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When we talk about the electron configuration of an atom, we are referring to the arrangement of the electrons in the atom's orbitals. Electrons are arranged according to increasing energy levels, filling from the lowest to the highest energy orbital available. The basic order of filling begins with the 1s orbital, then 2s, followed by 2p, 3s, and so on.

Each type of orbital can hold a set number of electrons; s orbitals can hold 2, p orbitals can hold 6, d orbitals can hold 10, and f orbitals can hold 14. This is crucial in understanding how to write the full orbital diagram for elements. Elements such as Nitrogen (N) with an atomic number of 7 will have an electron configuration of 1s² 2s² 2p³, arranging electrons first in the 1s orbital, followed by the 2s, and finally placing the remaining three electrons across the 2p orbitals.

Pauli's exclusion principle plays a pivotal role in how we fill these orbitals. It dictates that no two electrons in an atom can have the same set of four quantum numbers; essentially, an orbital can hold a maximum of two electrons and these electrons must have opposite spins.

This principle is represented in orbital diagrams by pointing arrows in opposite directions for two electrons occupying the same orbital. For example, in the 1s orbital of Nitrogen, you would draw two arrows, one pointing up and one pointing down, signifying two electrons with opposite spins. The proper implementation of this principle ensures that each electron has a unique quantum state, which is vital for the resulting chemical properties of the element.

The atomic number of an element, denoted by the letter Z, is defined as the number of protons found in the nucleus of an atom, and by extension, it also equals the number of electrons in a neutral atom. The atomic number is fundamental when determining the electron configuration of an element.

Every element in the periodic table has a unique atomic number, guiding us on how many electrons we need to distribute in the orbitals. For instance, the atomic number of Magnesium (Mg) is 12, signifying 12 electrons need to be placed in the orbitals according to the rules of electron configuration and Pauli's exclusion principle. Following the specific order of filling, the 12 electrons of Magnesium will occupy the 1s, 2s, 2p, and 3s orbitals, illustrating the direct relationship between an element's atomic number and its electron configuration.