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Quantum Theory

In 1887, Hertz' experiments confirmed Maxwells' theory of light. Seemingly, his electromagnetic theory of light explained all of optics. Except for two small problems that could not be explained by the wave theory of light. When light is shone on a metal surface, a current is created implying that the light caused electrons to be emitted from the surface. The electron flow depends upon the frequency of the light used. This is called the photoelectric effect. An incandescent light bulb emits a wide spectrum of frequencies. The higher the temperature of the light bulb, the "whiter" it appears. The spectrum of light produced doesn't depend upon the material, but the temperature.

In 1900, Max Planck explained the spectrum of the light produced by an incandescent body. He proposed that the atoms of the material didn't radiate electromagnetic waves continuously, but only at discrete values. He proposed that energy was quantized.

In 1905, Albert Einstein proposed a revolutionary theory of light, explaining the photoelectric effect. In his theory, light consists of discrete bundles of energy called photons. Einstein won the Nobel Prize for his theory in 1921.

Theories of light:

Maxwell's theory of light as an electromagnetic wave:

A magnetic field is produced in empty space by a changing electric field. Maxwell hypothesized that if a changing magnetic field produces an electric field, the electric field must also be changing. Maxwell found that the net result of these interacting fields was the production of a wave of magnetic and electric fields traveling through space at a speed of 3 x 108 m/s. Thus, light is an electromagnetic wave.

Photocell

A photocell is used in the experiment. When placed in the dark, the galvanometer reads zero. When light shines on a metal plate in the photocell, the galvanometer detects a current. When a variable voltage is used and the terminals reversed, a point is reached where no current is detected. This voltage is measures the maximum kinetic energy of the ejected electrons (or photoelectrons). The current flow does not depend upon the intensity of the light used, but upon the frequency of the light used.

Maxwell's wave theory predicts that as the intensity of light is increased, the current flow should increase. The frequency should not affect the maximum kinetic energy of the photoelectrons. According to this theory, the electric field of the electromagnetic wave exerts a force on the electrons in the metal and some are ejected from the surface.

Einstein's photon theory predicts that only the frequency of the light used affects the maximum kinetic energy of the photoelectrons. As the intensity of light is increased, no change is seen in the maximum kinetic energy of the photoelectrons. No photoelectrons are ejected until a minimum value of energy is reached, no matter how great the intensity. After this point, the maximum kinetic energy of the photoelectrons increases linearly as the frequency of light used increases.

Graph of KEmax vs f

Photon
the particle nature of light; discrete bundles of energy; the energy of a photon depends upon the frequency of light used; a photon has no rest mass
E = h f
E = h / l
momentum of a photon: p = hf/c = h/l

Threshold frequency (fo)
the minimum frequency of light that results in the emission of photoelectrons

Planck's constant (h)
h = 6.626 x 10-34J sec

Work function
the minimum amount of work needed to eject an electron from the surface
E = h fo

Stopping potential (Vo)
equivalent to the maximum kinetic energy of the ejected photoelectrons (KEmax)

Photoelectric equation
KEmax = hf - hfo

Electron volt (eV)
voltage in volts is equivalent to the magnitude of the energy in electron volts. The electron volt is an easier unit to use than Joules. An electron volt can be easily converted into Joules.
1 eV = 1.6 x 10-19J

Experimental proofs that light behaves like a wave:

  1. Photoelectric effect
  2. Compton effect - X-rays that irradiate a substance lose energy when they strike the substance (the wavelengths of the X-rays that are scattered by striking the substance are longer, or lower in energy)
  3. Pair production - a photon disappears in the process of creating electron/ positron pairs; rest mass is created from pure energy according to Einstein's E = m c2. If an electron collides with a positron, the pair annihilate each other and their energy appears as that of photons.

The dual nature of light is a very abstract concept that cannot be visualized. We cannot imagine light as a combination of a wave and a particle. When we do an experiment, we must think of light as a wave or as a particle -- not as a combination.

Early atomic models:

  1. Plum pudding model(approximately 1890's)
  2. Rutherford model (1911)
  3. Bohr model (1912)

In 1923, Louis de Broglie proposed that matter also behaved like a wave. He based his argument upon the symmetry of nature. If light acted like both a wave and a particle, then matter should also act like a particle and like a wave. He proposed that the wavelength of a material particle should be related to its momentum just as the wavelength of a photon is related to its momentum (p=h/l).

de Broglie wavelength is given by

l = h / m v

Quantum mechanics model of the atom:

Heisenberg Uncertainty Principle - a particle's momentum and position cannot both be known precisely at the same time

Quantum Physics Sample Problems

Quantum Physics Homework