Concept: The wavelength of an emitted photon is inversely proportional to the energy of the electron transition. Larger energy drops produce shorter (lower) wavelengths.
Formula: $$ E = \frac{hc}{\lambda} $$
Solution: - The energy of a transition depends on how close to the nucleus the electron falls.
- Transitions to \( n=1 \) (Lyman series) have the highest energy and lowest wavelength, but Lyman is not an option.
- Among the given options, the Balmer series drops to the lowest level (\( n=2 \)).
- This results in the largest energy gap compared to Paschen (\( n=3 \)), Brackett (\( n=4 \)), and Pfund (\( n=5 \)).
- Consequently, the Balmer series emits photons with the highest energy and the lowest wavelength among the choices provided.
Why other options are incorrect: The other series involve drops to higher principal quantum shells (smaller energy gaps), resulting in longer wavelengths (infrared region).
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