Chemistry
Chemistry
Problem
A low-pressure hydrogen discharge tube is observed through a diffraction grating. Four prominent visible lines appear at wavelengths 656 nm, 486 nm, 434 nm, and 410 nm. (a) Identify the physical reason why the emitted light forms discrete lines rather than a continuous spectrum. (b) Explain why a model in which the electron orbits the nucleus in arbitrary classical paths cannot account for the appearance of only these specific wavelengths. (c) Describe how restricting the electron to quantized orbital states leads to discrete photon energies and therefore to the observed spectral lines. (d) When the experiment is repeated with iron vapor, thousands of closely spaced lines are recorded. Explain why a multi-electron atom produces such a dense spectrum while still requiring quantum—and not classical—reasoning for its interpretation.Intuitive explanation
These wavelengths are the famous Balmer series—transitions where electrons fall into the level from higher orbits. The key insight is recognizing that each line corresponds to a specific pair of energy levels, and you can use the Rydberg formula to identify which transitions produced each line. Once you know the pattern, you can predict other visible lines or explain why only these four dominate in the visible region.
Intuitive explanation
These wavelengths are the famous Balmer series—transitions where electrons fall into the level from higher orbits. The key insight is recognizing that each line corresponds to a specific pair of energy levels, and you can use the Rydberg formula to identify which transitions produced each line. Once you know the pattern, you can predict other visible lines or explain why only these four dominate in the visible region.