Why Do Different Electron Transitions Emit Different Spectral Lines?

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Different elements emit electromagnetic waves at varying energies due to the nature of electron transitions between energy levels. Ultraviolet light has a shorter wavelength than visible light, resulting in higher energy emissions. Transitions occurring farther from the nucleus release more energy compared to those closer to the nucleus. Therefore, the ultraviolet line corresponds to a transition between higher energy levels, while the visible line corresponds to a transition between lower energy levels. Understanding these principles can enhance clarity and accuracy in discussing spectral lines.
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The emission spectrum of an unknown element contains two lines - one in the visible portion of the spectrum, and the other, ultraviolet. Based on the electromagnetic spectrum and Neil Bohr's model of the atom, account for the difference in energy between these two lines.

I'm having a bit of a difficult time understanding exactly why different elements emit electromagnetic waves as they decrease in energy. Anyways, my answer looks something like this so far...

The energy of a particle increases as the inverse of its wavelength. Due to the fact that ultraviolet light has a lesser wavelength than visible light, the line that is within the ultraviolet portion of the spectrum will have more energy. Also, electron transitions that occur farther away from the nucleus will emit more energy than those that occur closer to the nucleus. Thus, the electron transition that was responsible for producing the ultraviolet light must have occurred between two energy levels that were farther from the nucleus than the electron transition that was responsible for emitting visible light.

This is honestly the best I could come up with, and I know my terminology could use a lot of work, too. Any suggestions on how to improve this so I can get the full 3 marks? Any help would be much appreciated!
 
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