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There are spaces in the atomic spectrum of hydrogen because there are discrete energy levels that the electron in the hydrogen atom can be located in. Generally speaking the further away from the nucleus, the higher the potential energy of the electron. When hydrogen gas is excited, the electron can jump up to higher energy levels. When that electron falls back down to a lower energy level, a photon is emitted with an energy equal to the energy difference between the atomic orbital it jumped from and the one it jumped to. Since excited electrons can make a number of different jumps (ex. 4->3, 4->2, 5->3, 5->2, etc) there are a series of photons given off with discrete energies. Each one of these photons has a distinct wavelength (given by the equation E=hf, where E is the energy of the photon, h is planck's constant and f is the frequency of the photon). Each line you see on the spectrum is a photon produced from a different energy jump, with a different wavelength. We are only able to see the photons that emit a wavelength in the visible spectrum (roughly 400-700 nm).

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Q: Why there are discontinous spaces between spectrum of hydrogen?
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