Bohr Model

Bohr's three postulates for hydrogen-like atoms (1913): (i) electrons orbit only in certain ALLOWED orbits — no radiation in these; (ii) angular momentum is quantised, L = nℏ; (iii) photons emitted/absorbed when electron transitions between orbits, E_photon = E_i − E_f.

Orbit radius: r_n = (n²/Z) · a₀, where a₀ = 0.529 Å is the Bohr radius.

Energy in n-th level: E_n = −(13.6 eV/n²)·Z² for hydrogen-like atoms.

Ground state of H (n=1): E₁ = −13.6 eV, r₁ = 0.529 Å.

Velocity in n-th orbit: v_n = (Z/n) × αc, where α ≈ 1/137 is the fine-structure constant. For H, v₁ ≈ c/137.

Bohr's model is exact for one-electron atoms (H, He⁺, Li²⁺) but fails for multi-electron atoms.

Reduced to a wave-picture by de Broglie's standing-wave condition: 2πr_n = nλ_n — natural consequence of matter waves.