CHEM 101 1st Edition Lecture 18Outline of Last Lecture I. Bohr Model of the AtomII. Key TermsIII. Particle-Wave DualityOutline of Current Lecture I. The Schrödinger Wave EquationII. Electron SpinIII. Quantum NumbersIV. Pauli Exclusion PrincipleV. Hund’s RuleCurrent Lecture Chapter 6: The Structure of Atoms- The Schrödinger Wave Equation o Erwin Schrödinger: Electrons in atoms can be described as a wave in a model called quantum mechanics or wave mechanics. In this comprehensive theory, the electron is treated as both a wave anda particle. And electron described by a wavefunction, Ψ, that completely defines a system of mattero Standing waves:- only certain vibrations are allowedo Node- a part of a wave in which a “string” stands stillo Max Born: The value of the wavefunction Ψ represents the amplitude (maximum) fthe electron matter wave (+ or -). Ψ^2 is the probability density (the probability of finding an electron in the region around the nucleus) If the energy of an electron is known, the position has a large uncertainty (Heisenberg)o The wavefunction Ψ for an electron describes a so called atomic orbitalo 1s Orbital radial distribution plot: 4 r^(2)π Ψ^(2)o Bohr Model: Orbits, energy levels described by n (principle quantum number)o Atomic Orbital Model: Orbitals, energy levels described by n and the ns orbitals (simplest example 1s for the hydrogen atom) Electrons having the same n value belong to the same electron shell The angular momentum quantum number l describes a subshell which characterize the shape of an orbital (l = 0,1,2,3…,n-1) For ;=1, these orbitals are called p subshell or p orbitals Value of l: Subshell Label: 0 s 1 p 2 d 3 f The magnetic quantum number ml is related to the orientation in space of the orbitals within a subshell. Orbitals within a subshell with different ml are degenerate (they are equal in their energy)Name: Principal Quantum Angular Momentum Magnetic Quantum Number Quantum Number Number OrbitalsSymbol: n l mlValues: 1,2,3,… 0,n-1 +1, 0, -1 l 1 0 0 1s l 2 0 0 2s l 3 0 0 3s 1 +1,0,-1 3x3p 2 +2, +1,0,-1,-2 5x3p 4 0 0 4s 1 +1,0,-1 3x4p 2 +2,+1,0,-1,-2 5x4d 3 +3,+2,+1,0,-1,-2,-3 7x4fo Each s orbital have 0 nodal planes (l=0) o Each p orbital is characterized by one nodal plane (l=1)o Each d orbital (except from dz2) have 2 nodal places (l=2)o Each f orbital has 3 nodal planes (l=3)- Electron Spino The Stern-Gerlach Experiment: Source of silver atoms When an atom with one unpaired electron is passed through a magneticfield (usually in the gas phase), the path is altered into two (and only two) directions.o The electron spin is quantizedo The electron spin quantum number ms represents the 4th quantum number If ms = ½ then spin is counterclockwise and upward If ms = - ½ then spin is clockwise and downwardo Diamagnetic substances aren’t attracted to a magnetic fieldo Paramagnetic substances are attracted to a magnetic fieldo Substances with unpaired electrons are paramagnetico Behavior of substances in an electromagnetic balance: If a sample sealed in a glass tube is surrounded by a magnet to surroundan electromagnetic field and this field is turned on, the sample gets heavier.Chapter 7: Periodic Trends- Quantum Numberso Electrons in an atom are arranged by The principal quantum number (n)- Shells The angular momentum quantum number (l)- Subshells The magnetic quantum number (ml)- Orbitals The electron spin quantum number (ms)- Spin state- Pauli Exclusion Principleo No more than two electrons can occupy the same orbital, and, if there are two electrons in the same orbital, they must have opposite spins.o Two electrons of the same atom can’t have the same set of four quantum numbers (n, l, ml, and ms).o Ex: n=1, l=0:This shell has a single orbital (1s) to which 2 electrons can be assignedo Ex: n=2, l=0, 1:2s orbital: 2 electrons+3x2p orbitals: 6 electrons 8 electronso Ex: n=4, l=0, 1, 2, 3:4s orbital: 2 electrons3x4p orbitals: 6 electrons5x4d orbitals: 10 electrons7x4f orbitals: 14 electrons 32 electrons- Hund’s Ruleo Degenerate orbitals are filled with electrons until all are half-filled before pairing up of electrons can occuro Ex: the degenerate 2p orbitals- Subshell Energy Levels___8s___ ___ ___ ___7s 7p___ ___ ___ ___ ___ ___ ___ ___ ___6s 6p 6d___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___5s 5p 5d 5f___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___4s 4p 4d 4f___ ___ ___ ___ ___ ___ ___ ___ ___3s 3p 3d___ ___ ___ ___2s 2p___1so In a hydrogen atom (q electron) the orbitals of a subshell are equal in energy
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