In the Bohr model, the electron orbits the nucleus in quantized orbits. Radius rₙ = 0.529 n² Å (H); velocity vₙ = 2.19×10⁶/n m/s; energy Eₙ = −13.6 Z²/n² eV. Transitions: ΔE = 13.6 Z²(1/n₁² − 1/n₂²) eV. Rydberg: 1/λ = R Z²(1/n₁² − 1/n₂²). Angular momentum L = n ℏ. Series: Lyman (n₁=1), Balmer (n₁=2), Paschen (n₁=3).
Bohr model calculators
Radius, velocity, energy, transition, Rydberg, angular momentum
⚛️ Bohr model summary
| Concept | Formula | Notes |
|---|---|---|
| Radius of nth orbit | rₙ = 0.529 n² Å (H), rₙ ∝ n²/Z | Hydrogen-like atoms |
| Velocity of electron | vₙ = (2.19×10⁶ / n) m/s (H), vₙ ∝ Z/n | vₙ ∝ 1/n for fixed Z |
| Angular momentum | L = n ℏ = n h / (2π) | n = 1,2,3,... |
| Energy of nth orbit | Eₙ = −(13.6 Z² / n²) eV | Hydrogen (Z=1): −13.6/n² eV |
| Energy difference (transition) | ΔE = 13.6 Z² (1/n₁² − 1/n₂²) eV | Emission when n₂ > n₁ |
| Wavenumber (Rydberg) | 1/λ = R Z² (1/n₁² − 1/n₂²) | R ≈ 1.097×10⁷ m⁻¹ |
| Frequency of photon | ν = c/λ = ΔE/h | — |
| Series limits | Lyman (n₁=1), Balmer (n₁=2), Paschen (n₁=3) | UV, visible, IR |
About the Bohr model
In the Bohr model, the electron moves in circular orbits with quantized angular momentum L = n ℏ. For hydrogen-like atoms (nucleus charge Ze): radius rₙ = 0.529 n²/Z Å, velocity vₙ ∝ Z/n, and energy Eₙ = −(13.6 Z²/n²) eV. Transitions between orbits give spectral lines: ΔE = 13.6 Z²(1/n₁² − 1/n₂²) eV and 1/λ = R Z²(1/n₁² − 1/n₂²) (Rydberg formula).
Spectral series
Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen (n₁=3, IR), Brackett (n₁=4), Pfund (n₁=5).