Why Do Different Elements Have Unique Spectral Lines?

learning_phys
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why do different spectral lines appear for the excitation of different elements? I know that electrons jump to lower energy levels gives off photons of distinct frequencies but why characterizes them to be a certain frequency for each element? why doesn't an electron in a high orbital (say n=2) give off the same energy when they jump to the n=1 energy level for all elements? why is there a difference in frequency depending on the element?
 
There is a Z in the formula for the energy of a given level, like n=1 an n=2. Z is the number of protons in the nucleus. So the frequency depends on the element.
 

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