An Introduction to Physical Chemistry Konstantinos Petridis1,2, Nikolaos Lydakis3 and Minas Stilianakis1 1Nanomaterials and Organic Electronics Laboratory 2Department of Electronic Engineering 3Department of Natural Sources & Environment Technological Educational Institute of Crete, Greece Heraklion September 2014

An Introduction to Physical Chemistry: Part I Konstantinos Petridis1,2 1Nanomaterials and Organic Electronics Laboratory 2Department of Electronic Engineering Technological Educational Institute of Crete, Greece Heraklion September 2014

Course Description Course Description (5 ECTS) Grading This module refers presents an introduction to quantum theory and spectroscopy. It begins with a short historical review of quantum mechanics. Then examines the properties of particles and waves, the Schrodinger equation, systems like the particle in a box, the harmonic oscillator. The lectures continue with a discussion of atomic structure & orbitals and Periodic Table. Continuously the course presents the molecular bonding including valence bond and molecular orbital theory and structure. The final lectures are devoted spectroscopy: rotational & vibrational spectra, electronic transitions and magnetic resonance. The course consists from theoretical part and laboratory part. Grading Activities Percentage Lab Reports 20 Participation Final Exam & Evaluation Tests 50 (40 + 10) K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Content – Part I A Historical Review of Quantum Mechanics The Dual Nature of Particles and Waves The one dimensional Schrodinger equations The one dimensional Schrodinger equation’s Applications The 3D Schrodinger equation and the Hydrogen Atom The basic postulates of quantum mechanics Angular Momentum I (operators, angular eigenvalues, angular eigenfunctions) Angular Momentum II (Pauli spin Matrices, Dirac Notation, Zeeman effect) Time dependence Many particle systems K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Quantum Mechanics (QM) is a response to the inability of the classical theories of mechanics and electromagnetism to explain some of the properties of electromagnetic radiation and atomic structure QM basic principles are used to explain the structure & properties of molecules, solids but also those of nuclei and of elementary particles such as the proton and neutron The development of QM can be splitted into two periods: - Period #1: (1900 – 1923) the development of the old QM theory - Period #2: (1924 – 1927) the introduction to the modern QM theory Old QM theory: the dual nature of light & matter …until then K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Quantum Mechanics Describes rules that apply to electrons in atoms and molecules Non-deterministic, probalistic! A new philosophy of nature QM managed to explain unsolved problems of late 19th century physics Explains bonding, structure and reactivity in chemistry K. Petridis, N. Lydakis and M. Stilianakis

Part I: Historical Review of QM Classical Physics in the late 19th century: Atoms are the basic constituents of matter Newton’s Laws apply universally The world is deterministic According to the C.M.: Given the positions and velocities and given all forces all the future can be predicted Physics was complete since: Newtonian mechanics explained macroscopic behavior of matter –planetary motion, fluid flow, elasticity, etc Thermodynamics had its first two laws and most of their consequences Light was explained as an electromagnetic wave Basic statistical mechanics has been applied to chemical systems  K. Petridis, N. Lydakis and M. Stilianakis

Part I: Historical Review of QM …however there were several experiments that could not be explained by C.P. and the accepted dogma! Blackbody radiation Photoelectric effect Discrete atomic spectra The electron as a subatomic particle The study of the above experiments shows: Atoms are not the most microscopic objects Newton’s law do not apply to the microscopic world of electron Outcome: Quantum Mechanics !!!! K. Petridis, N. Lydakis and M. Stilianakis

