The atomic orbitals are progressively filled in order of increasing energy. The principle is called as: (a) Hund's rule (b) Aufbau principle (c) Exclusion principle (d) de-Broglie rule

Atomic orbitals are fundamental components in the structure of an atom. Imagine them as 'homes' where electrons reside. Each orbital can house a maximum of two electrons and exhibits a unique shape and energy level, which determines where electrons are most likely to be found at any given time.

Electrons fill these orbitals according to certain rules that guide their placement. The most basic type of orbitals are s, p, d, and f, each with a different shape, such as spherical for s orbitals and dumbbell-shaped for p orbitals. Understanding these orbitals is vital because they establish the ground for more complex principles such as the Aufbau principle, Hund's rule, and the Pauli Exclusion Principle, helping us determine the electronic structure and properties of an atom.

Hund's rule is a bit like a guideline for electrons when they're moving into their 'orbital homes'. When faced with a set of orbitals of equal energy (known as degenerate orbitals), Hund's rule suggests that electrons will first fill these orbitals singly, and with parallel spins, before pairing up.

This is akin to passengers filling up all the window seats on a bus before anyone sits in the middle seats. This arrangement is due to electrons repelling each other and consequently, they will spread out before pairing. This rule is essential for predicting the electronic configuration of an atom, especially when it involves multiple electrons occupying the same subshell.

Think of the Pauli Exclusion Principle as a strict dorm room policy: no two roommates can be completely alike. In electron terms, this means that no two electrons in an atom can have identical sets of quantum numbers; they must have at least one differing quantum number, which is often their spin.

This principle not only plays a critical role in determining the electron structure of an atom but also lays the foundation for many physical and chemical properties of elements. Electrons having opposite spins allow them to share an orbital without defying this rule, which is integral to filling atomic orbitals.

Quantum numbers are the address system for electrons within an atom. There are four types of quantum numbers: the principal quantum number (n), which indicates the main energy level; the angular momentum quantum number (l), relating to the shape of the orbital; the magnetic quantum number (m_l), which specifies the orientation of the orbital; and the spin quantum number (m_s), denoting the direction of the electron's spin.

Together, these numbers allow us not just to pinpoint an electron's location but also to understand the complex electron arrangements and behaviors. The interplay of quantum numbers with the principles of electron configuration is vital for comprehending the periodic table and the reactivity of elements.