1. What is Effective Nuclear Charge?

The effective nuclear charge (Z_eff) 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 effective nuclear charge equation:

Where:

• \( Z \) — Atomic number (number of protons)
• \( \sigma \) — Screening constant (accounts for electron shielding)

Explanation: The equation shows that the effective nuclear charge is the actual nuclear charge reduced by the shielding effect of other electrons.

3. Importance of Z_eff Calculation

Details: Effective nuclear charge helps explain periodic trends like atomic size, ionization energy, and electron affinity across the periodic table.

4. Using the Calculator

Tips: Enter the atomic number (1-118) and screening constant (typically between 0 and Z-1). The screening constant depends on electron configuration.

5. Frequently Asked Questions (FAQ)

Q1: How is the screening constant determined?
A: σ is calculated using Slater's rules which consider the shielding effects of different electron orbitals.

Q2: Why does Z_eff increase across a period?
A: While Z increases, shielding increases more slowly, resulting in higher effective nuclear charge.

Q3: How does Z_eff affect atomic radius?
A: Higher Z_eff pulls electrons closer, decreasing atomic radius.

Q4: What is Z_eff for valence electrons?
A: It's typically much less than Z due to shielding by core electrons.

Q5: How accurate is this simple calculation?
A: It provides a basic estimate; more sophisticated methods include quantum mechanical calculations.