LECTURE 1 Regimes of Physics Classical physics is a macroscopic regime and focuses on the motion of large objects It follows Newton s laws of motion In classical physics motion is particle like The total energy of a system is a continuous function and can have any value Quantum mechanics is a microscopic regime that focuses on the motion of atomic scale or smaller objects such as electrons and protons Motion is wave like and the total energy is restricted to discrete energy levels or quanta The physical properties are determined by wave functions and probability Energy and Motion Potential energy comes from the forces on a system An example is gravitational potential energy Total energy is the sum of the kinetic and potential energies In classical and quantum mechanics the total energy is called Hamilton s function In a conservative system the total energy is constant This relates to the law of conservation of energy Real mechanical systems are dissipative they lose energy from friction The first step in quantum mechanics is to figure out how to determine the total energy which involves determining how to get the forces that five rise to potential energy Coulomb s law pertains to attractive electrostatic forces Forms of Potential Energy in Atoms and Molecules Nuclear energy is the highs form of energy especially when concerning the binding energy Electronic energy is the next highest and comes from the interaction of the electrons with the nuclear charge Vibrational energy comes from motions that change the distance between the nuclei of the atoms in a molecule and is the next highest Rotational energy comes from rotation around the center of mass and is the next highest Translational energy is the lowest form of energy and comes from linear motion of the center of mass All of these forms of energy are quantized meaning they are restricted to distinct energy levels Photoelectric Effect When a monochromatic beam of light is incident upon a metal surface electrons are ejected if the frequency of the light is tuned higher than a certain threshold Above the frequency threshold the number of photoelectrons ejected per unit time is dependent on the intensity of the light Below the frequency threshold no photoelectrons are ejected no matter how tightly focused the beam is on the metal surface which is a real problem for classical physics Einstein accounted for the photoelectric effect by proposing the hypothesis that the energy required to detach a single electron from one of the atoms in the metal comes from a single particle of light a photon Prior to this point in time light and electromagnetic radiation were wavelike only LECTURE 2 Photoelectric Effect Electrons are released by the atoms that absorbed the light A photon is a quantum of light If the energy of a photon is less than the work function no electrons will be released If the energy of a photon is greater than the work function the excess energy from the photon will be converted to kinetic energy of the photoelectron The slope of a graph of frequency versus potential energy is Planck s constant The y intercept is the negative work function No photoelectrons are ejected if the kinetic energy is less than zero Spectroscopy Transitions between Energy Levels Absorption is when an atom or molecule absorbs a photon and climbs the ladder of energy levels An electron moves from the ground state to the excited state if and only if the energy of the photon is equal to the gap between those two levels This is the resonance condition If the energy of the photon is too small no light is absorbed Emission of light is relaxation from an excited state via emission of a photon Fluorescence is an example of emission An optical transition is a change in energy level caused by absorption or emission of a photon Photoelectric Effect in terms of Transitions between Electronic Energy Levels A photoelectron is ejected when an absorption transition occurs between a bound energy level to an energy level above the ionization potential the threshold for photoionization Hydrogen Atom Energy Levels of the Electron An electronvolt is the kinetic energy of an electron that has been accelerated through 1 volt of potential difference In bound states the electron is attached to the nucleus 1 Absorption Transition with Ephoton If the light source is tuned too far to the red longer wavelengths so that the energy of a single photon is less than the work function the transitions occur between the ground state and a bound energy level so no photoelectron is emitted 2 Absorption Transition with Ephoton If the light source is tuned far enough to the blue shorter wavelengths so that the energy of a single photon is larger than the work function the energy of the absorption transition is large enough that the electron goes from the ground state to the continuum of states above the E 0 level so a photoelectron is ejected The kinetic energy of the photoelectron is the excess energy of the photon above the ionization potential The final state after absorption of the photon is in the continuum of free electron states Wave Particle Duality Light has wave like and particle like properties The type of experiment determines which regime of properties is observed In particle like situations photons can be counted using the photoelectric effect Photomultiplier tubes and charge coupled devices CCD convert incident photons into photoelectrons using absorption transitions in a light absorbing material In wave like situations electromagnetic radiation has electric and magnetic field components that oscillate at the same frequency but are perpendicularly arranged with respect to the direction of propagation Constructive and destructive interference of electromagnetic waves gives rise to diffraction by a grating or slit Matter Waves de Broglie s hypothesis If light can be wavelike and particle like at the same time so should matter De Broglie suggested that the wavelength of a matter wave would be determined by the ratio of Planck s constant and the momentum of the particle This was proved by the Davisson and Germer experiment in 1927 which used diffraction of beams of electrons by a Ni crystal Quantum or Wave Mechanics Quantum mechanics concerns the physics of microscopic objects The physical properties are defined by a system s wavefunction All that can be known about a system is obtained by mathematical operations on the wavefunction Classical mechanics is the physics of large