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---------------------------- - 2342 - The Waves of Matter
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- In the early 1900 there were four experiments that failed. Physicists were trying to explain the Universe and were not getting the answers they expected.
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- The first experiment was Ernst Rutherford’s model for the atom. The massive nucleus surrounding by orbiting electrons. The nucleus and the electrons being held together by their opposite electric charges. Nucleus having positive protons and the electrons having a negative charge. Opposite charges attract, so what keeps them apart? This is probably the atomic model you have in your mind.
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- However, when you apply Maxwell’s equations to this model the atom would always collapse. The orbiting electron is a moving electric charge. It is accelerating because it is moving in a circle. A moving charge emits electromagnetic energy. If it is loosing energy it should soon spiral down into the nucleus. Obviously, this is not happening. So, what is keeping the atoms from collapsing?
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- The next experiment had to do with measuring the light spectrum of all the elements in the periodic table. Each element emits spectral lines at discrete wavelengths, or frequencies. Each element atom has a distinct set of color lines in its spectra. What causes these unique wavelengths to be generated? (See review #38 Rainbows)
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- The third experiment involved heating up objects. If you heat an iron poker its atoms vibrate more and more vigorously and it turns red hot , yellow , then white hot. Hot objects, since they are vibrating electric charges should give off electromagnetic waves.
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- However, using Maxwell’s equations again they should be giving off an infinite amount of electromagnetic radiation, concentrated at even higher energies and shorter wavelengths, ultraviolet and X-rays. Obviously this does not happen either.
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- The forth experiment fails the photoelectric effect. This happens in a cathode ray tube, a vacuum tube. Where you shine light on a particular metal surface and electrons are emitted from the surface. This is the same effect that is used in the electric eye that controls your automatic garage door closure. Except modern electronics uses semiconductor instead of vacuum tubes.
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- Physicists experimenting with the original photocells would get more electrons if the light was made brighter. Theoretically, the color of the light should not matter, just its amplitude or brightness. However, that is not what happened. If the color of the light was red fewer electrons were ejected. As the color was made bluer, the energy of the electrons increased. Why?
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- These four experiments were not getting the results expected. The math was not working. Something is missing. That something was the “quantum”. All of these effects can be explained once we realize that matter and energy is not continuously subdivided. It comes in discrete chunks. Each chuck is a quantum.
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- The quantum concept was first proposed in 1900 by Max Planck ( See review #8 Time Comes to Us in Particles). Planck came up with this as a fudge factor, a constant, that he picked for each color of light to explain the amount of energy in the vibrating atom.
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- Planck said:
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------------------------------- Energy = Planck’s constant * frequency
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------------------------------- E = h * f
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- In 1905 Albert Einstein used this explanation of for vibrating atoms to explain the photoelectric effect. He declared that energy in a light wave is not spread uniformly over the wave but it is concentrated in particle-like bundles, called photons.
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------------------------------ Energy of a photon = h * f
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- Red light is lower frequency and when it is lower than required energy to eject electrons, none will be ejected. Bluer light is higher frequency, therefore blue photons impart more energy to the surface and more electrons are ejected.
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- The structure of the atom and the orbiting electrons can now be explained because only certain discrete orbits are allowed. Each orbit corresponds to a discrete value of the electron’s energy. Instead of energy Niels Bohr in 1913 used angular momentum in his equation to explain quantized orbits.
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-------- Orbiting Angular Momentum = Planck’s constant / 2 * electron’s momentum
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------------------------- Angular momentum = h / 2*m*v
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------------------------ Where m*v is mass * velocity = the momentum of the electron
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- Atom’s radiate electromagnetic waves only when electrons move between orbits. This explains the spectra of atoms since each element has a unique atomic structure of electron orbits, each atom emit’s a unique color spectra.
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- So quantum‘s explain the results we are seeing. But, quantum’s, Planck’s constant is a very small number.
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------------------------- “h” = 6.625 * 10^-34 kilogram * meters^2 / second
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- Round this up and put in fraction from then Planck’s constant is:
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----------- “h” = 0.66 / 1,000,000,000,000,000,000,000,000,000,000,000 kg*m^2/sec
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- It is a very small number. That is the reason quantization effects are not noticeable in everyday events. The effects of quantum are only noticeable at the atomic scale or smaller.
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- The amount of energy in a light beam can not be less than that of a single photon. For a given color light there is a minimum amount of energy we can use to observe the world
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-------------------------------------------- Energy = h * f
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- This minimum energy is what causes the Heisenberg Uncertainty principle to exist. (See review #40 Life is Uncertain). This principle states that you can not measure the velocity and position of an atomic particle at the same time. The measurement is always indeterminant, a probability.
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- If you try to measure velocity when the photon of minimum energy hit’s the particle the particle’s velocity changes. If you try to measure its position the same thing happens. When the photon hit’s the particle the position changes.
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- Heisenberg’s formal statement is one of tradeoffs. He says that the product of the particles mass, the uncertainty of its velocity, the uncertainty of its position can not be less than Planck’s constant.
