Explain why the patterns of bright emission spectral lines have an identical spectral position to the pattern of dark absorption spectral lines for a given gaseous element.

(An element's atomic structure and energy levels) Atoms of an element contain a nucleus with protons and neutrons and electrons orbiting around the nucleus. Electrons are arranged in energy levels, each corresponding to different amounts of energy. When electrons transition between these energy levels, they absorb or emit radiation at specific wavelengths, which result in absorption and emission spectral lines.

(Energy transitions and emission) When an atom's electron absorbs energy, it becomes excited and jumps to a higher energy level. After some time, the electron will release the energy as it returns back to a lower energy level. The energy released is in the form of electromagnetic radiation with a specific wavelength, creating bright emission spectral lines.

(Energy transitions and absorption) When radiations with continuous spectra pass through a gaseous element, the electrons in the atom can absorb specific wavelengths of energy and jump to a higher energy level. This leaves a missing line (dark spectral line) at the absorbed wavelength in the transmitted continuous spectra. These dark lines correspond to the absorption spectral lines.

(Relation between emission and absorption spectral lines) The energy difference between the two energy levels determines the wavelength of the absorbed or emitted radiation. Since the energy levels are unique to each element and the energy difference remains consistent, the absorbed and emitted wavelengths correspond to the same transitions between energy levels for a specific gaseous element. This results in the identical spectral positions of bright emission lines and dark absorption lines for the same element. To summarize, the reason why the bright emission spectral lines have an identical spectral position to the pattern of dark absorption spectral lines for a given gaseous element is because these lines are associated with the same electron energy level transitions within the atoms of the element. The energy difference between these levels is unique for each element and determines the specific wavelengths of the absorbed and emitted radiation, resulting in identical spectral positions for both emission and absorption lines.