What is the significance of the quantum number n in atomic physics?

The quantum number n, known as the principal quantum number, plays a pivotal role in atomic physics as it primarily determines the energy level and size of an atomic orbital.

In the context of an atom, the principal quantum number can take positive integer values (1, 2, 3, etc.), and as n increases, the energy level of the electron increases as well. This means that electrons in higher energy levels are found further away from the nucleus, corresponding to larger atomic orbitals. Thus, n directly influences both how much energy an electron has and its average distance from the nucleus, which affects the atom's overall size and energy structure.

Understanding this quantum number is integral because it lays the foundation for further concepts in quantum mechanics and atomic structure, including the calculation of other quantum numbers, electron configurations, and the behavior of electrons within different elements.