Part I: Historical Review of QM …however there were several experiments that could not be explained by C.P. and the accepted dogma! Blackbody radiation Photoelectric effect Discrete atomic spectra The electron as a subatomic particle The study of the above experiments shows: Atoms are not the most microscopic objects Newton’s law do not apply to the microscopic world of electron Outcome: Quantum Mechanics !!!! K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The discovery of the electron Faraday in 1870 had already shown using electrochemistry that amounts of electric current proportional to amounts of some substances could be liberated in an electrolytic cell K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The discovery of the electron (continue) JJ Thomson in 1897 discovers the electron and measures (e/me). Inadvertently invents the cathode ray (TV) tube JJ Thomson experiment’s conclusions: The results are independent of the cathode material and gas composition. The electron is a distinct particle, present in all materials K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM 1909 Milliken oil drop experiment Milliken oil drop experiment determines e, me separately K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM 1909 Milliken oil drop experiment Milliken oil drop experiment conclusions: e = 1.59 × 10-19 Cb Combing the Thomson’s experiment result and the above value we manage to measure the electron mass, me = 9.1 × 10-31 kgr K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Where are the electrons ? 1st atomic model “the jelly” model This model was failed after Rutherford backscattering experiments demonstrated that the atoms are mostly empty !!! K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Where are the electrons ? 1st atomic model “the jelly” model This model was failed after Rutherford backscattering experiments demonstrated that the atoms are mostly empty !!! K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Where are the electrons ? Rutherford planetary model: K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Where are the electrons ? Rutherford planetary model failed because was not consistent with the classical electrodynamic theory: Accelerating charge emits radiation (1) And since light has energy, E must be getting more negative with time (2) Due to (1) and (2) we should be able (but we do not) to observe the following: K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Where are the electrons ? Rutherford planetary model failure to be consistent with the classical electrodynamics was also due to: As the radius r of an electron reduces with time its speed should increase. This means that the frequency of the supposed emitted light (due to electron acceleration) should change accordingly: K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM ……….BUT the emission from the atoms was known to be discrete which is another failure of the planetary Rutherford model!!! K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Summary: Rutherford’s model of the atom: Is not stable relative to collapse of electron into nucleus Does not yield discrete emission lines Does not explain the Rydberg formula K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Atom of Niels Bohr Niles Bohr a Danish Physicist who established the Copenhagen School Assumptions that underlying the Bohr atom: Atoms can exist in stable “states” without radiating. The states have quantized energy levels En, n = 1, 2, 3, …….where n = 1 corresponds to the fundamental state, n = 2 corresponds to the 1st excited state Number n is called a quantum number Transitions between states can be occurred with the absorption or the emission of a photon with a frequency f where Conclusion: These assumptions are further evidence of the discrete spectra of atoms K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Atom of Niels Bohr Assumptions that underlying the Bohr atom: (continue) The electrons in the various states have an angular momentum that is an integer multiple of the Planck’s constant: K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Atom of Niels Bohr Assumptions that underlying the Bohr atom: (continue) K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Atom of Niels Bohr Assumptions that underlying the Bohr atom: (continue) The application of the Bohr’s ideas in the Hydrogen atom (the results are valid also in hydrogen type atoms): K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Atom of Niels Bohr Assumptions that underlying the Bohr atom: (continue) The application of the Bohr’s ideas in the Hydrogen atom (the results are valid also in hydrogen type atoms): (continue) K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Atom of Niels Bohr Assumptions that underlying the Bohr atom: (continue) K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM A blackbody is an ideal body which allows the whole of the incident radiation to pass into itself (without reflecting the energy) and absorbs the total of the incident radiation (without passing on the energy). This property is valid for radiation corresponding to all wavelengths and to all angles of incidence. Therefore, the black body is an ideal absorber of incident radiation. When heated all objects, independent of their constituents, emit light!!! This radiation is called blackbody radiation The blackbody is used as a standard with which the absorption of real bodies is compared K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM According to the classical mechanics: Blackbody radiation is the result of electrons oscillating with frequency ν The electrons oscillate (& radiate) equally well at any frequency Rayleigh-Jeans Law describes the spectral density ρ(ν) of the blackbody radiation and predicts that the intensity, within a spectral region, I(v) ~ ν2 (UV catastrophe)!! K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Planck (~1900), 1st “quantum” ideas: The energy of the oscillator ~ frequency, The total energy of an electromagnetic wave is an integral multiple of ν, The analogy constant is the Planck’s constant h = 6.626 × 10-34 J – sec E = hν is known as “quantum” of energy Stefan – Boltzmann law: Wien’s law: K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Planck combined the Stefan – Boltzmann and the Wien law and described the blackbody radiation according to the following formula: where