What is Screening Effect (Shielding Effect) – Slater’s Rules | Calculation of Effective or Reduced Nuclear Charge

Anand Classes Notes explains in atoms with more than one electron, the outer electrons are repelled by the inner electrons due to electron–electron repulsion. This repulsion reduces the full attractive force of the positively charged nucleus on the valence electrons. This phenomenon is known as the screening effect or shielding effect. The greater the number of inner electrons, the larger the shielding effect, which decreases the effective nuclear charge (Z_eff) experienced by the outermost electrons. Slater, a scientist, formulated rules to calculate this shielding effect quantitatively, which are essential for understanding atomic structure and periodic trends.

🛡️ What is The Screening Effect (Shielding Effect) ?

In multi-electron atoms, electrons in the outermost shell (valence electrons) are not only attracted to the positively charged nucleus, but also repelled by the electrons present in the inner shells.

The net effect of:

• Attractive force from the nucleus
• Repulsive force from inner electrons

…causes the valence electrons to experience less nuclear attraction than they would in the absence of inner electrons.

This reduction in the effective pull of the nucleus on the valence electrons is known as the:

Screening Effect or Shielding Effect.

🔍 Why Does the Screening Effect Occur ?

• In a polyelectronic atom (an atom with more than one electron), electrons are arranged in different shells.
• The inner-shell electrons lie between the nucleus and the valence electrons.
• Since electrons carry a negative charge, they repel each other.
• This repulsion pushes the outer electrons slightly away from the nucleus and reduces the effective nuclear pull acting on them.

As a result:

• The outermost electrons do not feel the full positive charge of the nucleus.
• Only a part of the nuclear charge is effective in attracting them.

📌 What are the Factors Affecting the Screening Effect ?

1. Number of Inner Electrons
   • The greater the number of inner electrons, the stronger the repulsion they cause, leading to a greater screening effect.
2. Position of the Electron (Shell/Orbital Type)
   • Electrons in s-orbitals are closer to the nucleus and have lower shielding ability.
   • Electrons in p, d, and f orbitals are farther away and have higher shielding ability.
3. Nature of the Atom
   • In heavier atoms (with more electrons), the screening effect is generally stronger due to the presence of multiple inner shells.

⚡ What is Effective Nuclear Charge ?

Due to the screening effect, the valence electron in a multi-electron atom experiences less attraction from the nucleus.

This happens because the inner electrons shield or block part of the nuclear charge from reaching the valence electrons. As a result, the nuclear charge (Z) actually present on the nucleus is reduced for the valence electrons.

📌 Definition of Effective Nuclear Charge

The reduced nuclear charge experienced by a valence electron is called the:

Effective Nuclear Charge (denoted by Z_eff).

🧮 What is Relation Between Actual and Effective Nuclear Charge (Screening Constant (σ))

• The magnitude of the screening effect can be expressed by a screening constant (σ).
• Symbol: σ
• Calculation: Determined using Slater’s Rules (a set of empirical rules for estimating the screening constant).
• The effective nuclear charge (Z_eff) or reduced nuclear charge felt by a valence electron can be calculated as:

Z_eff = Z − σ

where:

• Z = Atomic number (total nuclear charge)
• σ = Screening constant

✅ Key Point: The greater the screening constant (σ), the smaller the effective nuclear charge felt by the valence electron.

📖 In Simple Words

The screening effect is like a crowd standing between you and a speaker’s voice — the more people between you and the speaker, the less clearly you can hear them.
In atoms, the inner electrons are the crowd, the nucleus is the speaker, and the valence electrons are you.

🌟 Slater’s Rules – A Clear Explanation

A scientist named John C. Slater developed a set of rules to calculate the shielding constant (σ), which helps us find the Effective Nuclear Charge (Z_eff) experienced by a valence electron.

1. First, why do we need shielding constant?

• In an atom, electrons repel each other due to their negative charges.
• This repulsion reduces the full attractive pull of the nucleus on outer electrons.
• The actual pull that an electron feels is called Effective Nuclear Charge (Z_eff).

📌 Formula: : Z_eff = Z − σ

Where:

• Z = actual nuclear charge (atomic number)
• σ = shielding constant (total repulsion effect from other electrons)

2. Slater’s Golden Rules for σ

Slater divided electrons into groups and gave specific shielding values:

1. Electrons in the same orbital (outermost shell)
   Contribution per electron = 0.35 (except 1s, where it’s 0.30)
   ⚠️ Do NOT count the electron for which you are calculating Z_eff. i.e [0.35 × No. of nth electrons)-1]
2. Electrons in (n–1) shell (penultimate shell)
   Contribution per electron = 0.85
3. Electrons in (n–2) or lower shells (inner core electrons)
   Contribution per electron = 1.00

3. Example: Second Period Elements (n = 2)

For Li, Be, B, C, N, O, F, Ne → valence electrons are in n = 2 shell.
Let’s calculate step-by-step for a few cases:

📚 Example 1 – Lithium (Li)

• Atomic number: Z = 3
• Electronic configuration: 1s² 2s¹
• Electron of interest: the 2s electron.

