#### Lecture17

CUNY Baruch, PHYSICS 330
Excerpt: ... Physics 330 Lecture #17 Quantum Mechanical Description of Atoms (IV) Dr. Yuhang Ren (1204 HN) yre@hunter.cuny.edu Atomic Physics Atomic Structure and the Periodic Table Total Angular Momentum Dimitri Mendeleev What distinguished Mendeleev was not only genius, but a passion for the elements. They became his personal friends; he knew every quirk and detail of their behavior. - J. Bronowski Atomic Structure and the Periodic Table What if theres more than one electron? Helium: a nucleus with charge +2e and two electrons, the two electrons repelling one another. Cannot solve problems exactly with the Schrdinger equation because of the complex potential interactions. Can understand experimental results without computing the wave functions of many-electron atoms by applying the boundary conditions and selection rules. Pauli Exclusion Principle We now want to start building more complicated atoms to study the Periodic Table. For atoms with many electrons (e.g., carbon: 6, iron: 26, etc.) - what energie ...

#### Exam 2 practice problems and review

University of Illinois, Urbana Champaign, PHYS 485
Excerpt: ... e to sketch the radial and angular wavefunctions up to n=4 Angular momentum in hydrogen Magnetism (Chapter 8) Electron spin and magnetic moment the spin orbit effect o total angular momentum: understand how and add to form o allowed values of j o energy shift (Dirac formula) Allowed transitions between states, including fine structure Exchange symmetry (Chapter 9) Fermions and bosons Allowed wavefunctions for fermions and bosons Pauli exclusion principle ...

#### Lecture 4 Notes 53750

University of Texas, CH 53750
Excerpt: ... ssign a spin = +1/2 (spin up). If clockwise, we assign a spin = -1/2 (spin down). The spin quantum number is designated ms. This is the fourth (and last) quantum number. This is the basis for the Aufbau order of filling rules, and ultimately determines the structure of the periodic table. Pauli Exclusion Principle The Pauli Exclusion Principle was formulated by Austrian physicist Wolfgang Pauli around 1926, concerning findings concerning the electron's spin. The Pauli Exclusion Principle states, In a given atom, no two electrons can have the same set of four quantum numbers. What this means is that in assigning electrons their quantum address, you cannot place two electrons with the same spin into an orbitalthey must be of opposite spins! This is a very fundamental feature of nature. Protons do not have this same restriction. Example Problem: If you were trying to assign two electrons to a 3d suborbital (let ml be 0), one electron would have the address n = 3, l = 2, ml = 0, and ms = +1/2, and the ot ...

#### spin3

University of Florida , PHY 3101
Excerpt: ... PHY3101 Modern Physics Lecture Notes Spin 3 Bose-Einstein Condensates Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study ...

#### lecture 10

Ohio State, CHEM 121
Excerpt: ... 10 20 30 40 50 60 70 80 0 09. 99 1st midterm distribution Average: 129 out of 175 20 -2 9. 99 40 -4 9. 99 60 -6 9. 99 80 -8 9. 99 10 010 9. 99 12 012 9. 99 14 014 9. 99 16 016 9. 99 Lecture 10, Oct. 23 Chapter 6. Electronic Structure of Atoms (continued) Reading: section 5-8 Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers Representations of Orbitals Representations of Orbitals The p-Orbitals Orbitals and Their Energies Many-Electron Atoms Many-Electron Atoms Electron Spin and the Pauli Exclusion Principle ...

#### lecture21

Rutgers, PHYSICS 361
Excerpt: ... Quantum Mechanics and Atomic Physics Lecture 21: Pauli Exclusion Principle and Multi-electron Atoms http:/www.physics.rutgers.edu/ugrad/361 Prof. Eva Halkiadakis Last Week Spin-Orbit Coupling Total Angular Momentum Land g-factor "The" magnetic moment Animation - Zeeman Effect http:/phys.educ.ksu.edu/vqm/free/zeemanspec.html Hyperfine Structure Proton and neutrons are also spin 1/2 particles So nuclear spin angular momentum can interact with the electron's J to split each Dirac energy level into two! But . it's a very tiny effect Because mproton > melectron This has only been observed for a few states of a few atoms Hyperfine splitting is ~ 10-6 - 10-7 eV Hyperfine structure in Hydrogen In Hydrogen the hyperfine structure of the ground state has been observed only in astronomic measurements, not in labs! The electron and proton spins can be parallel and antiparallel The antiparallel has slightly lower energy: E ~ 6 x 10 -6 eV A spin flip transition can occur, emittin ...

