Electron Orbital Radius
The radius of electron orbits in hydrogen-like atoms. Larger n means larger orbits; larger Z means smaller orbits due to stronger nuclear attraction.
Variables
Derivation
From Bohr model with nuclear charge Z modifying the Coulomb force.
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Constants in this formula
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- n = 2 (Principal quantum number)
- a0 = 5.292 × 10⁻¹¹ m (Bohr radius (5.29 × 10⁻¹¹ m))
- Z = 3 (Atomic number)
Result: rn = 7.056 × 10⁻¹¹ m
Other modern physics formulas with the same quantities
- Bohr Energy Levels (Atomic Physics) shares Principal quantum number
- Moseley's Law (Atomic Physics) shares Atomic number
Where this formula is listed
- Modern Physics formulas, under Atomic Physics, alongside Hydrogen Spectrum (Rydberg).
- In the modern physics list it comes after Hydrogen-like Atom Energy and before Moseley's Law.
- Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Electron Orbital Radius formula?
Electron Orbital Radius is written r_n = n²a₀/Z. The radius of electron orbits in hydrogen-like atoms. Larger n means larger orbits; larger Z means smaller orbits due to stronger nuclear attraction. It belongs to Modern Physics, under Atomic Physics.
What are the units in r_n = n²a₀/Z?
In SI units, r_n is orbital radius, measured in m; n is principal quantum number (dimensionless); a₀ is bohr radius (5.29 × 10⁻¹¹ m), measured in m; Z is atomic number (dimensionless).
How is the Electron Orbital Radius formula derived?
From Bohr model with nuclear charge Z modifying the Coulomb force. The result is r_n = n²a₀/Z.