Quantum Numbers PDF

Apply Quantum Mechanics to Chemistry A total of four quantum numbers are used to describe completely the movement and trajectories of each electron within an atom. The combination of all quantum numbers of all electrons in an atom is described by a wave function that complies with the Schrödi...

Apply Quantum Mechanics to Chemistry A total of four quantum numbers are used to describe completely the movement and trajectories of each electron within an atom. The combination of all quantum numbers of all electrons in an atom is described by a wave function that complies with the Schrödinger equation. Each electron in an atom has a unique set of quantum numbers….according to the Pauli Exclusion Principle. Quantum numbers are important because they can be used to determine the electron configuration of an atom and the probable location of the atom's electrons. QUANTUM MECHANICS- science dealing with the behavior of matter and light on the atomic and subatomic scale. The fundamental equation of the science of submicroscopic phenomena known as quantum mechanics. Essentially a wave equation describes the form of the probability waves that govern the motion of small particles, and it specifies how these waves are altered by external influences. The Pauli exclusion principle states that in a single atom, no two electrons will have an identical set or the same quantum numbers (n, l, ml, and ms). There are two salient rules that the Pauli exclusion principle follows: Only two electrons can occupy the same orbital. The two electrons that are present in the same orbital must have opposite spins, or they should be antiparallel. THE PRINCIPAL QUANTUM NUMBER (n) - describes the energy of an electron and the most probable distance of the electron from the nucleus. THE NUMBER OF SUBSHELLS (l) - describes the shape of the orbital. THE MAGNETIC QUANTUM NUMBER (ml) describes the energy levels in a subshell, SPIN QUANTUM NUMBER (ms) - refers to the spin on the electron, which can either be up or down.  n , designates the principal electron shell. Because n describes the most probable distance of the electrons from the nucleus, the larger the number n is, the farther the electron is from the nucleus, the larger the size of the orbital, and the larger the atom is. n can be any positive integer starting at 1, as n=1 designates the first principal shell (the innermost shell).  When an electron is in an excited state or it gains energy, it may jump to the second principle shell, where n=2. This is called absorption because the electron is "absorbing" photons, or energy. Known as emission, electrons can also "emit" energy as they jump to lower principle shells, where n decreases by whole numbers.  also known as angular momentum or orbital quantum number, describes the shape of the subshell in which the electron is present. It determines the magnitude of the electron’s angular momentum around the atom. Its values are whole numbers ranging from 0 to n – 1. For example, when n = 4, l = 0, 1, 2, 3. The various values of l represent the orbitals in which the electrons reside. The allowed subshells under different combinations of ‘n’ and ‘l’ are listed above. It can be understood that the ‘2d’ orbital cannot exist since the value of ‘l’ is always less than that of ‘n’. sharp, principle, diffuse, and fundamental The magnetic quantum number describes the split in the electron’s energy sublevel into two or more levels. It is used to project the angular momentum along a specific axis. For example, nitrogen has five electrons in its valence shell. Two are in the 2s-orbital and three are in the 2p- orbitals corresponding to l = 0 and l = 1, respectively. Therefore, the magnetic quantum number for l = 1 takes 2.1 + 1 = 3 values. These values and their corresponding orbitals are indicated as follows.  The spin quantum number represents the electron’s spin. It is used to project the spin angular momentum along a specific axis. When ms = +1/2, the electron is in “spin-up” state In a magnetic field, an electron has two possible orientations with different energies, one When ms = -1/2, the electron is in with spin up, aligned with the magnetic field, “spin-down” state and one with spin down, aligned against it. According to Pauli exclusion principle…. The number of values of the orbital angular number l can also be used to identify the number of subshells in a principal electron shell:  The number of orbitals in a subshell is equivalent to the number of values the magnetic quantum number ml takes on. A helpful equation to determine the number of orbitals in a subshell is 2l +1 This equation will not give you the value of ml, but the number of possible values that ml can take on in a particular orbital. For example, if l=1 and ml can have values -1, 0, or +1, the value of 2l+1 will be three and there will be three different orbitals. In general, both energy and radius decrease as the nuclear charge increases. Thus the most stable orbitals (those with the lowest energy) are those closest to the nucleus. Subshell Electrons s 2 p 6 d 10 f 14 Questions: 1. How many subshells are possible for n = 3? What are they? 2. State the number of electrons and orbitals that can occupy each subshell. a. 2s b. 3p c. 4d d. 6f  The electron configuration of an element is the arrangement of its electrons in its atomic orbitals. By knowing the electron configuration of an element, we can predict and explain a great deal of its chemistry. 3 Let’s Try: Complete the table: Electron Element (n) Configuration Orbital Notation Potassium Sulfur Chlorine  This principle is named after the German word ‘Aufbeen’ which means ‘build up’. The Aufbau principle dictates that electrons will occupy the orbitals having lower energies before occupying higher energy orbitals. Exceptions to the Aufbau principle… Although the Aufbau rule accurately predicts the electron configuration of most elements, there are notable exceptions among the transition metals and heavier elements.  Orbitals may have identical energy levels when they are of the same principal shell. These orbitals are called degenerate, or "equal energy.“ " According to Hund's Rule, electrons fill orbitals one at a time. This means that when drawing electron configurations using the model with the arrows, you must fill each shell with one electron each before starting to pair them up.  KEY TAKEAWAY There is a relationship between the motions of electrons in atoms and molecules and their energies that is described by quantum mechanics.