1 Introduction to quantum mechanics Lecture 3 MTX9100 Nanomaterjalid OUTLINE -What is electron particle or wave? - How large is a potential well? -What happens at nanoscale?
2 What is inside? Matter Molecule Atom Nucleus Baryon (Hadron) Quark u 10-2 m 10-9 m m m m <10-19 m Condensed matter/nano-science/chemistry Atomic Physics Nuclear Physics protons, neutrons, mesons, etc. π,ω,λ... Electron (Lepton) <10-18 m top, bottom, charm, strange, up, down High Energy Physics
3 Quantum mechanics milestones the Bohr atomic model Each energy level or shell is represented by the principal quantum number n the ground energy for the hydrogen atom is 13.6 ev Electron energy states for a hydrogen atom
4 Quantum mechanics basics The simplified Bohr atomic model, in which electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and the position of any particular electron is more or less well defined in terms of its orbital. The energies of electrons are quantized; electrons are permitted to have only specific values of energy. If an atom is in one of the excited states E1, E2, and so on, it does not remain in that state forever. Sooner or later it drops to a lower state and radiates energy in the form of light. The frequency of light υ that is liberated in a transition, for example, from energy E3 to energy E1, h is Planck s constant
5 Quantum mechanics milestones Between 1900 and 1925 Quantum Physics was developed by a number of physicists, including Planck, Einstein, Bohr and de Broglie. Werner Heisenberg and Erwin Schrödinger, founders of Quantum Mechanics -Wikipedia From 1925 onwards a more mathematical approach was developed by Schrödinger (wave mechanics), Heisenberg (matrix mechanics) and Dirac (who developed a more general formulation). If you are not confused by Quantum Physics then you haven't really understood it. N.Bohr
6 Quantum mechanics basics (2) Quantum mechanics is the study of mechanical systems whose dimensions are close to the atomic scale. Quantum mechanics is a fundamental branch of physics with wide applications. Quantum theory generalizes classical mechanics to provide accurate descriptions for many previously unexplained phenomena such as black body radiation and stable electron orbits. The effects of quantum mechanics become evident at the atomic and subatomic level, and they are typically not observable on macroscopic scales. - Wikipedia
7 What is quantum mechanics good for? Atoms are governed by the laws of quantum mechanics, and quantum mechanics is essential for an understanding of atomic physics. The interactions between atoms are governed by quantum mechanics, and so an understanding of quantum mechanics is a prerequisite for understanding the science This information enables us to calculate the average value of the measurement of a physical variable. Quantum mechanics does not explain how a quantum particle behaves. Instead, it gives a recipe for determining the probability of the measurement of the value of a physical variable (e.g. energy, position or momentum).
8 Wave-particle duality In physics and chemistry, wave particle duality is the concept that all matter and energy exhibits both wave-like and particle-like properties. Particles are waves, waves are particles. Probability distribution of the Bohr atom Wikipedia In quantum mechanics, the motion of particles is described with probabilities. 8
9 Exclusion principle The exclusion principle says that two electrons cannot get into exactly the same energy state. In other words, it is not possible for two electrons to have the same momentum, be at the same location, and spin in the same direction.
10 How many quantum numbers? Using wave mechanics, every electron in an atom is characterized by four parameters called quantum numbers. 10 The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by the n quantum number. Schrödinger's model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found. The three coordinates that come from Schrödinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.
