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When Bohr's model of the H atom was established, free electrons (not part of the atom) were considered to have 0 energy. Electrons closer to the nucleus have less energy than those that are farther away. Since free electrons are the farthest away (n=∞) and have 0 energy then in comparison electrons closer to the nucleus (n=1,2,3,4...∞) must have lower energy so they are given negative energy values.
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