equations

Chapter 27: Quantum Theory

OBJECTIVES:

The main purpose of this chapter is to understand the spectrum emitted by a hot body and the basics of the theory that explains this spectrum. The other objective is to define the photoelectric effect; recognize that the quantum theory can explain it while the wave theory can't; solve problems involving the photoelectric equation. The main focus is to also define the compton effect and explain in terms of the momentum and energy of the photon. lastly, describe experiments that demonstrate the particle-like properties of electromagnetic radiation.

KEY TERMS:

PHOTOELECTRIC EFFECT: The emission of electrons when electromagnetic radiation falls on an object. The photoelectric effect can be studied in a photocell. Photocells are used to turn lights on automatically at dusk.

THRESHOLD FREQUENCY (f0):, This varies with the metal. It depends on the cathode material. Not all radiation results in current flow. Electrons are ejected only if the frequency of the radiation is above a certain minimum value, called the threshold frequency.

PHOTONS: According to Einstein, light and other forms of radiation consist of discrete bundles of energy, which were later called photons. The energy of each photon depends on the frequency of the light.

WORK FUNCTION: The threshold frequency is related to the energy needed to free the most weakly-bound electron from a metal, called the work function of the metal. The work function is thus measured by hf0.

COMPTON EFFECT: is the shift in energy of scattered photons.

de Broglie wavelength of a particle: is given by ^=h/p=h/mv.

HEISENBERG UNCERTAINTY PRINICIPLE: after the German Physicist werner Heisenberg is when the position and momentum of a particle cannot both be precisely known at the same time.

SUMMARY:

WAVES BEHAVE LIKES PARTICLES

wave

The development of the quantum theory and its experimental confirmation is one of the highlights of the history of the twentieth century. Objects hot enough to be incandescent emit light because of the vibrations of the charged particles inside their atoms. The spectrum of incandescent objects covers a wide range of wavelengths. The spectrum depends on their temperature. Planck explained the spectrum of an incandescent object by supposing that a particle can have only certain energies that are multiples of a small constant now called Planck's constant. In 1900, the German Physicist Max Planck(1858-1947) found that he could calculate the spectrum only if he introduce a revolutionary hypothesis. Planck assumed that the energy of vibration of the atoms in a solid could have only the specific frequencies given by the equation, E=nhf. Further Planck proposed that atoms did not radiate electromagnetic waves as predicted by Maxwell. Instead, they could emit radiation only when their vibration energy changed. Planck found that the constant h was extremely small, about 7 x 10-34j/Hz. It was the first hint that the physics of Newton and Maxwell might be valid only under certain conditions. The second troubling experimental result unexplained by Maxwell was the photoelectric effect. The photoelectric effect is the emission of electrons when certain metals are exposed to light. The photoelectric effect can be studied in a photocell. Einstein explained the photoelectric effect by postulating that light came in bundles of energy called photons. The photoelectric effect allows the measurement of Planck's constant,h. Planck's constant,h is the slope of the graph of maximum kinetic energy of ejected electrons versus light frequency. The work function, the energy with which electrons are held inside metals, is measured by the threshold frequency in the photoelectric effect. The compton effect demonstrates the momentum of photons, first predicted by Einstein. Photons, or light quanta, are massless and travel at the speed of light. Yet they have energy, hf, and momentum, p=h/^.

PARTICLES BEHAVE LIKE WAVES

diffraction

The wave nature of material particles was suggested by de Broglie and verified experimentally by diffracting electrons off crystals. The particle and wave aspects are complementary parts of the complete nature of both matter and light. The Heisenberg uncertainty principle states that the position and momentum of a particle(light or matter) cannot both be known precisely at the same time. The photoelectric effect and compton scattering showed that electromagnetic waves had particle properties. The French Physicist Louis Victor de Broglie(1892-1987) suggested in 1923 that material particles have wave properties. His suggestions were ignored by other scientists until Einstein read his papers and supported his ideas.

EQUATIONS:
E=hf,  where  h  is  PLanck's  constant  6.626x10-34J/Hz.
KE=hf-hfo
KE=-qVo
h= DeltaKE      Change  in  maximum  KE  of  ejected  electrons
   --------  =  -----------------------------------------------
   Delta f      Change  in  frequency  of  incident  radiation
p= hf     h
   -- =  ---
   c      ^
E= hc
   --
   ^
p=mv=h
     -
     ^
^=h   h
  - = -
  p   mv

qV = 1/2mv2

^ = h/mv

IMPORTANT THEORIES IN THIS CHAPTER

  • Planck's theory states that spectrum of an incandescent object by assuming atoms could vibrate only at specific frequencies. The German Physicist Max Planck found that he could calculate the spectrum only if he introduce revolutionary hypothesis. Planck proposed that atoms did not radiate electromagnetic waves all the time they were vibrating, as predicted by Maxwell. Instead, they could emit radiation only when their vibration energy changed. For example, when energy changed from 3hf to 2hf, the atom emitted radiation. The energy radiated was equal to the change in energy of the atom, hf.

