A sealed discharge tube contains low-pressure hydrogen gas
CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom
Problem
A sealed discharge tube contains low-pressure hydrogen gas. When a potential difference is applied across the tube, light is emitted and analyzed with a spectroscope. The resulting spectrum consists of a series of narrow, bright lines at specific wavelengths rather than a continuous band. Answer the following about the physical origin and implications of the observed line spectrum.
(1) Part 1: (a) Describe, in terms of the atomic structure of hydrogen, why the emitted light appears at discrete wavelengths instead of across a continuous range.
(2) Part 2: (b) Explain how the principle of energy conservation governs the relationship between an electronic transition and the photon that is produced.
(3) Part 3: (c) An observer notices that one of the bright lines corresponds to a transition from an excited state to the first excited state (n=2), while a different line corresponds to a transition directly to the ground state (n=1). Compare the energies and wavelengths of these two photons and justify your comparison without performing numerical calculations.
(4) Part 4: (d) Discuss qualitatively how the spacing between successive spectral lines is expected to change as the initial quantum number of the transition increases (for example, n=4→2 versus n=7→2). Provide a physical explanation for this trend.