Free Atomic Radius Trend Calculator

Estimate the relative atomic radius from effective nuclear charge and principal quantum number using the simplified relationship r ~ n²/Z_eff.

Relative Atomic Radius (n²/Z_eff)

4.09 a.u.

Approximate Radius217 pm

Relative Atomic Radius (n²/Z_eff) vs Principal Quantum Number (n)

Atomic Radius Trend

Approximate Formula

r ∝ n² / Z_eff

In Bohr model terms: r ≈ (n² / Z_eff) × a₀

Where a₀ = 53 pm (Bohr radius)

Where:

  • n = principal quantum number (shell number)
  • Z_eff = effective nuclear charge
  • Atomic radius decreases across a period (Z_eff increases, same n) and increases down a group (n increases faster than Z_eff).

    Example Calculation

    Sodium: n = 3 (3rd period), Z_eff ≈ 2.2.

    1. 01r ∝ n²/Z_eff
    2. 02r ∝ 9/2.2
    3. 03r ∝ 4.09
    4. 04Approximate radius = 4.09 × 53 pm ≈ 217 pm
    5. 05Actual Na radius ≈ 186 pm (this is an estimate)

    Frequently Asked Questions

    Learn More

    Understanding Molarity

    Learn what molarity is, how to calculate it, and why it matters in chemistry. Covers moles, liters, dilution, and step-by-step examples for preparing solutions.

    Related Calculators