#### Lect13

University of Illinois, Urbana Champaign, PHYS 214
Excerpt: ... ccording to thePauli e tate s any le d xclusion principle q Review session Sunday Extra office hours (TBA) Re at from pe Le 12 ct. Let's start building more complicated atoms to study the Periodic Table. For atoms with many electrons (e.g., carbon: 6, iron: 26, etc.) - what energies do they have? Pauli Exclusion Principle Fromspe of com x atom Wolfgang Pauli (1925) de d a ne rule ctra ple s, duce w : " Pauli Exclusion Principle " "No two e ctrons* can bein thesam quantumstate i.e in a give atomthe cannot have le e , . n y thesam se of quantumnum rs n, l, m, m" e t be l s - i.e e ry atom orbital with n,l,m can hold 2 e ctrons: ( ) ., ve ic le l q The fore e ctrons do not pileup in thelowe e rgy state i.e the(1,0,0) orbital. re , le st ne , , q The aredistribute am y d ong thehighe e rgy le ls according to thePauli Principle r ne ve . q Particle that obe thePauli Principlearecalle "fe ions" s y d rm *Note Morege rally, no two ide : ne ntical fe ions (any particlewith spin of 3 e rm /2, /2, tc.) can bei ...

#### p3223_25

Southern Oregon, P 3223
Excerpt: ... Physics 3223 Lecture 25 November 5, 1999 1 Hund's Rule For the different combinations of L and S for a given single-electron configuration, how do we determine which is the lowest energy state, the ground state? Hund's rule give the recipe: 1. First find the maximum value of MS consistent with the Pauli Exclusion Principle ; then, S = MS,max . (1) 2. Then, for that MS , find the maximum value of ML consistent with the Pauli Exclusion Principle ; then L = ML,max . (2) 1.1 Examples For carbon, as we have seen, the 2p2 electrons can combine to form S = 0, S = 0, S = 1, L = 0, L = 2, L = 1, (3) The ground state is the S = 1, L = 1 state. 1 For praseodymium, the ground state single-electron configuration is Pr : [Xe]6s2 4f 3 , (4) which means that we have three l = 3 electrons in an unfilled subshell. Because each of these electrons can have a different ml value, there is no restriction of the value of MS , so the largest value of MS is 3/2, and so S = 3/2. Now if those three electrons are in the state i ...

#### Lec-10-Chap-07-2P

SUNY Stony Brook, CHE 131
Excerpt: ... Lecture 10 Electron Configuration and the Periodic Table Beyond the Bohr Model: The Quantum Mechanical Model of the Atom 7.4 Quantum Numbers, Energy Levels, and Orbitals 7.5 Shapes of Atomic Orbitals 7.6 Atom Electron Configurations (I) 7.7 Lecture 10, Knowledge and Skills Know about and work with the wave nature of moving matter Know the meaning of the Heisenbergs uncertainty principle Know and work with Schrdingers wave mechanical model of the hydrogen atom (and other atoms) Know the meaning of the term electron orbital Know the quantum numbers, n, l, ml, ms Significance of quantum numbers Know the shapes of orbitals: s, p, d Know about the internal structure of orbitals (nodes) Know the relative orbital energies Know the Pauli exclusion principle Know Hunds rule Determine the electron configuration of many-electron atoms Beyond the Bohr Model: Quantum Mechanics De Broglie (1924): All moving objects act as waves = h mv Electrons move in atom ...

