Concept: The Lyman series involves electron transitions terminating at the absolute ground state (\( n=1 \)) of the hydrogen atom, producing the most energetic spectral lines.
Formula:$$ E_{\text{photon}} = -13.6 \text{ eV} \left( \frac{1}{n^2} - \frac{1}{1^2} \right) $$
Solution:- Since the transitions terminate at the deeply bound \( n=1 \) shell, the energy difference \( \Delta E \) is exceptionally large (between 10.2 eV and 13.6 eV).
- Photons with these energy levels correspond to wavelengths ranging from roughly 91 nm to 121 nm.
- This wavelength span sits firmly in the Ultraviolet (UV) spectrum, completely invisible to the human eye.
Why other options are incorrect:Visible light (D) requires less energy (Balmer series). Infrared (B) and Far-infrared (A) require even less energy transitions, corresponding to series terminating at higher shells like Paschen or Brackett.
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