11 Quantum numbers The principal quantum number (n) describes the size (distance of an electron from the nucleus) of the orbital. Orbitals for which n = 2 are larger than those for which n = 1. The principal quantum number therefore indirectly describes the energy of an orbital. The angular quantum number (l) describes the shape of the orbital. Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2). They can even take on more complex shapes as the value of the angular quantum number becomes larger. A third quantum number, known as the magnetic quantum number (m), describes the orientation in space of a particular orbital and shows the energy states in sub-shells. 11
12 Shells and sub-shells of orbitals Orbitals that have the same value of the principal quantum number form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number. Bohr and (b) wavemechanical atom models in terms of electron distribution. 12
13 Sub-shells s, p, d and f signify the subshells which the electrons occupy. Different types of subshells have different numbers of energy states Within each energy state there are two possible spin orientations Schematic representation of the relative energies of the electrons for the various shells and subshells 13
14 14 Electron states
15 15 Electron configurations
16 Chemical Bonding Between Atoms Electron states is controlling factor for atomic bonding Types of primary (strong) bonds: ionic, covalent, metallic Types of secondary (weak) bonds: van der Waals, hydrogen Properties that are controlled by interatomic potentials: melting point, bond stiffness, thermal expansion coefficient 16
17 Bonding forces Many properties of materials are determined by the interatomic forces that bind the atoms together. Equilibrium spacing These forces are of two types, attractive and repulsive, and the magnitude of each is a function of the separation or interatomic distance. 17
18 Energy of bonding Bonding energy 18 Once in this position, the two atoms will counteract any attempt to separate them by an attractive force, or to push them together by a repulsive action.
19 This typical curve has a minimum at equilibrium distance R 0 R > R 0 ; the potential increases gradually, approaching 0 as R the force is attractive R < R 0 ; the potential increases very rapidly, approaching at small separation. the force is repulsive V(R) r 0 R 0 Repulsive R Attractive R Force between the atoms is the negative of the slope of this curve. At equlibrium, repulsive force becomes equals to the attractive part.
20 Heinserberg Uncertainty Principle This idea claims that we are not allowed to know simultaneously the definite location and the definite speed of a particle. The laws of motion for a quantum particle have to be framed in such a way that lets us make predictions only for quantities that are the average of many individual measurements. We can only say that there is a probability that a particle will have a position near some coordinate x. the uncertainty in position, x, and the uncertainty in momentum, p, The probability that a particle is at a certain point in space and time is given by the square of a complex number called the probability amplitude, ψ - wavefunction
21 Wavefunction (a) Si is in Group IV in the Periodic Table. An isolated Si atom has two electrons in the 3s and two electrons in the 3p orbitals. (b) When Si is about to bond, the one 3s orbital and the three 3p orbitals become perturbed and mixed to form four hybridized orbitals, ψ hyb, called sp 3 orbitals, which are directed toward the corners of a tetrahedron. The ψ hyb orbital has a large major lobe and a small back lobe. Each ψ hyb orbital takes one of the four valence electrons.
22 Probability In quantum mechanics the probability of finding a particle at a certain position at time t, P(x,y,z,t), is the square of the wave function. Probability densities for the electron of a hydrogen atom in different quantum states.-wikipedia
23 Wavefunctions and Probabilities
24 Summary The quantum state of a particle is characterized by a wave function, which contains all the information about the system an observer can possibly obtain. The wave function is interpreted as a probability amplitude of the particles presence. Ψ(r,t) 2 is the probability density. For a single particle the total probability of finding it anywhere in space at time t is equal to 1. A proper wave function must be square-integrable.
25 The Schrödinger equation - Intro The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system. It is a wave equation in terms of the wavefunction It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. The detailed outcome is not strictly determined, but given a large number of events, the Schrodinger equation will predict the distribution of results.
26 The Schrödinger equation - basics
27 Schrodinger equation The Schrodinger equation is a differential equation that describes the time evolution of Kinetic energy of a free particle For a particle moving in a potential V(x,t)
28 Schrodinger equation Js = = π h h Planck s constant wave function ( ) ( ) ( ) t t i t t V m,,, r r r ψ ψ = + h h
29 Time-independent Schrödinger equation values of E constitute the allowed energies H is the Hamiltonian operator The word operator means that it is a mathematical set of operations to be carried out on a function placed to its right in this case
30 Solution of the time-independent Schrodinger equation This is the quantum number of the state.
DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves.
AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity 7.1 Electromagnetic Radiation A. Types of EM Radiation (wavelengths in meters) 10-1 10-10 10-8 4 to 7x10-7 10-4 10-1 10 10 4 gamma
QUANTUM-MECHANICAL MODEL OF THE ATOM GENERAL CHEMISTRY by Dr. Istadi 1 Quantum Mechanics? Dual nature of matter and energy The uncertainty principle The wave nature of objects on the atomic scale Quantum
Lecture 18: Quantum Mechanics Reading: Zumdahl 1.5, 1.6 Outline Basic concepts of quantum mechanics and molecular structure A model system: particle in a box. Demos how Q.M. actually obtains a wave function.
Lecture 12 Quantum Mechanics and Atomic Orbitals Bohr and Einstein demonstrated the particle nature of light.e = hν. De Broglie demonstrated the wavelike properties of particles. λ = h/mv. However, these
Atomic Theory and the Periodic Table Petrucci, Harwood and Herring: Chapters 9 and 10 Aims: To examine the Quantum Theory, to understand the electronic structure of elements, To explain the periodic table
Quantum Theory and Atomic Structure Nuclear atom small, heavy, positive nucleus surrounded by a negative electron cloud Electronic structure arrangement of the electrons around the nucleus Classical mechanics
Topic 1 1-1 Atomic Structure and Periodic Properties Atomic Structure 1-2 History Rutherford s experiments Bohr model > Interpretation of hydrogen atom spectra Wave - particle duality Wave mechanics Heisenberg
Chemistry 417! 1! Fall 2012 Chapter 2 Notes September 3, 2012! Chapter 2, up to shielding 1. Atomic Structure in broad terms a. nucleus and electron cloud b. nomenclature, so we may communicate c. Carbon-12
Chapter 29: Atomic Structure What will we learn in this chapter? Contents: Electrons in atoms Wave functions Electron spin Pauli exclusion principle Atomic structure Periodic table W. Pauli & N. Bohr Both
Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.
Chapter 10 Modern Atomic Theory and the Periodic Table 1 10.1 A brief history 10.1 A brief history atoms proposed by Greek philosopher Dalton s model of atom Thomson s model Rutherford s model there remain
Chapter 3 (Lecture 4-5) Postulates of Quantum Mechanics Now we turn to an application of the preceding material, and move into the foundations of quantum mechanics. Quantum mechanics is based on a series
Wave Function, ψ Chapter 28 Atomic Physics The Hydrogen Atom The Bohr Model Electron Waves in the Atom The value of Ψ 2 for a particular object at a certain place and time is proportional to the probability
AP CHEMISTRY CHAPTER REVIEW CHAPTER 6: ELECTRONIC STRUCTURE AND THE PERIODIC TABLE You should be familiar with the wavelike properties of light: frequency ( ), wavelength ( ), and energy (E) as well as
SUBAREA I. ATOMIC STRUCTURE AND THE PROPERTIES OF MATTER COMPETENCY 1.0 UNDERSTAND THE VARIOUS MODELS OF ATOMIC STRUCTURE, THE PRINCIPLES OF QUANTUM THEORY, AND THE PROPERTIES AND INTERACTIONS OF SUBATOMIC
Chapter 11 Modern Atomic Theory Rutherford s Atom The concept of a nuclear atom (charged electrons moving around the nucleus) resulted from Ernest Rutherford s experiments. Question left unanswered: how
Quantum Mechanics Bohr's model: BUT: In 1925-26: by 1930s: - one of the first ones to use idea of matter waves to solve a problem - gives good explanation of spectrum of single electron atoms, like hydrogen
Match the Theorist to His Idea Discovered the neutron Said the positive charges were in nucleus Discovered the electron First proposed the idea of the atom Proposed that electrons were in energy levels
Atomic Structure Ron Robertson r2 n:\files\courses\1110-20\2010 possible slides for web\atomicstructuretrans.doc I. What is Light? Debate in 1600's: Since waves or particles can transfer energy, what is
What are the component of light? How are the electrons arranged in the atom?! What is the relationship between light and the atom? How does light give clues about the structure of the atom? 1 The Electro-
