As we continue to increase the available energy levels as shown by the principal quantum number and more electrons are added, the number of lines in the emission spectrum continues to increase.
What is a spectrum?
Following the Bohr model of the atom, We could have electrons travel from a higher to a lower energy level . Thus ow leads to the emission of light of a characteristic wavelength. This line is what constitutes the emission spectrum of an atom.
If is clear from the image attached to this answer that as we continue to increase the available energy levels as shown by the principal quantum number and more electrons are added, the number of lines in the emission spectrum continues to increase.
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