#### Chapter 7 Atomic Structure and Electron Config...

STLCOP, HIST 101
Excerpt: ... screte(allowed) energy states(levels). 2. Whenever an electron changes states in an atom it can only do so by absorbing or emitting a discrete amount of energy-just the amount needed to get to the next state. -88- 3. The allowed energy states of electrons in atoms can be described by sets of numbers called quantum numbers. E. Results for hydrogen atoms 1. Wave functions -89- 2. Quantum numbers a. Principal - n b. Secondary - l -90- c. Magnetic - ml -91- 3. Orbitals a. Plots of radial distribution functions b. Plots of angular distribution functions -92- -93- 4. Energy level diagram for hydrogen F. Results for multi-electron atoms 1. The fourth quantum number - spin - s 2. Pauli Exclusion Principle -94- CHAPTER 8 G. Electron configurations for atoms 1. Aufbau Principle a. Electrons enter and fill the empty orbitals of lowest available energy first. b. No two electrons in the same atom can have al ...

#### lecture19

Maryville MO, PHYS 3150
Excerpt: ... Physics 3150 Winter 2009 Introduction to Modern Physics Prof. Ioan Kosztin Lecture #19 Atomic Physics Hydrogenoid atoms Orbital magnetism and the normal Zeeman effect The spin of the electron and the anomalous Zeeman effect The Stern-Gerlach experiment The spin-orbit interaction and the fine structure of atoms Exchange interaction and the Pauli exclusion principle The energy levels of multi electron atoms The self consistent field method and the periodic table Exchange interaction Heisenberg uncertainty principle in QM identical particles are indistinguishable electron 2 (1, 2 ) = e i (2, 1 ) electron 1 (r, s ) e 2i = 1 e i = 1 Bosons: (integer spin) Exchange symmetry Fermions: (semi integer spin) (1, 2 ) = (2, 1 ) (1 , 2 ) = (2, 1 ) 1 Paulis Exclusion Principle Two identical fermions (e.g., electrons) cannot occupy the same single particle state, i.e., they cannot have ...

#### Lecture 01

SUNY Stony Brook, PHY 431
Textbook: Introductory Nuclear Physics
Excerpt: ... ples e,e, , , n,p,. ,', ,K*, J/,', . EM EM Forces Weak Weak Strong The fermionic character of leptons and quarks is essential in the building of atoms and of hadrons: the Pauli exclusion principle forbids identical fermions to co-exist. The Pauli exclusion principle follows from the fact that a wavefunction describing a system of fermions must be fully anti-symmetric under interchange of the coordinates of any pair of fermions. Thus, if two fermions are in the same state and therefore are indistinguishable, then under interchange the wavefunction stays the same, while at the same time it must also equal its opposite (be anti-symmetric), and therefore it must vanish. For bosons the situation is completely different: the wavefunction of a system of bosons is symmetric under coordinate interchange, and thus many bosons can occupy the same quantum state. Conservation Laws A mechanical system can be described by a Lagrangian that fully defines the system and its interactions. The equati ...

#### e2-notes

Georgia Tech, CHEM 1310
Excerpt: ... CHEM 1310: General Chemistry Sections L & M EXAM #2 Study Guide (covering Chemical Principles Chapters 12-13, and 16-17) Chapter 12: Quantum Mechanics and Atomic Theory Characteristics of electromagnetic radiation (Section 12.1) Relationship between energy and wavelength (Section 12.2) Quantum Mechanical Description of the Atom (Section 12.5) o What is quantum mechanics? o Heisenbergs Uncertainty Principle What information do we get from solutions to the Schredinger Equation? Quantum Numbers as described in Section 12.9 What is the Pauli Exclusion Principle (Section 12.10)? What is the Aufbau Priniciple and how is it used (Section 12.13)? What are some trends relating to atomic properties that we find in the Periodic Table (Section 12.15)? o Ionization Energy o Electron Affinity o Atomic Radius Chapter 13: Bonding General Concepts What is electronegativity and what electronegativity trend is observed in the Periodic Table? Know what a bond polarity is and how to recognize a polar bond Know what a di ...