Atomic Spectra and Energy Levels Atomic Spectra Excited atoms emit light (neon signs, etc.) Emission from different elements is different colors. Emission of only certain wavelengths Spectral lines Existence
Atomic Structure: Chapter Problems Bohr Model Class Work 1. Describe the nuclear model of the atom. 2. Explain the problems with the nuclear model of the atom. 3. According to Niels Bohr, what does n stand
Assignment 06 A 1- What is the energy in joules of an electron undergoing a transition from n = 3 to n = 5 in a Bohr hydrogen atom? a) -3.48 x 10-17 J b) 2.18 x 10-19 J c) 1.55 x 10-19 J d) -2.56 x 10-19
.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations
7 Atomic Structure and Periodicity Electromagnetic radiation (Maxwell, 1864) (nature of light) Composed of perpendicular electric field and magnetic field Electric field (E) (wavelength) t Magnetic field
Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)
AP Chemistry Chapter 6 Lecture Notes- Electrons! Chapter 6 Homework 6.1 The Wave Nature of Light pg 253 #3, 4, 13, 15, 17, 19, 21, 25, 29 The electronic structure of an atom refers to the arrangement of
Chapter 7. Quantum Theory and Atomic Structure A problem arose in Rutherford s nuclear model. A nucleus and electron attract each other; to remain apart the electron must move. The energy of the electron
2-Introduction to Structure and Bonding in Materials 2-1-Sub-Atomic Structure Electrons and their interaction with the nucleus of the atom. The Bohr model is a simplified view of the arrangement of sub-atomic
Chapter 7: Electrons in Atoms Dr. Chris Kozak Memorial University of Newfoundland, Canada 1 Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium.
Physics 97 Interatomic forces Section 3: rystal Binding Solids are stable structures, and therefore there exist interactions holding atoms in a crystal together. For example a crystal of sodium chloride
The Evolution of the Atom 1808: Dalton s model of the atom was the billiard ball model. He thought the atom was a solid, indivisible sphere. Atoms of each element were identical in mass and their properties.
PHYSICS 2 Grade 12 Unit of Credit: 1 Year (Elective) Prerequisite: Physics 1 and Algebra 2 Course Overview: Physics 2 is an attempt to further understand the universe, and is therefore, a study of matter,
AP* Atomic Structure & Periodicity ree Response Questions KEY page 1 1980 a) points 1s s p 6 3s 3p 6 4s 3d 10 4p 3 b) points for the two electrons in the 4s: 4, 0, 0, +1/ and 4, 0, 0, - 1/ for the three
Quantum Mechanics: mysteries and solutions ANGELO BASSI Department of Theoretical Physics, University of Trieste, Italy and INFN - Trieste Angelo Bassi 1 Quantization of light: Planck s hypothesis (1900)
. ATOMIC STRUCTURE FUNDAMENTALS LEARNING OBJECTIVES To review the basics concepts of atomic structure that have direct relevance to the fundamental concepts of organic chemistry. This material is essential
PX0101 THE STRUCTURE AND PROPERTIES OF MATTER Autumn semester: 10 credits. Module organiser: Dr D I Westwood. Deputy Module Organiser: Prof P A R Ade. Teaching and feedback methods: Lectures 22 x 1 hr,
2. Atomic Structure 2.1 Historical Development of Atomic Theory Remember!? Dmitri I. Mendeleev s Periodic Table (17 Feb. 1869 ) 1 2.1.1 The Periodic Table of the Elements 2.1.2 Discovery of Subatomic Particles
Unit 1: Atoms Level 3 Achievement Scale Can state the key results of the experiments associated with Dalton, Rutherford, Thomson, Chadwick, and Bohr and what this lead each to conclude. Can explain that
CHEM3023: Spins, Atoms and Molecules Lecture 2 Bra-ket notation and molecular Hamiltonians C.-K. Skylaris Learning outcomes Be able to manipulate quantum chemistry expressions using bra-ket notation Be
Chemical energy thread: Readings These readings were designed for students to read online before class, in a flipped classroom environment. ENERGY AT THE SUB-MOLECULAR LEVEL We have developed the concepts
