Question

Scientists made the following two observations about emission spectra:

Each element has a unique emission spectrum.

Atoms emit energy only at specific wavelengths.

Describe how the Bohr model explains both of these observations.

Answer 1

The Bohr model explains both observations by postulating that electrons occupy only certain allowed (quantized) energy levels in an atom and that light is emitted when an electron jumps from a higher allowed level to a lower allowed level.

- Quantized energy levels: In Bohr’s model an electron in a stationary orbit n has a specific energy En (for hydrogen-like atoms En = −13.6 eV · Z^2 / n^2). Electrons cannot have energies between these allowed values.
- Discrete wavelengths: When an electron drops from level ni to nf it emits a photon with energy equal to the difference ΔE = Eni − Enf = hν = hc/λ. Because En takes only certain values, ΔE can take only certain values, so only photons of specific energies (and therefore specific wavelengths) are emitted. This explains why atoms emit light only at particular wavelengths (discrete spectral lines).
- Uniqueness for each element: The allowed energy levels depend on the nucleus’s charge (Z) and the electron configuration, so the set of possible ΔE values differs for each element. That gives each element its own characteristic (unique) emission spectrum. (For hydrogen-like ions the wavelengths follow the Rydberg form 1/λ = R Z^2 (1/nf^2 − 1/ni^2).)

(Bohr’s model is exact for hydrogen-like atoms and gives the correct qualitative explanation for multi-electron atoms, although full quantitative treatment of complex atoms requires quantum mechanics.)