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----------------------------- 2683 - LIGHT - the wave-particle duality?
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- Light is what we take for granted. We don’t think about it. It travels very fast. 180,000 miles per second. It takes 8 minutes to reach us coming from the Sun. From the nearest star it takes 4 ½ years to get here.
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- If it is a particle it must be very, very small. Light brings us all the colors. Scientists have been thinking about light for very long time. Here is some of what they have come up with:
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- Light is a wave. Diffraction results in the boundary of a shadow not being sharp. The light is not propagated strictly in straight lines and peculiar patterns are produced near the edges of the shadow. Both of these behaviors are not that of particles, but of a wave nature of light.
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- Maxwell’s equations for electricity and magnetism determined that the light was made up of an electromagnetic wave. Light is electromagnetic radiation consisting of interdependent mutually perpendicular transverse oscillations of alternating electric and magnetic fields. That’s a mouthful. The alternating fields are the frequency of light and they extend from radio waves, to visible light, to X-rays and Gamma rays.
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- There are three experiments in the 1900’s that discovered the wave-particle duality of light. One was the blackbody radiation, the second the photoelectric effect and the third the Compton scattering effect.
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- Every body radiates light depending on its temperature. Infrared we can not see, but a hotter body gets red hot, and hotter still it gets white hot. If you plot this radiation intensity versus the wavelength of light you get the same curve for every Blackbody.
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- A Blackbody is a physics term for a perfect emitter or absorber of energy. Science expected the energy to keep increasing with frequency. But, that is not what happens. The curve rises then peaks and decreases with the same shape for all Blackbodies.
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- Light is a particle. Max Planck came up with the solution to explain the Blackbody Curve, light intensity versus wavelength. The equations for the curve worked perfectly if you assumed that light came in discrete quantum. It was not a continuous wave as everyone was assuming.
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- In 1905 Einstein used this data to propose the “particle theory of light“. He called each discrete quantum a “photon “ and he claimed that each photon contained energy equal to:
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----------------------------- 6.6*10^-34 times the frequency
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- The Planck Constant of Action = 6.626076*10^-34 kilogram * m^2 / sec.
Energy is the rate of change of Action with respect to time.
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------------------------ Energy = 6.6*10^-34 * frequency
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- The photoelectric effect was first discovered in 1887 by Heinrich Hertz. It is the process of shining light on a metal surface causing a current to flow. The metal is given an electric potential by hooking it up to a battery. When light shines on the metal surface a current instantaneously flows. (This is how the safety beam works with your garage door opener).
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- Experiments with the photoelectric effect show that for each metal there is a threshold light frequency that must be exceeded before the current will flow. No electrons are emitted from the metal unless this frequency is exceeded regardless of how great the light intensity is.
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- The energy of electron emission then increases with a constant rate of change with frequency. The plot of energy versus frequency is then a straight line with a constant slope. The slope is the same for all metals and it is called:
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---------------------- Planck’s Constant of Action = 6.6*10^-34.
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--------------------- Energy = 6.6*10^-34 * frequency, above that threshold frequency
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- Some 20 years later the “Compton Effect” was used to demonstrate that the “photon” actually existed. In 1923 the experiment concerned the collision of a photon with a charge particle, an electron. When the photon collides with an electron it scatters at an angle and its frequency changes.
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- Applying the Conservation of Energy Before the collision and After the collision:
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---------------- h * frequency + Eo = h * frequency 2 + E1
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---------------- without going through the math, the change in wavelength that occurs with this collision is:
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---------------- Change in w = h / m*c * (1 - cosine angle)
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---------------- Change in w is the change in wavelength
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---------------- h = Planck’s Constant = 6.6*10^-34
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---------------- m = mass of the electron = 9.108 * 10^- 31 kilograms
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---------------- c = speed of light = 3*10^8 meters /sec
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----------------- angle is the scattering angle.
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---------------- h / m*c = 2.43*10^-12 meters and is known as the Compton wavelength.
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------------------ Change in w = 2.43*10^-12 * (1 - cosine angle)
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- Compton scattering occurs in all materials with photons of medium energy ( 0.5 to 3.5 * 10^6 electron volts). High energy photons have sufficient energy to eject the bound electrons from the atoms. This is called the “photoelectric effect“.
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- In 1913 Neils Bohr used these theories of what was to become Quantum Mechanics to develop a model for the hydrogen atom. He determined that the electrons move in orbits restricted by the requirement that the angular momentum be an integral multiple of;
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------------------------------ h/2*pi = 6.6/6.28 = 1.05*10^-34.
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----------------------------- For a circular orbit of radius, r, the electron velocity, v, then:
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---------------------------- m*v*r = n * 1.05*10^-34 where n = 1,2,3,4,etc
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- The relation between the Coulomb force, the electrostatic attraction between the positive proton and the negative electron, and , the centrifugal force of the electron’s orbit -
------------------------- e^2*r^2 = m*v^2 / r
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------------------------ where e is the electric charge of the electron
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-------------------- m*v^2 is the kinetic energy of the electron in orbit, mass * velocity^2.
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- When electrons make discontinuous transitions from one orbit to another the change in energy will appear as the emission or the absorption or radiation at a particular frequency equal to that energy level.
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------------------------------- Frequency = (E1 - E2) / 6.6*10^-34
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------------- In 1923 De Broglie determined that:
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------------- Wavelength = 6.6*10^-34 / momentum
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------------- Wavelength = 6.6*10^-34 / mass * velocity
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- This conclusion states that not only light but all particles, all mass, even your body has a dual wave-particle duality. But, do the math. If the mass is very large at all you will not notice the wave nature of matter. It only comes into effect at the atomic level of masses. But, it is still there.
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- If you feel a little queasy it is probably the wave nature of your body atoms acting up again.
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- March 29, 2020 768 2683
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--------------------- Monday, March 30, 2020 -------------------------
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