Chapter 5: Electrons in Atoms Light (Electromagnetic Radiation) Light has the properties of both waves and particles. Light waves carry energy through space. wavelength (λ) meters frequency (ν) Hz (s -1
History of Atomic Theory Alchemy ~ Before 400 B.C. Experiment: Pseudoscience concerned with: Changing metal to gold Finding an eternal life elixir Aristotle Beliefs: All matter was made up of a combination
The Bohr model for the electrons Electronic structure how the electrons are arranged inside the atom Applying the quantum principle of energy Two parameters: Energy Position Learning objectives Describe
Chapter 1: Introduction to Quantum Physics Luis M. Molina Departamento de Física Teórica, Atómica y Óptica Quantum Physics Luis M. Molina (FTAO) Chapter 1: Introduction to Quantum Physics Quantum Physics
Name: Class: Date: ID: A Practice questions for Ch. 7 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. When ignited, a uranium compound burns with a green
Chapter 5 Perodicity and Atomic Structure Mendeleev s Periodic Table In the 1869, Dmitri Mendeleev proposed that the properties of the chemical elements repeat at regular intervals when arranged in order
SCH4U UNIT TEST Atomic & Molecular Structure Name: _ Date: Part A - Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Who postulated that electrons
CHAPTER 6: ANSWERS TO ASSIGNED PROBLEMS Hauser- General Chemistry I revised 8/03/08 6.9 What are the basic SI units for? (a) the wavelength of light meters, although colors are usually reported in 3 digit
Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson Rules for this test 1. This test is open book and open notes, including our class notes page online, and your homework solutions.
PHYS 1624 Physics I An introduction to mechanics, heat, and wave motion. This is a calculus- based course for Scientists and Engineers. 4 hours (3 lecture/3 lab) Prerequisites: Credit for MATH 2413 (Calculus
The Schrödinger Equation Erwin Schrödinger 1887-1961 Nobel Prize in Physics 1933 The Schrödinger Wave Equation The Schrödinger wave equation in its time-dependent form for a particle of energy E moving
Electro-magnetic radiation (light) The nature of light light is a wave The nature of waves What is a wave? What is waving? Waves A time Wave: some sort of periodic function something that periodicaly changes
Chapter 2: Atomic Structure and Chemical Bonding Materials Molecules Atoms Atoms = protons (p) + neutrons (n) + electrons (e) Protons and neutrons are made of quarks Quantitative measurements need units:
Atoms and the Periodic Table Chapter Three Subatomic Particles Atoms are composed of subatomic particles Particle Symbol Mass (g) Mass (amu) Charge Proton p 1.672622 x 10-24 1.007276 +1 Neutron n 1.674927
Final Exam, Chem 311, 120 minutes, Dr. H. Guo, Dec. 17, 2008 You are allowed to bring a two page sheet containing equations and a calculator I. Answer the following multiple choice questions (5 pts each),
CHAPTER 30 THE NATURE OF THE ATOM CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION A tube is filled with atomic hydrogen at room temperature. Electromagnetic radiation with a continuous spectrum of wavelengths,
BIO 5099: Molecular Biology for Computer Scientists (et al) Lecture 6: A little bit of chemistry http://compbio.uchsc.edu/hunter/bio5099 Larry.Hunter@uchsc.edu A tiny bit more on Dinosaurs Go back to the
Lecture 13 Page 1 Lectures 13-14 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and
CHEM6085: Density Functional Theory Lecture 2 Hamiltonian operators for molecules C.-K. Skylaris 1 The (time-independent) Schrödinger equation is an eigenvalue equation operator for property A eigenfunction
The Structure of Physics Intermediate Quantum Mechanics Notes for Lecture 1 Structure of Physics, Classical Physics and Quantum Mechanics vs. Classical Physics The two pillars of physics are the Special
