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Because n=1 is the smallest orbital and orbital size increases with increased energy. The orbital number represents the amount of energy released when the electron moves from being a "free" electron to the orbital it occupies. The more energy is released the lower the energy ends up being and the closer the electron is to the nucleus and the smaller the orbital.
It helps to think of the diagram that Professor Lavelle draws within class with n = 1 on the bottom followed by n = 2 and so forth. n = 1 is the lowest on the diagram meaning there is no energy for it to lose, emit as a photon, thus it is the lowest energy state.
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