Which one among the following transitions of electron of hydrogen atom emits radiation of the shortest wavelength?

The wavelength of radiation emitted during an electron transition in a hydrogen atom is inversely proportional to the energy difference between the levels, as described by the Rydberg formula. According to the Bohr model, the energy levels are quantized, and the energy gap between levels decreases significantly as the principal quantum number (n) increases. The transition from n = 2 to n = 1 (Lyman series) involves a much larger energy change than transitions between higher levels like n = 3 to n = 2 (Balmer series) or n = 4 to n = 3. Specifically, the n = 2 to n = 1 transition emits ultraviolet light with a wavelength of approximately 121.6 nm, which is shorter than the visible or infrared light produced by the other listed transitions. Therefore, the largest energy jump (n = 2 to n = 1) results in the shortest wavelength.

Sources

1. [1] https://en.wikipedia.org/wiki/Hydrogen_spectral_series