Name Honors Chemistry / / History of the Atom Democritus 470-380 B.C. Democritus was known as the "Laughing Philosopher" because of his joyous spirit. First to suggest the idea of atoms (atomos - Greek
Covalent Crystals - covalent bonding by shared electrons in common orbitals (as in molecules) - covalent bonds lead to the strongest bound crystals, e.g. diamond in the tetrahedral structure determined
Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents
C10J ATOMIC STRUCTURE (6 lectures) Introduction The Atomic Structure course is considered as an important part of the core course for Introductory Chemistry as concepts which are learnt here will be employed
CHEMICAL MATTER: ELEMENTS AND THEIR CLASSIFICATION THROUGH THE PERIODIC SYSTEM Renato Ugo Università di Milano, Italy Keywords: chemical elements, electrochemical properties, electron affinities, electronegativity,
Chapter 2 The Chemical Context of Life Multiple-Choice Questions 1) About 25 of the 92 natural elements are known to be essential to life. Which four of these 25 elements make up approximately 96% of living
Principles of Imaging Science I (RAD119) Atomic Structure Atomic Structure & Matter In radiography, it is important to understand the structure of matter and the fundamentals of electromagnetic radiation
5.6 Physical Chemistry 5 Helium Atom page HELIUM ATOM Now that we have treated the Hydrogen like atoms in some detail, we now proceed to discuss the next simplest system: the Helium atom. In this situation,
hapter 5 1. Kinetic Molecular Theory. 2. Average kinetic energy and velocity. 3. Graham s Law of Effusion. 4. Real gases and the van der Waals equation. Kinetic Molecular Theory The curves below represent
Introduction to Chemistry and Physics UNIT I: Introduction to the Physical Sciences The student will demonstrate the ability to explore and apply the processes of science. a. Describe and apply the steps
rganic hemistry (EM311) Fall 2005 Dr. Robert F. Dias 1. ATMS, MLEULES, RBITALS AND BNDING: All the stuff you are not allowed to forget from general chemistry k, So now you are a sophomore. The last thing
Objectives 1. To review Rutherford s model of the atom 2. To explore the nature of electromagnetic radiation 3. To see how atoms emit light A. Rutherford s Atom.but there is a problem here!! Using Rutherford
PH3 Modern Physics SP11 Last time: Photons, atomic spectra & lasers Today: Balmer formula and ideas about atoms Bohr model of hydrogen de Broglie waves Some people say, "How can you live without knowing?"
CHAPTER 4 Structure of the Atom 4.1 The Atomic Models of Thomson and Rutherford 4.2 Rutherford Scattering 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydrogen Atom 4.5 Successes and Failures
Electronic Structure of Atoms (Quantum Theory) Classical Theory: By the early 1900 s, classical theory viewed light as behaving like a wave, as demonstrated in 1801 by Thomas Young in his double slit experiment.
SKILL FOCUS Analyzing and interpreting Communicating results Atomic Emission Spectra (Teacher Demonstration) When a high voltage current is passed through a glass tube that contains hydrogen gas at low
Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section
How are these samples all the same? What makes them different? Answer: ATOMS A Look inside at Protons, Neutrons and Electrons IRON HELIUM COPPER The samples are similar in that they are all made of atoms.
Chapter 38C - Atomic Physics A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 007 Objectives: After completing this module, you should be able to:
The force equation of quantum mechanics. by M. W. Evans, Civil List and Guild of Graduates, University of Wales, (www.webarchive.org.uk, www.aias.us,, www.atomicprecision.com, www.upitec.org, www.et3m.net)
Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate