In the quantum mechanical treatment of the hydrogen atom, the energy depends on the principal quantum number n but not on the values of l or m_l.

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This is true because in the hydrogen atom, the energy depends only on the principal quantum number n, which determines the average distance of the electron from the nucleus. The values of l and m do affect the shape and orientation of the electron cloud, but do not affect the energy. This is because the hydrogen atom is spherically symmetric, so there is no preferred direction in space.

In the Quantum Mechanical Treatment of the Hydrogen Atom, the Energy