The Bohr model explains the hydrogen atom by placing the electron in specific allowed orbits around a small positive nucleus. It matters because it was one of the first models to show that atomic energy is quantized, not continuous. This idea helps explain why hydrogen gives off only certain colors of light instead of a smooth rainbow.
Atomic spectra became powerful evidence that electrons in atoms can have only certain energies.
In the Bohr model, each orbit has a fixed energy level labeled by the quantum number n. When an electron drops from a higher level to a lower level, the atom emits a photon with energy equal to the difference between the two levels. The photon energy determines its frequency and wavelength, so each electron transition creates a specific spectral line.
For hydrogen, the visible Balmer series comes from electrons falling to n = 2.
Key Facts
- Bohr energy levels for hydrogen are En = -13.6 eV / n^2, where n = 1, 2, 3, ...
- A photon emitted in a transition has energy E = hf = hc / lambda.
- The photon energy equals the level difference: Delta E = Ei - Ef for emission.
- Larger energy drops produce higher frequency photons and shorter wavelengths.
- The ground state of hydrogen is n = 1 with energy -13.6 eV.
- The Balmer series occurs when electrons fall to n = 2 and includes visible hydrogen spectral lines.
Vocabulary
- Bohr model
- A model of the atom in which electrons occupy fixed energy levels around the nucleus and change levels by absorbing or emitting photons.
- Energy level
- A specific allowed energy that an electron can have inside an atom.
- Photon
- A particle of electromagnetic radiation with energy E = hf.
- Atomic spectrum
- The set of wavelengths of light emitted or absorbed by atoms due to electron transitions.
- Balmer series
- The group of hydrogen spectral lines produced when electrons transition from higher levels down to n = 2.
Common Mistakes to Avoid
- Treating Bohr orbits as ordinary planet-like paths is wrong because the model describes allowed energy states, not classical circular motion that can have any radius.
- Using Ei - Ef with the wrong sign is wrong because emission requires the electron to move to a lower energy level and the photon energy must be positive.
- Assuming any photon energy can be emitted is wrong because atoms emit only photons whose energies match differences between allowed energy levels.
- Confusing frequency and wavelength is wrong because higher photon energy means higher frequency but shorter wavelength, according to E = hf and c = f lambda.
Practice Questions
- 1 A hydrogen electron falls from n = 3 to n = 2. Using En = -13.6 eV / n^2, find the photon energy in eV.
- 2 A photon emitted by hydrogen has energy 10.2 eV. Using E = hc / lambda with hc = 1240 eV nm, find its wavelength in nm.
- 3 Explain why the hydrogen emission spectrum has separate bright lines instead of a continuous band of colors.