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Interesting Questions, Facts and Information
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 Interesting Questions, Facts, and Information
 Quantum and Orbital Mechanics
Nu. While nu is used to show frequency, lambda is used to show wavelength.
| The Heisenberg Uncertainty Principle states that it is impossible to determine accurately what of fast moving particles simultaneously? | Elementary Quantum Mechanics
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No. The pricipal quantum number represents energy levels in the atom. The secondary quantum number represents the shape of the orbital (s, p, d, f). The magnetic quantum number represents the different ways an orbital is oriented in space, and the spin quantum number represents the two ways an electron can spin on its axis.
Once upon a time, a little electron named Ernie lived happily in an outer orbital shell of an important copper atom. The copper atom was important because it was part of a wire in the laboratory of the Department of Fiendish Physics of Subatomic University. The wire was frayed, and Ernie had a perfect view of the laboratory. One day, Ernie heard Dr. Max Plankton and the evil wizard physicist, Dr. J Robert Atomhammer, discussing electrons. He heard Atomhammer ask, "Are the little devils particles or waves, that's what I want to know?"
"Ooh, ooh! I know! Electrons are…" Ernie said. But his answer was drowned out in the hum of the machinery. (What did Ernie answer?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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Both. Quantum theory requires a dualism. One particle can interact with another as either a particle or a wave.
"Did you hear something?" Plankton asked.
"Probably just the ether wind," answered Atomhammer dismissively.
"Let's have a look at the cat," suggested Plankton. Ernie had watched earlier as the two scientists constructed their evil, baleful box and placed their cat, Schroedinger, into it. The box had been calibrated so that there was a 50% probability that high-energy photons from a photon gun would pierce the walls. In the box with the cat, they placed a cyanide capsule that could be pierced by the photon. They closed the box, aimed the photon gun at the capsule inside the box and pulled the trigger. Afterward, they argued for hours about whether, inside that baleful box, there was a live cat or a dead cat. (Ernie could have told them. What would he have said?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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According to quantum theory, the cat was neither dead nor alive until the box was opened.. Schroedinger's famous thought experiment was similar to that described above. According to quantum theory, the cat's probability wave does not "collapse" until the box is opened. The cat is, therefore, neither alive nor dead until the box is opened.
| Ernie breathed a sigh of relief when the two men opened the box and pulled out a happily purring Schroedinger. They grilled the cat for hours, asking whether he had been alive or dead before they opened the box. Schroedinger meowed and purred contentedly at first, but eventually he became annoyed with their questions. He scratched out a single equation and stalked off, tail lashing angrily. They asked one of the other laboratory cats, Heisenberg, what he thought. Heisenberg drew out some boxes with figures in them. At first they thought Schroedinger and Heisenberg had given different answers, but when they analyzed the boxes, Heisenberg's boxes reduced to the same equation that Schroedinger had written. (Respectively, what were Schroedinger and Heisenberg's two formulations of quantum mechanics called?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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Schroedinger's equation and Heisenberg's matrix mechanics. Schroedinger and Heisenberg independently formulated what proved to be equivalent mathematical treatments of quantum mechanics. Both were shown to give correct values for the spectral lines of hydrogen. Heisenberg's uncertainty principle could be viewed as a corollary of the basic equations.
"These are interesting equations," conceded Plankton, looking at Schroedinger and Heisenberg's formulation of quantum mechanics.
Atomhammer's eyes gleamed wickedly. "We could, Atomhammer began, "put an innocent little electron into our box. We could make the walls impenetrable except by an infinitely powerful particle or by a wave that obeyed these equations. According to these equations, at times, if the electron is really a wave, the electron will be out of the box. If we open the box and the electron is gone, we know our cats are on to something."
"What if the electron is there every time we open the box? Plankton asked.
"If he's still there over and over again," Atomhammer grinned malevolently, "we'll annihilate him in the electron-positron collider." (Is there actually such a thing as an electron-positron collider (outside of a fairy tale)? | Ernie and the Baleful Box: A Quantum Fairy Tale
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Yes. Electron-positron colliders, such as the one at CERN, study interactions between positrons and electrons and the new particles created in these interactions.
| Ernie the electron's blood would have frozen, if electrons had blood. Those fiends! Ernie felt a tug. Suddenly he was ripped from the copper atom's electron shell. In a rush he hurtled down the wire, shot out into black space and then heard the sickening thud of a lid being shut. He was alone in a box with infinite energy walls. Flash! For just an instant he was outside the box and then back in. These momentary escapes occurred repeatedly but not often. He was never out of the baleful box for more than nanoseconds. The odds of Ernie being out of that box when Atomhammer looked in seemed infinitesimal. (The box has infinite energy walls. How can Ernie be getting out?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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Ernie's probability wave extends outside the box.. In the quantum world, particles are thought of as being geometric points. The wave function is a three dimensional equation that, if solvable, would give the probability of the particle being at any particular point in the space.
