Quick questions on Atomic spectra emission and absorption: WACE Year 12 Physics Unit 4

The energy levels depend on the number of protons and the arrangement of electrons, which is unique to each element. So the set of spectral lines, their positions and spacings, is a unique signature. The dark Fraunhofer lines in sunlight reveal which elements are present in the Sun's outer layers, and the same method identifies the composition of distant stars.

A common question gives a set of energy levels and asks how many spectral lines are possible. Each distinct pair of levels gives one transition, so $n$ levels produce $\dfrac{n(n-1)}{2}$ lines: three levels give three lines, four levels give six, five levels give ten. The largest energy gap (from the top level to the ground state) gives the highest-energy, shortest-wavelength line, while the smallest gap between adjacent levels gives the lowest-energy, longest-wavelength line. Sketching the levels and drawing every downward arrow is the reliable way to make sure you count each transition exactly once and can then rank the lines by wavelength.

The practical power of this topic is that spectra let us learn the composition, temperature and motion of objects we can never sample directly. The dark absorption lines in sunlight (the Fraunhofer lines) reveal which elements are present in the Sun's cooler outer layers, because each set of missing wavelengths matches a known element's fingerprint. The same method identifies the elements in distant stars and galaxies. Beyond composition, the lines also shift: if a star is moving away, all its lines are red-shifted to longer wavelengths, and the size of the shift gives the speed of recession.