Lecture 3 The Quantum Story: How It All Started, Exams of Electromagnetism and Electromagnetic Fields Theory

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ECE 3030 – Summer 2009 – Cornell University Lecture 3 The Quantum Story: How It All Started In this lecture you will learn: • The historical developments leading to the quantum theory ECE 3030 – Summer 2009 – Cornell University The Nature of Light The nature of light has been a puzzle for centuries The corpuscular theory of light, arguably set forward by Descartes in 1637, states that light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity Sir Issac Newton was a big champion of the corpuscular theory of light Rene Descartes (1596-1650) Issac Newton (1642-1726) But the corpuscular theory of light could not explain phenomena like interference and diffraction which had been demonstrated for light by early 1800s by Thomas Young Christiaan Huygens (1629–1695) Christiaan Huygens worked out a mathematical wave theory of light in 1678, and published it in his Treatise on light in 1690. He proposed that light was a wave in a medium called the Luminiferous ether. Huygens theory could explain interference and diffraction of light very well. ECE 3030 – Summer 2009 – Cornell University Planck’s Constant The smallest unit by which energy can be added or taken away from an electromagnetic wave is which Planck called a “quantum” of energy:  22 cf        341.05458 10  Joules-sec Planck’s constant Lets look at green light: Wavelength =  ~550 nm 1922 3.6 10cf          Energy of a single quantum of green light: Joules Very small ! Because ℏ is so small ! = 2.26 eV ECE 3030 – Summer 2009 – Cornell University Einstein and the Photoelectric Effect The Photoelectric Effect: When light of frequency  larger than a threshold frequency  is shone upon a metal, electrons are ejected from the metal. And if  is smaller than the threshold frequency  , no electrons are ejected however intense the light may be. In 1905, Einstein used Max Planck’s discovery and postulated that light of frequency  is made up of particles, each with energy ℏ𝝎. An electron inside the metal needs a certain minimum energy Eo to come out of the metal. And an electron may only absorb one particle of light at a time. So, an electron will come out by absorbing a particle of light if: o oE    Albert Einstein (1879-1955) Nobel Prize: 1921So Einstein’s explanation favored the particle theory of light !! ECE 3030 – Summer 2009 – Cornell University Neils Bohr and the Hydrogen Atom Niels Bohr (1885-1962) Nobel Prize: 1922 During the 1910s and 1920s, Niels Bohr, a Danish Physicist, was studying the behavior of electrons in atoms and the light emitted by atoms The spectrum of light emitted by the lightest element, Hydrogen, was found to consist of very sharp and well defined frequencies (or wavelengths) +ve initial finalE E   So what are the energies that an electron can have in a Hydrogen atom? ECE 3030 – Summer 2009 – Cornell University Electromagnetic Momentum and Wavelength By 1900s, it was known that any electromagnetic wave packet of energy E and moving with velocity c carried a momentum given by: Ep c  Since the above expression holds for light packets of all big and small energies, it must also hold for the packet with the smallest energy for which: 2 cE      Therefore, the momentum of the smallest energy light packet or light “quantum” is: 2Ep c c         This means that associated with a light particle of momentum p there is a wave of wavelength  that is given by: 2 p    What does this mean?? Is light a wave or made up of particles?? (Follows from classical Maxwell’s equations) ECE 3030 – Summer 2009 – Cornell University The De Broglie Hypothesis In 1924, a French physicist Louis De Broglie hypothesized that since light seems to display certain particle-like features, it might also be possible that particles display certain wave-like qualities Louis De Broglie (1892-1987) Nobel Prize: 1929 To quantify this hypothesis, De Broglie assumed that “associated” with a particle of momentum p=mv, there is a wave of some sort with a wavelength  equal to: 2 p    Basically, he just extended the relation known previously for light particles to matter particles De Broglie further assumed that “associated” with a particle of energy E, there is a wave of some sort with a frequency  equal to: E   Again, he just extended the relation known previously for light particles to matter particles These were some really wild assumptions !! ECE 3030 – Summer 2009 – Cornell University The De Broglie Hypothesis and the Atom According to the Be Broglie hypothesis, since the electron has an associated wave, the circumference of the electron orbit in an atom must be an integral multiple of the electron wave’s wavelength for the associated wave to smoothly fit in the orbit: 2 r n  2 2 p mv       But: Therefore: 22 r n mv L mvr n        n = 1,2,3,…… Bohr quantization rule!!! The fact that the De Broglie hypothesis led to the Bohr quantization rule was a phenomenal success for the hypothesis!