Which one of the following electronictransition between energy levels producesthe line of shortest wavelength in hydrogenspectrum ?(1) n2 → n1 (2) n3 → n1(3) n4 → n1 (4) n4 → n3
Question
Which one of the following electronictransition between energy levels producesthe line of shortest wavelength in hydrogenspectrum ?(1) n2 → n1 (2) n3 → n1(3) n4 → n1 (4) n4 → n3
Solution
The line of shortest wavelength in the hydrogen spectrum is produced by the electronic transition that involves the highest energy difference. In a hydrogen atom, the energy levels are quantized and the energy difference between levels increases as you move further from the nucleus.
The options given are:
(1) n2 → n1 (2) n3 → n1 (3) n4 → n1 (4) n4 → n3
The energy difference (and thus the frequency and inversely the wavelength of the emitted light) is greatest for transitions to the lowest energy level, n1. Therefore, the transition from the highest initial energy level to n1 will result in the shortest wavelength.
So, the transition n4 → n1 (option 3) will produce the line of shortest wavelength in the hydrogen spectrum.
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