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8-1. Photoelectric Effect
  1. The photoelectric effect is the emission of electrons from a metal surface when light shines on it.
  2. The discovery of the photoelectric effect could not be explained by the electromagnetic theory of light.
  3. Albert Einstein developed the quantum theory of light in 1905.
8-2. Photons
  1. Einstein’s quantum theory of light was based on a hypothesis suggested by the German physicist Max Planck in 1900.
    1. Planck stated that the light emitted by a hot object is given off in discrete units or quanta.
    2. The higher the frequency of the light, the greater the energy per quantum.
    3. All the quanta associated with a particular frequency of light have the same energy. The equation is

      E = hf

      where E = energy, h = Planck’s constant (6.63 × 10—34 J · s), and f = frequency.
  2. Einstein expanded Planck’s hypothesis by proposing that light could travel through space as quanta of energy called photons. These photons, if of sufficient energy, could dislodge electrons from a metal surface causing the photoelectric effect.
  3. Einstein’s equation for the photoelectric effect is

    hf = KE + w

    where hf = energy of a photon whose frequency is f, KE = kinetic energy of the emitted electron, and w = energy needed to pull the electron from the metal.
  4. Although photons have no mass and travel with the speed of light, they have most of the other properties of particles.
8-3. What Is Light?
  1. Light exhibits either wave characteristics or particle (photon) characteristics, but never both at the same time.
  2. The wave theory of light and the quantum theory of light are both needed to explain the nature of light and therefore complement each other.
8-4. X-rays
  1. Wilhelm Roentgen accidentally discovered x-rays in 1895.
  2. In 1912, Max von Laue showed that x-rays are extremely high frequency em waves.
  3. X-rays are produced by high energy electrons that are stopped suddenly; the electron KE is transformed into photon energy.
8-5. De Broglie Waves
  1. In 1924, the French physicist Louis de Broglie proposed that moving objects behave like waves; these are called matter waves.
  2. The de Broglie wavelength of a particle of mass m and speed v is

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    where l = de Broglie wavelength, h = Planck’s constant, and mv = momentum of the particle.
  3. Matter waves are significant only on an atomic scale.
  4. A moving body exhibits wave properties in certain situations and exhibits particle properties in other situations.
8-6. Waves of What?
  1. The quantity that varies in a matter wave is called the wave function (ψ).
  2. The square of the wave function (ψ2) is called the probability density. For a given object, the greater the probability density at a certain time and place, the greater the likelihood of finding the object there at that time.
  3. The de Broglie waves of a moving object are in the form of a group, or packet, of waves that travel with the same speed as the object.
8-7. Uncertainty Principle
  1. The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time.
  2. The discoverer of the uncertainty principle was Werner Heisenberg.
  3. The position and motion of any object at a given time can only be expressed as probabilities.
8-8. Atomic Spectra
  1. A gas whose electrons have absorbed energy is said to be excited.
  2. A spectroscope is an instrument that disperses the light emitted by an excited gas into the different frequencies the light contains.
  3. An emission spectrum consists of the various frequencies of light given off by an excited substance.
  4. A continuous spectrum consists of all frequencies of light given off by an excited substance.
  5. An absorption spectrum consists of the various frequencies absorbed by a substance when white light is passed through it.
  6. The frequencies in the spectrum of an element fall into sets called spectral series.
8-9. The Bohr Model
  1. The Niels Bohr model of the atom, proposed in 1913, suggested that an electron in an atom possesses a specific energy level that is dependent on the orbit it is in. An electron in the innermost orbit has the least energy.
  2. Electron orbits are identified by a quantum number  n, and each orbit corresponds to a specific energy level of the atom.
    1. Electrons cannot possess energies between specific energy levels or orbits.
    2. An electron can be raised to a higher energy level by absorbing a photon or, by emitting a photon, fall to a lower energy level.
    3. When an electron “jumps” from one orbit (energy level) to another, the difference in energy between the two orbits is hf, where h is the frequency of the emitted or absorbed light.
  3. An atom having the lowest possible energy is in its ground state; an atom that has absorbed energy is in an excited state.
8-10. Electron Waves and Orbits
  1. An electron can circle a nucleus only in orbits that contain a whole number of de Broglie wavelengths.
  2. The quantum number n of an orbit is the number of electron waves that fit into the orbit.
8-11. The Laser
  1. A laser is a device that produces an intense beam of single-frequency, coherent light from the cooperative radiation of excited atoms.
  2. The word laser comes from light amplification by stimulated emission of radiation.
  3. Lasers use materials whose atoms have metastable states, which are excited states with relatively long lifetimes.
    1. Ruby lasers use xenon-filled flash lamps to excite chromium ions in ruby rods.
    2. Helium-neon lasers use an electric discharge to bring the atoms of the gas mixture to metastable levels.
  4. The metastable atoms, as they return to their ground states, create photons all of the same frequency and all of whose waves are coherent or exactly in step.
8-12. Quantum Mechanics
  1. The theory of quantum mechanics was developed by Erwin Schrödinger, Werner Heisenberg, and others during the mid-1920s.
  2. According to quantum mechanics, the position and momentum of a particle cannot both be accurately known at the same time. Only its most probable position or momentum can be determined.
  3. Quantum mechanics includes newtonian mechanics as a special case.
8-13. Quantum Numbers
  1. According to quantum theory, an electron is not restricted to a fixed orbit, but is free to move about in a three-dimensional probability cloud.
  2. Where the probability cloud is most dense (where ψ2 has a high value), the greatest the probability of finding the electron.
  3. Three quantum numbers determine the size and shape of the probability cloud.
    1. The principal quantum number  n governs the electron’s energy and average distance from the nucleus.
    2. The orbital quantum number  l determines the magnitude of an atomic electron’s angular momentum.
    3. The magnetic quantum number  ml specifies the direction of an atomic electron’s angular momentum.
    4. The spin magnetic quantum number  ms of an atomic electron has two possible values, +1/2 or -1/2, depending on whether the electron aligns itself along a magnetic field (+1/2) or opposite to the field (-1/2).
8-14. Exclusion Principle
  1. The exclusion principle, first proposed by Wolfgang Pauli in 1925, states that only one electron in an atom can exist in a given quantum state.
  2. Each atomic electron must have a different set of quantum numbers n, l, ml, and ms.





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