
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Calculate S:
- Electrons in the same (2s, 2p) group: There are 5 other electrons ($2s^2 2p^4 - 1 \text{ electron}$) = 5 electrons. Contribution: $5 \times 0.35 = 1.75$.
- Electrons in the (n-1) group (1s): There are 2 electrons in the 1s shell. Contribution: $2 \times 0.85 = 1.70$.
- Electrons in (n-2) or lower: None.
Total S = $1.75 + 1.70 = 3.45$
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Calculate Zeff:
$Z_{eff} = Z - S = 8 - 3.45 = 4.55$
So, a valence electron in Oxygen experiences an effective nuclear charge of approximately 4.55.
For more detailed information on Slater's rules, you can consult resources like LibreTexts Chemistry.
Periodic Trends of Z Effective
Understanding how Zeff changes across the periodic table is crucial for predicting other atomic properties.
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Across a Period (Left to Right):
- Zeff generally increases.
- As you move across a period, the atomic number (Z) increases by one with each successive element, meaning an additional proton is added to the nucleus.
- Electrons are added to the same principal energy level. While these new electrons provide some shielding, their contribution is less significant than the increase in nuclear charge.
- The increasing Zeff leads to a stronger pull on the valence electrons, resulting in a decrease in atomic radius and an increase in ionization energy.
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Down a Group (Top to Bottom):
- Zeff generally increases slightly or remains relatively constant.
- As you move down a group, new principal energy levels are added, and the number of core electrons significantly increases.
- This increased shielding by inner electrons largely counteracts the increase in the actual nuclear charge (Z).
- The slight increase or constancy of Zeff, combined with the addition of new electron shells, results in an increase in atomic radius down a group.
| Trend Direction | Change in Z | Change in S | Net Change in Zeff |
|---|---|---|---|
| Across Period | Increases | Increases | Increases |
| Down Group | Increases | Increases | Slight Increase |
Importance and Applications of Z Effective
The concept of effective nuclear charge is central to explaining various atomic properties and chemical behaviors:
- Atomic Radius: A higher Zeff pulls valence electrons closer to the nucleus, resulting in a smaller atomic radius.
- Ionization Energy: Elements with a higher Zeff require more energy to remove an electron, leading to higher ionization energies.
- Electron Affinity: Atoms with a higher Zeff have a stronger attraction for additional electrons, often resulting in more negative (exothermic) electron affinities.
- Electronegativity: Zeff directly influences an atom's ability to attract electrons in a chemical bond, which is quantified by its electronegativity.
- Chemical Reactivity: The strength with which valence electrons are held dictates how an atom will interact with other atoms, influencing its propensity to lose, gain, or share electrons.
