As changes in energy levels of electrons increase, why do the frequencies of atomic line spectra they emit decrease?

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I think you made a mistake here or have been misinformed.  When energy levels increase the frequency also increases.  It is the wavelength that decreases.  This happens because energy is inversely proportional to wavelength.  The mathematical statement of this is:

E = hc/`lambda`

where E is energy, h is Planck's...

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I think you made a mistake here or have been misinformed.  When energy levels increase the frequency also increases.  It is the wavelength that decreases.  This happens because energy is inversely proportional to wavelength.  The mathematical statement of this is:

E = hc/`lambda`

where E is energy, h is Planck's constant, c is the speed of light, and `lambda` is the wavelength of the radiation.  Since both h and c are constants, E and `lambda` are the only two variables here.  So when the difference in energy levels of electrons increase, the wavelength of the energy required to traverse the two levels decreases.  The take home message here is that high energy electromagnetic radiation has shorter wavelengths.

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