Why are atomic spectra of an element discontinuous?
Quick answer: Atomic spectra are continuous because the energy levels of electrons in atoms are quantized.
The electrons in an atom can have only certain energy levels. There is no middle ground.
If an electron is excited to a new energy level, it jumps to that level instantaneously.
When it returns to a lower level, it releases energy in a quantized packet.
This release occurs in the form of light of a specific wavelength (colour). Hence, atomic emission spectra represent the electrons returning to lower energy levels.
Each packet of energy corresponds to a line in the atomic spectrum. There is nothing between each line, so the spectrum is discontinuous.