比移值计算器
计算色谱分析中的比移值（Rf值）。
Relative Atomic Radius (n²/Z_eff)
4.09 a.u.
Relative Atomic Radius (n²/Z_eff) vs Principal Quantum Number (n)
公式
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).
计算示例
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)
常见问题
Why does atomic radius decrease across a period?
Across a period, protons are added to the nucleus but electrons are added to the same shell. Z_eff increases, pulling electrons closer.
Why does atomic radius increase down a group?
Down a group, electrons are added to higher shells (larger n). Although Z_eff also increases, the n² factor dominates.
Is this formula exact?
No, it is a simplified estimate from the Bohr model. Real atoms are multi-electron systems where electron-electron repulsion and orbital shapes affect the radius.
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