1. What is Effective Nuclear Charge?

The effective nuclear charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for both the attraction to the nucleus and repulsion from other electrons.

2. How Does the Calculator Work?

The calculator uses the Zeff equation:

Where:

• \( Z \) — Atomic number (number of protons in nucleus)
• \( \sigma \) — Shielding constant (empirical value)

Explanation: The shielding constant represents how much the inner electrons shield the outer electrons from the full nuclear charge.

3. Importance of Zeff Calculation

Details: Zeff helps explain periodic trends like atomic size, ionization energy, and electronegativity. Higher Zeff means electrons are held more tightly.

4. Using the Calculator

Tips: Enter the atomic number (1-118) and shielding constant (typically between 0 and Z-1). The shielding constant can be found in chemistry reference tables.

5. Frequently Asked Questions (FAQ)

Q1: How does Zeff vary across the periodic table?
A: Zeff increases across a period (left to right) and remains relatively constant down a group.

Q2: What are typical shielding constant values?
A: For valence electrons, σ ≈ number of core electrons. For example, Na (Z=11) has σ≈10 for its valence electron.

Q3: Why does Zeff matter in chemistry?
A: Zeff explains why atoms get smaller across a period (increased attraction) and why ionization energy increases.

Q4: How accurate is this simple calculation?
A: It provides a good estimate, but quantum mechanical calculations give more precise values.

Q5: Can Zeff be greater than Z?
A: No, Zeff is always less than Z since shielding can't be negative.