What is Effective Nuclear Charge?

Effective Nuclear Charge Z_eff

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi‑electron atom, especially a valence (outer) electron. The term “effective” is used because inner (core) electrons shield or screen the valence electron from feeling the full nuclear charge.

How to Understand Effective Nuclear Charge?

• Actual Nuclear Charge (Z): Number of protons in the nucleus (atomic number).
• Shielding Effect (S): Core electrons repel and partially block the attraction between the nucleus and outer electrons; more inner shells ⇒ greater shielding.
• Effective Nuclear Charge (Z_eff): The net attraction after accounting for shielding, given by Z_eff = Z − S.

Example: Lithium (Z = 3) has two core electrons that shield its single valence electron, so Z_eff ≈ 3 − 2 = 1 for the valence electron.

Why Is Effective Nuclear Charge Important?

• Atomic size: As Z_eff increases across a period, electrons are pulled closer, so atomic radius decreases.
• Ionization energy: Higher Z_eff means electrons are held more tightly, so more energy is required to remove them.
• Periodic trends: Z_eff generally increases left → right across a period and decreases down a group, explaining many periodic properties.

Effective Nuclear Charge Analogy

Imagine listening to a speaker (nucleus) across a crowded room. The people between you and the speaker (inner electrons) create “noise” that reduces how strongly you perceive the speaker’s voice. The strength you actually perceive is the effective nuclear charge.

Effective Nuclear Charge Key Formula

Z_eff = Z − S

Here, Z is the atomic number (proton count), and S is the shielding/screening constant (often approximated by the number of core electrons for simple estimates).