Bohr Model
Circular orbits rₙ = n²a₀/Z with standing wave pattern nλ = 2πr.
Key Notes
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.
Formulas
Quantised angular momentum
n = 1, 2, 3, ... (principal quantum number).
Bohr radius
Natural unit of atomic length.
n-th orbit radius
Grows as n².
n-th level energy
Negative — bound state. n = ∞ is ionised.
Transition (photon emission)
Predicts the hydrogen spectrum exactly.
Important Points
Bohr model only works for HYDROGEN-LIKE (one-electron) atoms: H, He⁺, Li²⁺, Be³⁺. Multi-electron atoms need full quantum mechanics.
Quantization of L ⇒ quantization of r and E. The integer n is the principal quantum number.
Energy is NEGATIVE: bound electron. Ionisation = lifting from E_n to E_∞ = 0 ⇒ requires +|E_n| of energy.
Smaller n ⇒ smaller r ⇒ tighter binding (deeper E).
Hydrogen Lyman series: transitions to n=1 (UV). Balmer: n=2 (visible). Paschen: n=3 (IR).
Bohr's quantization is justified by de Broglie's matter waves: stable orbits = standing waves fitting an integer number of wavelengths.
Bohr Model notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.