Bohr Model of Hydrogen
MediumVisualize electron orbits, energy levels, and the emission of light when electrons transition between levels.
💡 Key Concepts:
- Energy levels are quantized: En = -13.6/n² eV
- Ground state (n=1) has lowest energy at -13.6 eV
- Photon emitted when electron drops to lower level
- Photon energy: ΔE = Efinal - Einitial
- Balmer series (n→2) produces visible light
- Higher n levels are closer together in energy
The Bohr Model
Proposed by Niels Bohr in 1913, the Bohr model was the first successful quantum model of the atom. It explained the discrete spectral lines of hydrogen by postulating that electrons orbit the nucleus in specific allowed energy levels.
While superseded by modern quantum mechanics, the Bohr model remains valuable for understanding atomic structure and provides accurate predictions for hydrogen-like atoms.
Key Postulates
1. Quantized Orbits
Electrons can only occupy certain discrete orbits where angular momentum is quantized: L = nℏ, where n = 1, 2, 3, ... and ℏ = h/2π.
2. Stationary States
Electrons in allowed orbits do not radiate energy. They maintain constant energy in these "stationary states" without spiraling into the nucleus.
3. Quantum Jumps
When an electron transitions between orbits, it absorbs or emits a photon with energy exactly equal to the energy difference: ΔE = hf = Efinal - Einitial.
⚡ Energy Levels
The energy of an electron in the nth orbit is given by:
En = -13.6 eV / n²
The negative sign indicates that the electron is bound to the nucleus. Key features:
- Ground State (n=1): E1 = -13.6 eV (lowest energy, most stable)
- Excited States (n≥2): Higher energy levels with less binding
- Ionization (n=∞): E∞ = 0 eV (electron completely removed)
- Energy levels converge as n increases
🌈 Spectral Series
When electrons transition between energy levels, they emit photons with specific wavelengths, creating spectral lines grouped into series:
| Series | Transitions | Spectrum Region |
|---|---|---|
| Lyman | n → 1 | Ultraviolet |
| Balmer | n → 2 | Visible |
| Paschen | n → 3 | Infrared |
| Brackett | n → 4 | Infrared |
The Balmer series (transitions to n=2) produces visible light and was historically important in discovering the structure of the hydrogen atom.
📏 Orbital Radii
The radius of the nth orbit follows:
rn = n² × a0
where a0 = 0.529 Å (Bohr radius). The ground state has the smallest radius, and orbital size increases quadratically with n.
🌍 Applications
- Spectroscopy: Identifying elements by their characteristic spectral lines
- Astronomy: Analyzing light from stars and galaxies
- Lasers: Understanding electron transitions in laser media
- Quantum Chemistry: Foundation for understanding atomic bonding
- Plasma Physics: Studying ionized gases and fusion reactions
⚠️ Limitations
While revolutionary, the Bohr model has limitations:
- Only accurately predicts hydrogen and hydrogen-like ions (single electron)
- Cannot explain fine structure or hyperfine splitting
- Doesn't account for electron spin
- Incompatible with the Heisenberg uncertainty principle
- Cannot predict intensity of spectral lines
- Replaced by the Schrödinger equation and quantum mechanics
Despite these limitations, the Bohr model remains a valuable pedagogical tool and provides qualitatively correct insights into atomic structure.