Yes. According to Schroedinger's equation, the probability of a particle in a box with infinite energy walls being located at some particular set of spatial coordinates is never 0.
| Flash! Ernie the electron was outside the box. He found himself right next to another electron. It was his old friend Pauli the electron. Suddenly, a stray alpha particle collided with them. (Of what does the alpha particle consist?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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Two protons, two neutrons. Keep in mind, this is a fairy tale. If you've already accepted a box with infinite energy walls, why not the random collision of an alpha particle with an electron during one of the instants the electron is outside the box?
| Ernie was pulled toward the alpha particle. His friend tried to follow him, but something seemed to prevent them both from entering the orbital. He noticed that he and Pauli were spinning in the same direction and groaned. In an instant, a different electron was pulled into the orbital with Ernie, and Pauli bounced away. (Why couldn't Pauli be in the same orbital as Ernie?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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Because of the Pauli Exclusion Principle. The Pauli Exclusion Principle requires that fermions, such as electrons, not share all the same quantum numbers. For an atomic orbital that could contain two electrons, this necessitates that the spin of the two electrons be different.
| The alpha particle had gained two electrons. Ernie felt immense relief. He had escaped the box and was floating free in a stable orbital as part of an inert gaseous atom.
(Of what atom is Ernie part?) | Ernie and the Baleful Box: A Quantum Fairy Tale
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Helium. An alpha particle is, in essence, a helium nucleus. The other elements are much larger and certainly not inert.
| Rocky wants to go to a higher orbit. He performs a burn in his direction of motion increasing his apogee, then while at the orbital apogee, performs another burn to circularize his new orbit. What did Rocky just perform? | Journey Through Orbital Mechanics
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Hohmann Transfer. A Hohmann Transfer is the simplest maneuver to reach a higher altitude and uses the least amount of fuel, but takes a long time to complete.
| Rocky has a mass of 10,000 kg. He is in the same orbit as a small piece of orbital debris, with a mass of 1g, and a 10kg asteroid. Which one takes longer to orbit the Earth? | Journey Through Orbital Mechanics
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They take the same amount of time. According to Kepler's Third Law, the period of an orbit, or the amount of time it takes to travel one complete orbit, does not depend on mass. The square of the period is directly proportional to the cube of the semi-major axis.
| In order to escape Earth's gravity, Rocky must launch with a velocity, or delta V, of 11.3 km/s. On his first launch, he launched into orbit with a delta V of 9 km/s, and the second time with a delta V of 10 km/s. After reaching orbit, which launch allowed Rocky to orbit the Earth in less time, or had a smaller period? | Journey Through Orbital Mechanics
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The first time, launching at 9 km/s. A higher delta V places an object in a higher altitude, but according to Kepler's Third Law, the higher the altitude, the longer it takes to complete an orbit. It's counterintuitive, but launching with a lower initial speed allows an object to travel around Earth in less time. In order to escape Earth's gravitational pull, the minimum escape velocity is 11.3 km/s.
| Rocky is travelling around the Moon and back to Earth using a gravitational slingshot. His trajectory is much like that of Apollo 13. Which can best describe a gravitational slingshot? | Journey Through Orbital Mechanics
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Hyperbolic. According to Kepler’s First Law of Planetary Motion, a planet’s orbit is an ellipse with the Sun at one focus. A lunar gravitational slingshot is simply a hyperbolic orbit, with the Moon at one focus. Though they have very different shapes, a hyperbola can be defined as an ellipse with an eccentricity greater than 1. For an orbital eccentricity less than 1, a spacecraft would never be able to escape the gravitational field of its orbiting body.
| Rocky decides to venture out into space even further. He is now in a heliocentric orbit in a special place where the Earth and Sun always appear in the same relative locations. How many locations are there where he might be, and what are their names? | Journey Through Orbital Mechanics
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5, Lagrangian Points. The five Lagrangian Points are of special interest to the scientific community, since the Sun and the Earth always appear in the same relative locations due to the interaction between gravity from both the Sun and Earth. L1 is a point in space aligned between the Sun and the Earth. It has a smaller orbital radius than the Earth, but because of Earth’s gravitational influence they have the same period. Currently, the Solar and Heliospheric Observatory, or SOHO, is orbiting at L1. L2 is on the same line, but is beyond Earth. In this case, Earth’s gravity causes a shorter orbital period. L3 is in the same orbit as Earth, just 180° apart. This has been the subject of science fiction, since if a planet existed there, we would never be able to detect it since it would be forever blocked by the Sun. L4 and L5 are at opposite 60° angles between the Sun and Earth, also on the same orbit as Earth.
