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The negative sign means that the bound electron has a lower energy value that a free electron, and in the calculations the sign is negative because energy is released and decreasing as a result of the reaction. The distinction does matter and it is important to ensure that ΔE is calculated using the final minus the initial n level.
Since the electron is decreasing in energy levels, it is losing energy and therefore would have a negative value. However, as it decreases in energy level it releases a photon which has a positive value in order to offset the previous negative values since energy can neither be created nor destroyed.
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