Applying Slater’s Rules:

• Same group (2s, 2p): No other electrons here ⇒ (1-1) × 0.35 = 0 × 0.35 = 0
• (n – 1) shell = 1s electrons: 2 × 0.85 = 1.70

Total shielding constant: σ = 0 + 1.70 = 1.70

Effective nuclear charge: Z_eff = Z − σ = 3 − 1.70 = 1.30

✅ The 2s electron in Li feels an effective charge of +1.30.

📚 Example 2 – Boron (B)

• Atomic number: Z = 5
• Electronic configuration: 1s² 2s² 2p¹
• Electron of interest: one 2p electron.

Applying Slater’s Rules:

• Same group (2s, 2p) : 2 other electrons in 2s +0 other electron in 2p = 2 electrons = 2 × 0.35 = 0.70
• (n – 1) shell = 1s electrons: 2 × 0.85 = 1.70

Total shielding constant: σ=0.70 + 1.70 = 2.40

Effective nuclear charge: Z_eff = 5 − 2.40 = 2.60

✅ A 2p electron in Boron feels an effective charge of +2.60.

📚 Example 3 – Oxygen (O)

• Atomic number: Z = 8
• Electronic configuration: 1s² 2s² 2p⁴
• Electron of interest: one 2p electron.

Applying Slater’s Rules:

• Same group (2s, 2p):
  2 other electrons in 2s + 3 other electrons in 2p = 5 electrons
  5 × 0.35 = 1.75
• (n – 1) shell = 1s electrons:
  2 × 0.85 = 1.70

Total shielding constant: σ = 1.75 + 1.70 = 3.45

Effective nuclear charge: Z_eff = 8 − 3.45 = 4.55

✅ A 2p electron in Oxygen feels an effective charge of +4.55.

4. Summary Table – Second Period Elements

📊 Screening Effect Trends in the Periodic Table

For s- and p-block elements:

• Across a Period:
  The screening effect increases slightly because the number of inner electrons increases as atomic number rises.
• Down a Group:
  The screening effect increases significantly because more inner shells are added, increasing electron repulsion.

FAQs — Screening (Shielding) Effect

What is the screening (shielding) effect?

The screening effect, also known as the shielding effect, refers to the phenomenon where inner-shell electrons reduce the effective nuclear charge experienced by valence electrons. This happens because these inner electrons repel the outer electrons, thereby diminishing the nucleus’s pull on them.

Is there a difference between the screening effect and the shielding effect?

No — both terms mean the same thing! They describe how inner electrons buffer or screen the attraction from the nucleus, weakening the force felt by the outermost electrons.

Why does the screening effect occur?

In atoms with multiple electrons, valence electrons are simultaneously attracted by the nucleus and repelled by inner electrons. This repulsion reduces the net attractive force, making the outer electrons less tightly bound.

What factors affect the magnitude of the shielding effect?

• Number of inner shells: More shells between the nucleus and outer electrons lead to greater shielding.
• Orbital type: Electrons in s-orbitals shield more effectively than those in p, d, or f orbitals, due to their higher penetration toward the nucleus.

How is the screening constant (σ) calculated?

The shielding constant (σ) can be estimated using Slater’s Rules, which assign specific shield values per electron based on its orbital and proximity to the valence electron. Examples include:

• 0.35 for electrons in the same shell (except 1s, which is 0.30)
• 0.85 for electrons in the penultimate shell
• 1.00 for electrons in deeper shells

How is the effective nuclear charge (Z_eff) determined?

Once σ is known, effective nuclear charge is calculated as: Z_eff = Z − σ

Where Z is the atomic number (actual nuclear charge). This describes the net attraction an outer electron experiences.

What is Screening Constant and Effective nuclear charge of Scandium ? [JEE]

Given: Sc (Z = 21), configuration: $$1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^1 \, 4s^2$$

We find σ for the last 4s electron:

• Same shell (n = 4): 1 other electron → 1 × 0.35 = 0.35
• (n – 1) shell (n = 3): 9 electrons → 9 × 0.85 =7.65
• (n – 2) and lower shells: 10 electrons → 10 × 1.00 = 10

σ = 0.35 + 7.65 + 10 = 18

Z_eff = 21 − 18 = 3

Why is the concept of shielding important?

It helps explain periodic properties such as:

• Atomic radius (decreases across a period due to rising Z_eff)
• Ionization energy (higher Z_eff → stronger nuclear pull → higher ionization energy)
• Chemical reactivity (metals tend to have less shielding, making valence electrons easier to remove)

Can shielding explain irregularities in periodic trends?

Yes, shielding helps clarify anomalies in elements like the Group 13 elements (B, Al, Ga…), transition series, and lanthanides & actinides where expected trends don’t always match the idealized pattern due to variable shielding.

💡 Summary of the Concept

• Cause: Repulsion by inner electrons.
• Effect: Reduction of nuclear pull on valence electrons.
• Result: Outer electrons are less tightly held by the nucleus.
• Importance: The screening effect influences atomic radius, ionization energy, electron affinity, and reactivity.

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