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----------------------------------- Mass * delta v * delta x > h
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- Again, because Planck’s constant is so small the principle has negligible effect in everyday life. However, at the atomic scale it has enormous effect.
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- In order to make Maxwell’s equations work at the atomic scale the solutions must be given in the probabilities of detecting a photon. The link between the wave equation and the particle becomes one of statistics and probabilities.
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- Small atomic structures like photons and electrons will behave like waves as well as like particles depending on the concentration of energies the size of the probabilities. In 1923 Louis De Borglie proposed that matter has waves, that a particles associated wave depends on the particles mass and velocity. This is the same as the particle’s momentum, mass * velocity.
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-------------------------- Wavelength = Planck’s constant / mass * velocity
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- Again, because Planck’s constant is so small the wave-particle duality is not noticeable in everyday life. At the atomic scale it explains a lot.
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------------------------------ Wavelength of an electron = h / m*v
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------------------------------ “h” = Planck’s constant = 6.625*10^-34 kg*m^2/sec
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------------------------------ “m” = mass of electron = 10^-30 kilograms
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------------------------------ “v” = velocity of electron = 10^6 meters / second
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------------------------------ v = 2,236,936 miles/hour
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------------------- Wavelength 6.625 * 10^-34 / 1^-30 * 10^6 = 6.625 * 10^-10 meters
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- This is about the same as the diameter of the atom, 10^-10 meters.
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- The diameter of an electron is 5.6 * 10^-15 meters.
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- The wavelength of the electron is in the same ballpark as the atomic structure. In fact the allowed orbits of electrons within the atom can be explained as the “ standing wave” that can just fit in a specific orbit. Just as a standing wave of a particular note played on a violin string are those that can just fit on the string at each specific length.
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- All matter has waves. My brother is 180 pounds of matter and he has waves. A baseball has waves. Let’s see what happens when we calculate the wavelength of a baseball:
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---------------------------------- Wavelength of a baseball = h / m*v
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---------------------------------- “h” = Planck’s constant
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---------------------------------- “m” = mass of baseball = 0.1 kilograms
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-------------------- “v” = velocity of baseball = 10 meters / second (22 miles per hour)
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--------------- Wavelength of baseball = 6.625*10^-34 kg*m^2/sec / 0.1kg * 10 m/sec
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-------------------------------- Wavelength of baseball = 6.625 * 10-34 meters
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- Granted it was a slow pitch but the wavelength of the baseball is so minuscule that it could never be used to explain the number of strike outs in the major leagues.
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- What we have shown is that at the quantum level matter is both waves and particles. In fact, we could consider the particle to be the concentration of energy in the wave.
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- If you do your own experiment, take a glass slide, paint it black, hold two razor blades together tightly, and make two small scratches on the glass slide. Now, shine a light through the glass slide and project the image on the wall. The light emitting from the slots will project a circular interference pattern on the wall.
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- The wave characteristic of the photons will pass through both slots and begin emanating from the slide as two waves adding and subtracting as their peaks and troughs interfere with each other. This will happen even if you shine one photon at a time on the slide. The buildup of interference will eventually plot the same interference pattern.
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- Amazingly, the same experiment can be conducted using electrons instead of light photons. These are thought of as particles with known mass. We need to use the closely spread atoms of a crystal instead of slits on a glass slide, but the exact same interference pattern will be generated. The electrons will behave as waves.
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If all matter is waves then this could explain how matter interacts with all other matter in the Universe. Maybe some day we will understand how gravity is produced by matter. If all matter in the Universe is interconnected how big should the Universe be?
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- The minimum size of a wave-particle is 10^-14 meter radius. The number of particles in the Universe is 10^80. If all these particles were connected in a sphere the surface area of the sphere would be:
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------------------------ Area of one wave-particle = pi* radius^2 = 3.14 * (10^-14)^2
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------------------------ All interconnected the total area = 10^80 * 3.14 * (10^-14)^2
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------------------------ The surface area of any sphere is = 4 * pi * radius^2
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- If we set these two surface areas equal to each other we can calculate the radius of the Universe:
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------------------------ 4 * pi * radius^2 = 10^80 * 3.14 * (10^-14)^2
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------------------------ Radius = 0.5 * 10^26 meters.
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- The Coma-Virgo Cluster of galaxies is measured at 1.2 * 10^23 meters in radius. It is just one of many galaxy clusters the trace the structure of the Universe. This radius we calculated is about 1000 times bigger. So it is in the ballpark for the observable universe, if not on the low side.
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- The wave characteristics of matter and make up of the Universe is still leaving a lot for us to learn. The matter that we are made of and that we can see makes up only 5% of the observable universe. There is still 95% we call dark matter and dark energy because we don’t know what they are.
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- It is so interesting that we are using the smallest things we know, the quantum, to help us explain the largest thing we know the Universe.
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- April 25, 2019. 51
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--------------------- Thursday, April 25, 2019 -------------------------
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