Bohr Model Formula
Quantized energy levels in hydrogen-like atoms
Energy Levels
En = -13.6 eV × Z² / n²
- En = energy of level n (eV)
- Z = atomic number (1 for H)
- n = principal quantum number (1, 2, 3...)
- Negative sign: electron is bound to nucleus
Orbital Radius
rn = a₀ n² / Z
a₀ = 0.529 Å (Bohr radius)
Example: Hydrogen n = 2
E₂ = -13.6 × 1² / 2² = -13.6 / 4 = -3.4 eV
r₂ = 0.529 × 2² / 1 = 0.529 × 4 = 2.116 Å
Answer: E₂ = -3.4 eV, r₂ = 2.12 Å
Transition Energy
ΔE = Efinal - Einitial = -13.6 Z² (1/nf² - 1/ni²)
Photon emitted if nf < ni; absorbed if nf > ni.