Final answer:
The longest Balmer series wavelength is for n2=2 to n1=3, while the shortest is for n2=2 to n1=∞, theoretically. The visible Balmer lines range from n1=3 to n1=7, but there are no UV Balmer lines. No suitable transition corresponds to a 4.653 µm wavelength ending at nf=5, likely due to an error in the wavelength provided.
Step-by-step explanation:
The longest wavelength in the Balmer series corresponds to the transition n₂=2 to n₁=3, and the shortest wavelength is associated with a transition n₂=2 to n₁=∞ (which theoretically represents the limit as the initial energy level goes to infinity).
The absorption spectrum consists of dark lines or bands on a continuous spectrum because photons with specific energies are absorbed as electrons are excited to higher energy levels. Conversely, an emission spectrum comprises bright lines indicating the emission of photons as electrons transition to lower energy levels. Measuring an absorption spectrum can be done by shining white light through a sample of the material and analyzing the resulting spectrum with a spectrometer to observe the missing wavelengths.
Balmer series lines found in the visible spectrum range from n₁=3 to n₁=7. There are no transition lines in the Balmer series that fall in the ultraviolet (UV); UV lines are associated with the Lyman series, not the Balmer series.
To find the n for the initial level of the electron for the observed wavelength of 4.653 µm ending at nf = 5 level, one would use Rydberg's formula. However, 4.653 µm does not correspond to any transition to nf=5, as lines in the Balmer series that end at nf=5 are in the visible range.