  • Einstein's photon theory states that light and other forms of electromagnetic radiation consists of particles. Einstein's theory of the photon reinterpreted and extended Planck's theory of hot bodies. Einstein's photoelectric-effect theory explains the existence of a threshold frequency.

  • CONNECTIONS OF THIS CHAPTER TO SOCIETY

    LIGHT POLLUTION AND OBSERVATORIES

    Light pollution is a general glow in the night sky caused by thousands of unshielded lights along highways and in cities to make them safer for travelers. Most of these lights emit light over virtually the entire visible spectrum. Observatories must attempt to filter out skyglow from star light. Today, there is almost no observatory on earth where illumination from distant cities has not or will not become a problem. Earth's atmosphere causes problems of his own for astronomers. The atmosphere also blocks almost all ultraviolet light, which due to its shorter wavelength, could be focused into much sharper images than visible light. The hubble space telescope, orbiting 370 miles above Earth's surface, is designed to receive light of all wavelengths. The goal is for astronomers to be able to see five to ten times farther and more clearly than ever before.

    SOCIOLOGY CONNECTION

    Many public buildings have doors that open automatically as people approach. These doors are often operated by so called "electric eyes". A light beam shines across the door opening onto a photovoltaic cell, causing electrons to be given off and a current to flow in a circuit. When the beam is broken, the current stops, and a mechanism is triggered that opens the door. These devices have allowed easier access to many people who would otherwise find door opening mechanisms difficult to use.

    PHYSICS LABORATORY: photoelectric Steel Balls

    PURPOSE: To simulate the photoelectric effect.

    MATERIALS

  • 4 2-cm steel balls

  • grooved channel(U Channel or shelf bracket)

  • red, orange, yellow, green, blue, violet colored marking pens or colored stickers

  • PROCEDURE

  • Shape the grooved channel as shown in the diagram. Mark a point 4cm above the table, on the channel, as "R" for red.

  • Mark a point 14cm above the table, on the channel with a "V" for violet. Place marks for B, G, y, and O uniformly between them.

  • Place two steel balls at the lowest point on the channel. These steel balls represent valence electrons in the atom.

  • Place a steel ball on the channel at the red mark. This represents a photon of red light.

  • Release the photon and see if the electrons are removed from the atom. See if either steel ball escapes from the channel.

  • Remove the steel ball that represents the photon from the lower part of the channel.

  • Repeat steps 4-6 for each color mark on the channel. Note: Always start with two electrons at the low point in the channel.

  • OBSERVATIONS AND DATA

  • WHICH COLOR PHOTONS WERE ABLE TO REMOVE THE ELECTRONS?

  • ANSWER:

  • The color photons that were able to remove the electrons were green, yellow, orange, and red.

  • DID ONE PHOTON EVER REMOVE MORE THAN ONE ELECTRON?

    ANSWER:

  • Yes, the red photon was the one photon that ever remove more than one electron.

  • ANALYSIS

    PREDICT WHAT WOULD HAPPEN IF TWO RED PHOTONS COULD HIT THE ELECTRONS AT THE SAME TIME.

    ANSWER

    The electrons would be removed from the atom if the two red photons could hit the electrons at the same time.

    START TWO STEEL BALLS(PHOTONS) AT THE RED MARK ON THE CHANNEL AND SEE WHAT HAPPENS. DESCRIBE THE RESULTS.

    ANSWER

    The red two photons would move faster than before and would escape from the channel speedily.

    APPLICATIONS

    PHOTOGRAPHERS OFTEN HAVE A RED LIGHT IN THEIR DARKROOMS. EXPLAIN WHY A RED LIGHT IS SAFE, BUT A BLUE LIGHT IS NOT SAFE.

    ANSWER

    A red light in safe because it produces more photoelectric effect more than the blue light. A red light is a very powerful transmission of electrons from one point to another.

    LINKS TO OTHER SOURCES

    WEBSITES:
    enclycopedia
    wikipedia
    newsscientist.com
    theory.uwinnipeg.ca
    quantum_field_theory.wikiverse

    PERIODICALS

    1.  DISCOVER:  Loops  of  space.  (a  possible  theory  of  quantum  gravity)
        April  1,  1993;  Bartusaik,  Marcia
    
    2.  SCIENCE:  Quantum  Mechanics:  Quantum  Computing  makes  solid  progress
        April  30,  1999;  Service,  Robert F
    
    3.  SCIENCE:  Quantum  information  theory:  A  general  surrenders  the  field,  
        but  black  hole  battle rages  on
        August  13,  2004;  Seise,  Charles
    
    4.  DISCOVER:  Faster  than  a  speeding  photon
        August  1,  1998;  Freedman,  David  H
    
    5.  POPULAR  MECHANICS:  Quantum  Theory
        October  1,  1997;  Wilson,  Jim
    
    REFERENCES  USE  IN  THIS  PROJECT
          A  Glencoe/McGraw-Hill  Program
          Merill  Physics:  Priniciples  &  Problems
          Author:  Paul  W.  Zitzewitz,Robert  F.  Neff,Mark  Davids
          Content  Consultants:  Robert  B.  Clark,  Ph.D.,Patrick  Kenealy,  Ph.D.
    
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    Quantum Theory By Vivian·