| Every good physicist knows that Maxwell Planck was the first to elucidate the concept of a quantum, an integral part of quantum theory (so integral in fact that the theory bears its name!). But what are the units of the fundamental physical quantum? | The Quantum Quiz
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Joule-second. Planck first proposed his theory in 1900 after working on a discrepancy related to black-body radiation (the phenomenon in which extremely hot objects radiate light). For those who are wondering, Planck's constant, denoted as "h", which describes the size of the fundamental quantum, has a value of 6.626x10^-34 Joule-seconds. The extremely small value of this constant explains why we don't experience any obvious effects of quantization in everyday life.
| The revelation that light exhibited particle-wave duality was revolutionary, but it wasn't long before another physicist, Louis de Broglie, proposed that in fact all matter exhibited particle-wave duality. According to de Broglie, an object's wavelength depends on which of its properties? | The Quantum Quiz
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momentum. De Broglie's hypothesis stated that any object with a non-zero momentum (in other words any moving object) had a characteristic wave associated with it, with a wavelength inversely proportional to its momentum. So yes, even PEOPLE are part-particle/part-wave. Of course, the wavelength of an object is inversely proportional to its mass, so the wavelengths of macroscopic objects are so small that their wave nature is literally undetectable.
| In quantum theory, there is a famous relationship named the Heisenberg Indeterminacy Principle, which says that what two properties of a system cannot both be determined with arbitrarily small uncertainties simultaneously? | The Quantum Quiz
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position and momentum. An interesting consequence of the Indeterminancy Principle is that you cannot confine an object to an arbitrarily small space. If you were to attempt to do so, you would be attempting to decrease both the uncertainty in the object's position and the uncertainty in its momentum simultaneously, which is impossible, and you would inevitably see the object escape its cage. This would be analogous to dropping a ping pong ball into a small cup and watching it shoot out right through the walls of the cup.
| The famous Schrodinger Equation can be said to be the backbone of quantum theory. The equation says that if you apply an operator to the wavefunction of a system, the result is simply the original wavefunction multiplied by the energy of the system. What is the name of the operator? | The Quantum Quiz
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Hamiltonian. For a particle, the Hamiltonian of the wavefunction is a constant (related to Planck's constant and the particle's mass) multiplied by the second derivative of the wavefunction plus the potential energy of the particle all multiplied by the particle's wavefunction.
| The Schrodinger Equation was actually not the first successful attempt to describe the world quantum mechanically. Another physicist had already achieved what Schrodinger did with his equation at an earlier time, albeit in a different manner. Who was this physicist? | The Quantum Quiz
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Werner Heisenberg. Heisenberg, in collaboration with Max Born, essentially "invented" Schrodinger's Equation before Schrodinger! They took a different approach using matrix mechanics, however, and Schrodinger's solution is arguably more elegant. Interestingly enough, only Heisenberg was awarded the Nobel Prize for his efforts; Born was not recognized despite being nominated alongside Heisenberg by Albert Einstein.
| The Dirac Equation is an example of when theory predicts the existence of something that had not yet been discovered (such as when Neptune's existence was predicted from the pertubations in Uranus' orbit). What did the Dirac Equation predict existed (and would later be confirmed)? | The Quantum Quiz
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antimatter. The Dirac Equation necessitated the existence of positions, the antiparticle to electrons. Dirac himself predicted the the existence of such particles in 1931, and in 1932, cloud chamber experiments confirmed his prediction.
| While Dirac showed with his equation that quantum theory and relativity are at least not incompatible, fully merging quantum theory with relativity would require the development of what is called quantum field theory. What was the first fully developed quantum field theory? | The Quantum Quiz
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quantum electrodynamics. Quantum electrodynamics (quantum field theory of light) matured in the 1940s, while quantum chromodynamics came about in the 1970s. The electroweak theory was developed in the 1970s and 1980s. The fundamental difference between quantum field theory and just plain old quantum theory is that quantum field theory treats fields as quantized (hence quantum FIELD theory) as opposed to individual particles.
| So far, quantum field theories have been formulated for 3 of the 4 fundamental forces of nature. Which fundamental force has yet to be described by a quantum field theory? | The Quantum Quiz
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gravity. Quantum chromodynamics is the quantum field theory for the strong nuclear force, while electroweak theory is a unification of the electromagnetic and weak nuclear forces. The merging of gravity, which is currently best described by general relativity, with quantum theory is perhaps the greatest unsolved mystery in modern physics. Numerous attempts have been made to reconcile general relativity with quantum mechanics, such as string theory and M-theory. Perhaps it is fitting that the crown jewel of Einstein's scientific career now so stubbornly resists the theory that Einstein himself disliked so much.
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