Phy 102: Fundamentals of Physics II Chapter 32: The Atom & the Quantum Lecture Notes

Albert Einstein (1879-1955) Nobel Prize winner and most prominent physicist of the 20th century Studies led to the development of whole sub-fields of physics including Relativistic physics Solid-state physics Low-temperature physics Quantum physics Published paper describing the “photo-electric effect” in 1905 Demonstrated that light interacts with matter as photons not waves Laid the groundwork for the quantum theory of light Offered critical guidance to de Broglie with his “wave theory of the electron”

History of Quantum Theory 1900: Planck proposes that the energy of radiated light is proportional & introduced the idea of the “quantum” 1905: Einstein publishes paper of photo-electric effect, supporting Planck’s quantum hypothesis 1911: Rutherford proposes “nuclear” model of the atom 1913: Bohr proposes “planetary” model of the hydrogen atom 1924: de Broglie publishes doctoral thesis proposing wave-particle duality of matter 1926: Schrodinger develops wave equation for hydrogen atom 1926 to present: Physicists & philosophers debate the meaning of Quantum Theory

The Atom (just a reminder) Two important regions The nucleus Represent most of the mass of the atom Consists of protons (positive charge) and neutrons Determines the identity of the atom (element) The electron cloud Represents the volume of the atom Consists of electrons (negative charge) Determines the chemical properties of the atom

The Bohr Model Ephoton = Ehigh - Elow Planetary model of the hydrogen atom Model explains the spectra for hydrogen Electron orbits nucleus held in place by electrical attraction between electron and protons When electron is “excited” It absorbs energy (exactly equal to the energy difference between the higher and lower states of the transition) “jumps” to a higher energy level (larger orbit) When electron “relaxes” It drops back to lower energy level Releases energy in the form of a photon The energy of the photon is exactly the amount equal to the energy difference between the the energy levels of the transition: Ephoton = Ehigh - Elow

Ephoton = hf or Ephoton = hc/l Energy & the Photon A photon is a quantum (or single packet) of electromagnetic energy All photons travel at the same speed in a vacuum (through empty space) The speed of a photon (in vacuum) is Equal to 3x108 m/s: vphoton = c = 3x108 m/s Equal to the product of the wavelength (l) times the frequency (f) of the photon: c = l.f = 3x108 m/s The energy of a photon is Proportional to the frequency: Ephoton ~ f Inversely proportional to the wavelength: Ephoton~ 1/l To calculate the energy of a photon: Ephoton = hf or Ephoton = hc/l {where h is planck’s constant, h = 6.63x10-34 J.s}

Wave Model of the atom Electrons orbiting the nucleus of an atom exist as “standing waves” They exist as “cloud” and are not actually “particles” The cloud is the “standing wave” (which just means that it is self reinforcing and thus stable in that state) The electron waves are described by Schrodinger’s equation Electrons are described by a wave function, y The square of the wave function, y2, represents the “probability density function” (or, probability per unit volume of finding the electron at any particular position at a particular time) According to Schrodinger’s equation there are a certain number of allowed states the electron can have The organization and geometry of the allowed states ultimately defines the properties of an atom’s electrons & the structure of the periodic table