← Labs|Atomic Structure — Model Evolution, Bohr Model & Spectral Lines
Atomic Models
Key Experiments
• Cathode ray tube → electron (Thomson)
• Gold foil scattering → nucleus (Rutherford)
• Photoelectric effect → photon (Einstein)
• Hydrogen spectrum → energy levels (Bohr)
• de Broglie: λ=h/mv (wave-particle)
Bohr's Model
Niels Bohr · 1913
Quantisation
Angular momentum: L = mvr = nh/2π
Energy levels: Eₙ = −13.6/n² eV
Radius: rₙ = 0.529n² Å (Bohr radius a₀)
Spectral Success
Explained Lyman, Balmer, Paschen series of H exactly. Rydberg constant from first principles: RH = me⁴/(8ε₀²h³c)
Failure
Cannot explain: multi-electron atoms, fine structure (Zeeman/Stark effects), or wave nature of electron (de Broglie)
Bohr Postulates
• Electrons move in fixed circular orbits (stationary states) — no energy radiated
• Only orbits where mvr = nh/2π are allowed (angular momentum quantised)
• Energy emitted/absorbed = ΔE = hν when electron jumps between orbits
• Energy of nth orbit: Eₙ = −13.6/n² eV (for H)
• Radius of nth orbit: rₙ = 0.529n² Å (Bohr radius)
Formulae (H-like atoms)
Eₙ = −13.6 Z²/n² eV = −2.18×10⁻¹⁸ Z²/n² J
rₙ = 0.529 n²/Z Å
vₙ = 2.18×10⁶ Z/n m/s
1/λ = RH·Z²·(1/n₁² − 1/n₂²) RH = 1.097×10⁷ m⁻¹
ΔE = hν = hc/λ h = 6.626×10⁻³⁴ J·s
Hydrogen Spectral Series — Bohr Model
Spectral lines in Balmer series (n→2, Visible)
n=3 → n=2656.3 nm-1.89 eV
n=4 → n=2486.2 nm-2.55 eV
n=5 → n=2434.1 nm-2.86 eV
n=6 → n=2410.2 nm-3.02 eV
n=7 → n=2397 nm-3.12 eV
Energy levels (eV) — H atom
ni:
nf:
λ = 656.3 nm · ΔE = -1.89 eV