Section 7.3: Bohr Model
The Bohr model describes electrons in atoms as orbiting the nucleus in discrete energy levels. Transitions between levels result in emission or absorption of photons: \[ E_n = -\frac{13.6\, \text{eV}}{n^2} \] \[ \Delta E = E_f - E_i = h \nu \]
- Electron orbits are quantized, only certain radii allowed.
- Photon energy corresponds to the energy difference between levels.
- Explains hydrogen emission spectrum and spectral lines.
Example: Photon Emission
An electron in a hydrogen atom falls from n = 3 to n = 2. Calculate the photon energy emitted.
\( E_3 = -\frac{13.6}{3^2} = -1.51\, \text{eV} \)
\( E_2 = -\frac{13.6}{2^2} = -3.40\, \text{eV} \)
\( \Delta E = E_2 - E_3 = -3.40 - (-1.51) = -1.89\, \text{eV} \)
Photon energy = 1.89 eV
Practice Problems
- Calculate the wavelength of a photon emitted during n=4 → n=2 transition in hydrogen.
- Determine the energy levels for n=1, 2, 3 in hydrogen.
- Explain why the Bohr model only works for hydrogen-like atoms.
- Find the frequency of radiation for the n=5 → n=3 transition.
- Sketch the energy level diagram showing n=1 to n=4 levels and possible transitions.