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If you get a negative value when calculating the Energy difference, then that means that the electrons went from a higher energy level(n) to a lower energy level(n) and therefore are losing energy. If they're losing energy, that would mean that the atom will EMIT light.
the E resulting from this equation should be negative because you are going from a higher E level to a lower E level, during which E is given off as light, so the loss of E as photons are expressed through the negative sign
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