Understanding Effective Nuclear Charge (Z_eff) and Slater's Rule

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in an atom, accounting for shielding by other electrons. Slater's Rule provides a method to calculate Z_eff by estimating shielding constants (s).

Step 1: Shielding Power Order

According to Slater's Rule, electrons in the same group (same n and l quantum numbers) shield more effectively than those in different groups. The order of shielding power is: ns > np > nd > nf. This is because s-electrons are closer to the nucleus on average and provide better shielding.

Conclusion: The statement "Order of shielding power of electron corresponds to ns > np > nd > nf" is true.

Step 2: Variation in s and p-block

In s and p-block elements across a period, valence electrons are in the same shell (same n). Each additional electron experiences an increase in Z_eff by approximately 0.65 due to poor shielding by electrons in the same shell. For example, in period 2: Li (Z_eff ≈ 1.30) to Ne (Z_eff ≈ 6.85), increasing by about 0.65 per step.

Conclusion: The statement "On moving along the period from left to right Z_eff increases by 0.65 in s and p-block" is true.

Step 3: Variation in 3d Series

In the 3d series (first transition series), valence electrons are added to the (n-1)d subshell. Shielding by d-electrons is less effective (s ≈ 0.35 per electron from same group). Z_eff increases by about 0.15 per step, but there are exceptions due to electron-electron repulsion and stability (e.g., Cr and Cu have anomalous configurations).

Conclusion: The statement "On moving along the period, from left to right in 3d series Z_eff increases by 0.15 without any exception" is false due to exceptions.

Step 4: Variation in Inner Transition Elements

In inner transition elements (lanthanides and actinides), electrons are added to the (n-2)f subshell. The f-electrons shield very poorly (s ≈ 0.35 per electron from same group), but the increase in nuclear charge is almost perfectly offset by the poor shielding, resulting in a nearly constant Z_eff for the outer electrons.

Conclusion: The statement "On moving along the period from left to right in inner transition elements, Z_eff remains constant" is true.

Final Answer

The true statements are:

• Order of shielding power of electron corresponds to ns > np > nd > nf.
• On moving along the period from left to right Z_eff increases by 0.65 in s and p-block.
• On moving along the period from left to right in inner transition elements, Z_eff remains constant.

Related Topics

• Periodic Trends: Atomic radius, ionization energy, electron affinity.
• Quantum Numbers and Electron Configuration.
• Shielding Effect and Penetration Power.

Formulae and Theory

Slater's Rule for Z_eff:

Where Z is the atomic number and s is the shielding constant.

Shielding constants (s) per electron:

• Electrons in groups higher than the electron considered: s = 0.
• Electrons in the same group: s = 0.35 (except 1s, where s = 0.30).
• Electrons in (n-1) shell: s = 0.85.
• Electrons in (n-2) or lower shells: s = 1.00.