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