#### 3-23

Wisc Eau Claire, PHYS 229
Excerpt: ... Physics 229 Lecture Outline for March 23 Today's lecture will cover what happens to a star when after it has burned through its hydrogen. We will discuss core and shell fusion, determine main sequence lifetimes, and explain helium flash. Sections in the text that coincide with today's lecture are 19.12. After today's lecture you should be able to: Understand why the luminosity and temperature of main sequence stars is not constant Calculate the main sequence lifetime of a star given its mass Know why shell burning happens Know the conditions required for helium burning Understand the role quantum degeneracy plays in stellar cores Main sequence evolution Main sequence lifetimes Shell burning Helium burning Triple alpha process Pauli Exclusion Principle and degeneracy Helium flash ...

#### 244lec19

Wisconsin, PHYS 244
Excerpt: ... )1/2 = (32n)1/3, which is typically an angstrom or so in metals, and maybe 100 angstroms in doped semiconductors (where it is controlled by doping). Fermi function What about at finite temperatures? Can we use the Boltzmann factor, that the probability of occupation of a quantum state is A exp(-E/kT) ? The answer is clearly no. A grows to be very big at low temperatures, but the Pauli exclusion principle says that the occupation of a state can only be 0 or 1. So the Boltzmann distribution would violate this quantum principle. It needs to be modified slightly. The Boltzmann distribution can be written as FB(E) = 1 / [(1/A) exp(E/kT)], where the normalization constant A depends on the total number and the temperature, as we saw before. The modification is to add a +1 to the denominator, and the correct occupation function for electrons is the Fermi-Dirac distribution: fFD(E) = 1/ [(1/A)exp(E/kT) +1]. Since A and exp(E/kT) are always positive, this is always less than 1, as required. The normalization constant ...

#### what_final

New Mexico, PHYS 330
Excerpt: ... Physics 330 What is on the final? May 11, 2005 1 HOW TO STUDY: Review all homework and exam solutions. As time permits, do extra problems from the textbook in chapters 1-8. 1. special relativity: Lorentz contraction time dilation relativistic energy momentum conservation of energy and momentum lorentz transformation (boost) boost to the center-of-momentum frame. 2. One dim quantum mechanics: time-independent Schrodinger equation superposition principle collapse postulate particle in a box 1d scattering tunneling harmonic oscillator, 3. Hydrogen atom: quantum numbers n, , m , ms degeneracy addition of angular momentum multiplets of total angular momentum spin-orbit interaction Pauli exclusion principle and multi-electron atoms 4. quantum statistics density of states statistical distributions: Maxwell Boltzmann, Fermi-Dirac, BoseEinstein, Photons ...

#### lecture1

University of Florida , CHM 2210
Excerpt: ... CHM 2210 Lecture One January 9, 2009 Concepts Atomic Structure Protons, neutrons and electrons Aufbau Principle, Hunds Rule, Pauli Exclusion Principle Electrons Duality of Particle and Wave Function concepts Valence Electrons Lewis Dot Structures Delocalization Chemical Bonding Ionic vs. Covalent Electronegativity Dipole Moments (effect on reactivity) Polar vs. Non-Polar bonds The Octet Rule The Language of Organic Chemistry Know how to determine the. 1. Empirical Formula 2. Molecular Weight 3. Molecular Formula 4. Condensed Structural Formula 5. Lewis Structure 6. Line Angle Formula 7. Three-Dimensional Structure (purchase model kit. Inexpensive on-line.) ...

#### Chapter 6 Outline

Clayton, CHEM 1211
Excerpt: ... Dr. Caroline Clower Chemistry 1211 Chapter 6: Electronic Structure of Atoms Lecture Outline I. The Nature of Light A. Light as a Wave 1. Frequency 2. Wavelength 3. Amplitude B. Light as a Particle C. Atomic Spectra The Hydrogen Atom A. Bohr Model B. Quantum Mechanical Model Electronic Structure of Atoms A. Atomic Orbitals 1. Quantum Numbers a. Principal b. Angular Momentum c. Magnetic d. Electron Spin 2. Pauli Exclusion Principle 3. Size/Shape 4. Energy Levels B. Electron Configurations and Orbital Diagrams 1. Aufbau Principle 2. Hund's Rule 3. Magnetic Properties 4. Group Similarities 5. Ions 6. Transition Metals II. III. ...