Physics · Ch 13 — Atoms
The Line Spectra of the Hydrogen Atom
The Line Spectra of the Hydrogen Atom
The Origin of Spectral Lines
When an electron in a hydrogen atom jumps from a higher energy level (quantum number ) to a lower one (, where ), the atom loses energy. This energy is not lost into nothing — it is carried away by a single photon. The photon’s frequency is determined by the energy difference between the two states:
This is Bohr’s third postulate applied directly. Because and are integers, the right-hand side can only take certain discrete values. Consequently, the emitted photon can only have certain discrete frequencies. This is why the spectrum of hydrogen is a line spectrum — a series of sharp, distinct lines — rather than a continuous rainbow.
The discrete frequencies of emitted light are a direct consequence of the quantisation of atomic energy levels. If energy levels were continuous, the spectrum would be continuous too.
Emission and Absorption
The lines we see in a spectrum come from two complementary processes.
Emission lines are produced when an electron falls from a higher energy state to a lower one, releasing a photon. The atom is initially excited (it has absorbed energy earlier), and it de-excites by radiating light. Each downward jump gives one spectral line at a specific frequency.
Absorption lines appear when a beam of white light (which contains all frequencies) passes through a cool, rarefied gas. The atoms in the gas absorb photons whose energies exactly match the gap between a lower occupied state and a higher empty state. The electron jumps up, and that particular frequency is removed from the beam. When the transmitted light is analysed, dark lines appear at those frequencies — these are the absorption lines of the atom.
The frequencies of the absorption lines are exactly the same as the frequencies of some of the emission lines, because the same energy differences are involved — just the direction of the transition is reversed.