J(f,T) expresses the intensity per frequency at temperature T K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Summary: Planck’s theory: Solves the problem of the infinite energy: UV catastrophe Blackbody radiation emits it’s energy in quanta of energy The minimum energy is this of E = hν K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Comment: When light strikes a clean metal surface in a vacuum it causes electrons to be emitted with a range of energies! K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Comment: h/2π = 1.054571 * 10^(-34) J s K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Φ represents how hard it is to remove an electron… Comment: There are two parameters that describe the KE of the emitted electrons: parameter#1 depends on the light frequency and the parameter #2 that depends on the metal that is used. There is no dependency on light intensity!!! Comment: Φ is called work function K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Summary: Einstein’s theory about photoelectric effect: Structure of atom can not be explained classically Discrete atomic spectra and Rydberg’s formula can not be explained Blackbody radiation can be “explained” by quantifying energy of oscillators, E = hν Photoelectric effect can be “explained” by quantifying energy of light K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Classroom Solved Example: The maximum energy of photoelectrons emitted from potassium is 2.1 eV when illuminated by light of wavelength 300 nm and 0.5 eV when the light wavelength is 500 nm. Use these results to obtain values for Planck’s constant and the minimum energy needed to free an electron from potassium K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Compton Effect The existence of photons also demonstrated by A.H. Compton A.H. Compton experiments involved the scattering of x-rays by electrons K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Compton Effect Compton scattering experiment demonstrated that a photon apart of its energy carries momentum, p The photon momentum expression can be shown using Classical Mechanics Terminology: The Compton experiment noticed the incident photon scattering from an electron of mass m. After the collision the scattered photon has different momentum p’ and direction k’ K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Conclusion K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM The Compton Effect Compton & Photoelectric effects provide conclusive evidence for the photon nature of electromagnetic waves Both experiments described the interaction of electromagnetic radiation with electrons Question: Why in Photoelectric effect the photon (optical) transfers all its’ energy to photoelectrons whereas in Compton effect the X-rays are scattered by the electrons? Classroom Solved Example: An x-ray photon of wavelength 1× 10-12 m is incident on a stationary electron. Calculate the wavelength of the scattered photon if it is detected at an angle 60o to the incident radiation. Comment: answer to the question: The X-rays have much higher energy than the binding energy of an electron and the solid; therefore the electron is knocked out of the solid In the photoelectric effect the photon energy is just above the binding energy of electrons with solid and its whole energy is transferred to the electrons K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM De Broglie Waves Compton experiment demonstrated that the photons have particle properties L. De Broglie suggested that particles such as electrons might also have wave properties (matter waves) The matter properties, energy & momentum, related with wave properties, frequency & wavenumber: (De Broglie relations) The matter waves are exploited in electron microscopes that are used to display diffraction patterns created by the objects under investigation. Neutrons can be used as matter waves to investigate the structural properties of matter Electron microscope student essay for the next lecture Neutrons to detect explosives essay for the students K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM De Broglie principle states that all the objects have and a wave nature in parallel with their material nature. They are particles and waves at the same time. De Broglie principle explains the 2nd Bohr condition. Electron microscope student essay for the next lecture Neutrons to detect explosives essay for the students K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Electron microscope student essay for the next lecture Neutrons to detect explosives essay for the students K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Part I: Historical Review of QM Classroom Solved Example: Calculate the wavelength and speed of the neutrons in a double slit diffraction experiment assuming the following: slit separation equals to 0.12 mm, neutron mass equals to 1,675 * 10-21 kg, separation of diffraction peaks about 75 μm, distance from the slit 5 m K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality QM predicts that both the wave and the particle models apply to all objects whatever the size Depends on the energy (and thus the wavelength) if for an example an electron behaves as a wave or as a particle Depends on with a photon interacts in order to know how to handle it: when a photon interacts with a photon has wave properties and when a photon interacts with matter has a particle properties K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality Light as a wave K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality Light as a wave (continue) K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality Light as a wave (continue) K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality Light as a particle K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality Matter as wave K. Petridis, N. Lydakis and M. Stilianakis

Wave – Particle Duality Part I: Historical Review of QM Wave – Particle Duality Matter as a wave K. Petridis, N. Lydakis and M. Stilianakis

K. Petridis, N. Lydakis and M. Stilianakis Bibliography • Quantum Mechanics by Alastair I.M. Rae (Taylor and Francis Group, 2008) Quantum Mechanics by Yoav Peleg, Schaum’s outlines Quantum Mechanics I and II by Stepahnos Trachanas (University of Crete Press, 2012) Physical Chemistry by Atkins Physical Chemistry notes in MIT Opencourseware K. Petridis, N. Lydakis and M. Stilianakis