Particles and Waves Joseph F. Alward, PhD     Department of  Physics   University of the Pacific

Louis deBroglie            (1892-1987)

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 Important Terms and Concepts

Blackbody:  An ideal entity which absorbs all electromagnetic radiation incident on it, and reemits it all. Planck's Constant:  h = 6.63 x 10-34 J-s Photon Energy:   E = h f Work Function W0 :  The least energy an electron in metal must acquire to escape the metal's surface KEmax = hf - W0

Electron mometum:  p = mv deBroglie Wavelength:  l = h / p Heisenberg Uncertainty Principle:    DpDx  > h / 2p   DEDt  > h / 2p

 Blackbody Radiation

Prism disperses electromagnetic energy into its component parts.

Hot objects emit red and orange, while very hot   objects emit red, orange, and blue light.

    The Radiation Spectrum from Hot Objects

This filament is not yet hot enough   to emit significant amounts of blue   light.

This filament is emitting all of the colors of   the rainbow, which makes it "white" hot.

 
  Planck's Quantum

Max Planck (1858-1947) German physicist 1918 Nobel Prize

Planck explained the blackbody radiation spectrum by postulating that the radiation was emitted by oscillating atoms, and furthermore that the energy was quantized. The energy of these "atomic oscillators" had to be an integer multiple of hf, where f is the frequency of vibration of the atoms and h = 6.63 x 10-34 J-s. E = nhf       n = 0, 1, 2, 3, ......... Albert Einstein later applied a similar quantum concept to light.

   The Photoelectric Effect

Blue light will eject electrons from metal, but red light will not.

 
  Important Persons in Early 20th Century Physics

Solvay Conference, 1911

Einstein explained the photoelectric effect by assuming that electromagnetic energy (light) manifests itself as quanta of energy--or, "photons"--of energy hf:  E = hf   f = frequency of light

   Work Function

KEmax = hf - W0 ----------------------------------------------- Problem:   A metal has a workfunction 8 x 10-19 J. What is the maximum kinetic energy of electrons emitted from the metal when light of frequency f = 2 x 1015 Hz is shone on the surface? Solution: KEmax = 5.26 x 10-19 J

 
  Photon Energy Example

How many photons stream forth in one hour from a light bulb radiating 100 watts of light energy?  Assume l = 500 nm. -------------------------------------------------------- c = l f f = c / l   = (3 x 108 m/s) / (500 x10-9 m)   = 6 x 1014 Hz E = h f     = (6.63 x 10-34 J-s) (6 x 1014 s-1)     = 3.98 x 10-19 J

(Solution continued) 100 watts = 100 J/s  One hour = 3600 s  Total energy radiated = 3.6 x 105 J  N = 3.6 x 105 J / 3.98 x 10-19 J        = 9 x 1023

 The ElectronVolt (eV) and the Rule of 1240

The kinetic energy of an electron accelerated across a potential difference of one volt is one electronvolt (eV). The eV is not a unit of charge, or a unit of voltage; it is a unit of energy.

The energy E in electronvolts (eV) of a photon is related to its wavelength l in nanometers (nm) through the following relationship: E = (1240 eV-nm) / l

 
  Photoelectric Effect

Problem Light of wavelengh  l = 400 nm is shone on a metal surface whose work function W0 is 2.0 ev. What is the maximum kinetic energy of the photoemitted electrons?

Solution E = 1240 / 400     = 3.1 eV KE = 3.1 - 2.0       = 1.1 eV

 
  Photocells in Medicine

Absorption of light by a bacteria cell causes a drop in the number of photons absorbed by the photocell and a drop in the current.

   Photocells in Garage Door Openers

Light to photocell is interrupted, and the corresponding drop in photocurrent signals the motor to reverse.

 
  Photocells in Movie Film

Optical sound track is like a bar-code, but much more detailed.  Track modulates the intensity of the light at a frequency which is the same as the sound which was used to produced the track.

  
 The De Broglie Wavelength

Louis deBroglie  (1892-1987)  (rhymes with Troy)  French aristocrat  1929 Nobel Prize

In 1923 PhD thesis submitted at the University of Sorbonne, in Paris, deBroglie postulated that matter has a wave-like attribute--a wavelength given by  l = h/mv  This theory was compatible with Einstein's E = mc2 theory, which held that matter and radiant energy were interconvertible.

Louis deBroglie's proposal was considered outlandish until Herr Professor Einstein gave his enthusiastic approval, and deBroglie's degree was granted

  
     The De Broglie Wavelength

Louis deBroglie     (1892-1987)  1929 Nobel Prize --------------------------  p = momentum  l = h/p

Electron beam produces a pattern similar to the one produced by light

  
  Electron's de Broglie
  Wavelength

What is the wavelength of an electron moving at a speed v = 2 x 104 m/s? ----------------------------------------------------- m = 9.1 x 10-31 kg p = 18.2 x 10-27 kg-m/s h = 6.63 x 10-34 J-s l = h / p    = 3.6 x 10-8 m    = 360 x 10-10 m    = 36 x 10-9 m    = 36 nm

   The Heisenberg Uncertainty Principle

Werner Heisenberg         (1901-1976)        1932 Nobel Prize

Observing an object changes its momentum and energy.

 
 The Heisenberg Uncertainty Relations

DpDx  > h/2p  If one attempts to locate a particle to within an uncertainty Dx, then the least uncertainty  Dp there will be in the particle's momentum is     Dp = (h/2p) / Dx

DEDt  > h/2p If a particle exists for a time period, then the least uncertainty  DE there will be in the particle's energy is     DE = (h/2p) / Dt

  Heisenberg Uncertainty Example

Example:   An electron is observed for a period of time long enough to ascertain its position to within one angstrom.  What is the least uncertainty in the electron's velocity?

Dx = 1 x 10-8 m Dp = (6.63 x 10-34) / (2p) / (1 x 10-8)       = 1.055 x 10-26 kg-m/s m = 9.1 x 10-31 kg mDv = Dp Dv = 1.2 x 104 m/s