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The light emission spectrum for an element is discontinuous because
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In Bohr's Model of the atom, we suppose that an electron rotates around the nucleus in discrete, and not continuous, energy levels which have a fixed distance and a fixed energy. Light is emitted when an electron jumps from an outer energy level to an inner energy level. However, since the energy of each orbit is specified, the light spectrum will be in discrete steps, as the photons will have a fixed energy for a given electron jumping from one level to another.
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