Question

Explain in your own words what is meant by (a) the Pauli exclusion principle. (b) Hund's rule. (c) a line in an atomic spectrum. (d) the principal quantum number.

Short answer

Question: Briefly explain the Pauli Exclusion Principle and its significance in atomic structure. Answer: The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers. This principle is responsible for the arrangement of electrons in different orbitals and energy levels within atoms, limiting the number of electrons that can occupy a specific energy level or orbital. This leads to the structure of the periodic table and is crucial for understanding the electronic configuration of elements.

Step-by-step solution

(a) Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers. This principle is responsible for the arrangement of electrons in different orbitals and energy levels within atoms. It can be understood by the fact that electrons are fermions, a type of particle that obeys the exclusion principle. In practice, this principle limits the number of electrons that can occupy a specific energy level or orbital and leads to the structure of the periodic table.

(b) Hund's Rule

Hund's Rule is an empirical rule that describes the order in which electrons fill the orbitals within a specific energy level. It states that for a collection of orbitals with the same energy (degenerate orbitals), electrons will first occupy these orbitals one at a time, with the same spin, before beginning to pair up. This maximizes the total spin (and hence, total angular momentum) of a multi-electron atom, which in turn makes the atom more stable energetically. In practice, when filling electron configurations, this means that you should place one electron in each degenerate orbital before doubling up.

(c) Line in an Atomic Spectrum

A line in an atomic spectrum represents a specific transition of electrons between energy levels in an atom. When an electron moves from a higher energy level to a lower energy level, energy is released in the form of a photon with a specific wavelength. This results in a line at that specific wavelength in the atomic spectrum, which can be observed using a spectrometer. These lines are unique for each element and can be used to identify the presence of the element in samples or to study the electronic structure of the atom.

(d) Principal Quantum Number

The principal quantum number, denoted by the letter 'n', is an integer value (n = 1, 2, 3, ...) that represents the main energy level of an electron in an atom. It is one of the four quantum numbers used to describe an electron's state in an atom, and it is related to the size and energy of the electron's orbital and energy level. As the principal quantum number increases, the energy of the electron also increases, as well as the average distance from the nucleus. The principal quantum number essentially determines the electron shell in which an electron is present and is crucial for understanding the electronic structure of an atom and the periodic table.