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Quantum Physics

Wave and Particle Model
  • Particle Model: Objects that are hard, have mass and move about according to the laws of Newtonian mechanics
  • Wave Model: They are shaped like a sine graph, do not have mass or charge. their defining characteristics are diffraction and interference
Photoelectric Effect
  • Photoelectric Effect: When an electromagnetic radiation of sufficiently high frequency falls on a metal surface, electrons are emitted
  • Delocalized electrons in metal are removed by supplying a small amount of energy provided by the incident electromagnetic radiation
  • Emitted electrons are called photoelectrons
  • Photoelectric Current: Current due to photoelectrons
Properties of Magnets

    • The first is a positively charged electroscope
    • The second, a negatively charged electroscope
  • Positively Charged: When the zinc plate is exposed to u.v., the leaf remains open because though electrons are emitted, that are attracted back due to the +ve charge on zinc plate
  • Negatively Charged: When the zinc plate is exposed to u.v., the leaf slowly collapses as electrons are emitted, hence, -ve charge on the electroscope decreases
  • Laws of Photoelectric Emission:
    • First Law: The number of photo-electrons emitted per second is directly proportional to the intensity of the incident radiation
    • Second Law: The maximum kinetic energy of photo-electrons is directly proportional to the frequency of the incident radiation but independent of its intensity
    • Third Law: For every metal, there is a minimum frequency of incident radiation below which photo-electric emission does not take place; it is called the threshold frequency
    • Threshold Frequency: It is the minimum frequency required to release electrons from the surface of a metal
Particulate Nature of Electromagnetic Radiation
  • The energy of an electromagnetic wave does not flow continuously but in discrete quanta
  • Photon: Each quantum (particle) of electromagnetic radiation
  • Energy of a photon of an electromagnetic radiation of frequency f is given by
    • E = hf
    • where h is the Planck’s constant = 6.63 × 10-34 Js
  • Work Function (Φ): The minimum amount of energy required by an electron to escape its surface
  • For a given frequency, electrons are emitted with a range of k.e. because electrons deeper inside the metal lose energy in collision with atoms as they are emitted
Einstein’s Photo-electric Equation
  • hf = Φ0 + Emax
  • where Φ0 is the work function of the metal
  • Thus, the energy of the absorbed photon is partly used to release the electron from the metal and partly to give it a kinetic energy
    • hf = hf0 + ½mv²max
Wave-particle Duality
  • Wave Behavior: Electromagnetic radiation shows properties of diffraction and interference
  • Particle Behavior: Photo-electric effect
  • Thus electromagnetic radiations have a dual nature and their particles are photons
Electron Diffraction
  • de Brogile suggested since waves can behave like particles, particles should be able to behave like waves
  • Matter Wave: A moving particle pf matter of momentum p will have an associated wave of wavelength λ, where λ = h/p = h/mv
    • where h is Planck’s constant
    • m is the mass
    • v is the velocity of the particle
    • λ is the de Brogile wavelength
  • Diffraction of Electrons:

    • When a beam of electrons strikes a thin carbon foil, a diffraction pattern is obtained on a screen
    • When the velocity of the electrons in a bean was increased by increasing the voltage, the rings in the pattern became narrower, showing the wavelength decreases as the velocity is increased, agreeing with de Brogile’s equation
Energy Levels
  • The energy of an atom is the total energy of its electrons
  • Under normal conditions, an atom is in its ground state where it possesses the minimum possible energy
  • When the atom absorbs energy, the energy of the atom increases and the atom is in an excited state
  • The excited state is unstable, so the atoms eventually emit absorbed energy, bringing the atom back to its ground state
  • Transition: is the shifting of electrons between energy levels
  • Electrons release energy in the form of electromagnetic radiation
  • The frequency of the emitted radiation is given by:
    • hf = E2 – E1
    • where f is the frequency,
    • E2 is the energy of the higher level, and
    • E1 is the energy of the lower level
  • The frequencies of the electromagnetic radiation emitted by electrons when they come down to their ground state were found to be discrete, showing electrons can only absorb certain discrete values, therefore the energy of an atom is quantized
Line Spectra

  • Emission Line Spectra: The composition of light emitted by a hot gas
    • The frequencies emitted by the atoms of a substance when they de-excite from higher to lower energy levels
  • Absorption Line Spectra: When white light is passed through a cool gas
    • The frequencies absorbed from a continuous spectrum by the electrons
  • The emission and absorption spectra are characteristic of each element
Band Energies in Solids
  • Atoms in solids are close together and electrons from one atom interacts with those of neighboring atoms, altering energy level diagrams
  • An electron can have an energy at any level in one of the energy bands
  • However, it cannot have an energy which lies in the forbidden gap
Band Theory and Electrical Conduction
  • In a metal, the conduction band is only partially filled with free electrons which gives the metal is conductivity
  • In an insulator, the conduction band is unoccupied and the valence band is fully occupied
  • In a metal, the conduction band overlaps with the valence band allowing it to conduct electricity
    • When a metal is heated, resistance increases because there is no increase in density of electrons in the conducting band; instead atoms vibrate more and electrons collide more frequently
  • In an insulator, there is a large forbidden gap between the valence and conduction band and voltage is insufficient to lift electrons across
  • In an intrinsic semiconductor, its conduction band is also empty, however, the gap between the two is very small
    • When heated, electrons gain energy to jump into the conduction band and the material will conduct better
  • In an LDR, photons of light are absorbed by electrons in valence bands so they jump the gap into the conduction band
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