The principal quantum number, symbolized as n, is the first of a set of quantum numbers (which includes: the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) of an atomic orbital. The principal quantum number can only have positive integer values. As n increases, the orbital becomes larger and the electron spends more time farther from the nucleus. As n increases, the electron is also at a higher potential energy and is therefore less tightly bound to the nucleus. This is the only quantum number introduced by the Bohr model.
For an analogy, one could imagine a multistoried building with an elevator structure. The building has an integer number of floors, and a (well-functioning) elevator which can only stop at a particular floor. Furthermore the elevator can only travel an integer number of levels. As with the principal quantum number, higher numbers are associated with higher potential energy.
Beyond this point the analogy breaks down; in the case of elevators the potential energy is gravitational but with the quantum number it is electromagnetic. The gains and losses in energy are approximate with the elevator, but precise with quantum state. The elevator ride from floor to floor is continuous whereas quantum transitions are discontinuous. Finally the constraints of elevator design are imposed by the requirements of architecture, but quantum behavior reflects fundamental laws of physics.
Read more about Principal Quantum Number: Derivation
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