List the four different sub levels. Given that only a maximum of two electrons can occupy an orbital, determine the maximum number of electrons that can exist in each sub level.

The notion of atomic sublevels is key to understanding the intricate architecture of an atom's electrons. These sublevels are further divisions within the main energy levels or shells of an atom. They are designated as s, p, d, and f, each possessing a unique shape that influences the behavior of electrons within them.

The simplest, the s sublevel, has a spherical shape, allowing it to be present in all principal energy levels and consist of a single orbital. Moving on to the p sublevel, we encounter a dumbbell-like shape that is capable of housing three orbitals. It begins to appear in the second principal energy level. The more complex d sublevel, with its cloverleaf shape, enters the scene at the third principal energy level and contains five orbitals. Last but not least, the f sublevel, which exhibits an even more intricate shape, has seven orbitals and is located in the fourth energy level and beyond.

Each of these sublevels serves as a 'home' for electrons, which can only reside in specified quantities within each sublevel's orbitals, dictated by fundamental quantum principles and the Pauli exclusion principle.

When dealing with the electron capacity of orbitals, it's essential to remember a simple yet fundamental rule: each orbital can hold up to two electrons. This rule is founded on the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers.

Let's visualize an orbital as a room with space for only two electrons. For the s sublevel, there is one such 'room', thus it can accommodate a total of 2 electrons. Expand this to the p sublevel, and you have three 'rooms', or orbitals, yielding a maximum of 6 electrons. In the case of the d sublevel, with five orbitals, up to 10 electrons can be hosted. Finally, the f sublevel, having seven orbitals, has the potential to hold a maximum of 14 electrons.

Understanding the spatial arrangement and capacities of these orbitals is pivotal not just for determining the electronic structure of the elements but also for predicting their chemical behavior and properties.

Quantum numbers are the DNA of an electron within an atom—they describe the electron’s unique state and position within the atom. There are four types of quantum numbers: principal (n), angular momentum (l), magnetic (m_l), and spin (m_s).

The principal quantum number, 'n', indicates the main energy level occupied by the electron. As 'n' increases, the electron's energy and its average distance from the nucleus also increase. The angular momentum quantum number, 'l', determines the shape of the orbital and the sublevel in which the electron resides. It can have values ranging from 0 to (n-1), where 'l' corresponds to the sublevels, with 0 for s, 1 for p, 2 for d, and 3 for f.

The magnetic quantum number, 'm_l', designates the orbital within a sublevel, with possible values between -l to +l, including 0. It dictates the orientation of the orbital in three-dimensional space. Lastly, the spin quantum number, 'm_s', specifies the electron's spin direction, which can either be +1/2 or -1/2. These quantum numbers are not just abstract concepts; they are imperative for chemists to predict the types of bonds that an electron can form and its reactivity in chemical reactions.