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 Fun Trivia: Q : Quantum and Orbital Mechanics

### Special Sub-Topic: The Slits of Doom: A Quantum Adventure

 Freda and Ernie were electrons sharing a helium orbital; a state of affairs pleasing to Ernie but intolerable to Freda. "There is no more tame and uninspiring energy state in the universe!" Freda complained. "Orbiting a stable nucleus, stuck in the electron shell of the chemically least reactive element and part of...of..." "Part of a boson?" Ernie offered. "Yes!" Freda screamed. "A Boson. Me, the odd, peaceable, individualistic Freda Fermion - part of a boson. And I swear, Ernie, I think you like being a victim of boson oppression." Ernie couldn't understand his friend. Was she that much of a "ferminist"? Why did she detest being part of a boson so much? Which of the following is not a true statement about bosons and fermions? (Hint: remember that odd, peaceable, individualistic Freda is a fermion, not a boson.)

You can tell a boson from a fermion simply by knowing the electrical charge.. "Boson" and "fermion" are descriptive terms relating to spin. Bosons have spins that are even multiples of 1/2 (0, 1, 2). Fermions have odd multiples of 1/2 (1/2, 3/2, 5/2). There are two varieties of fundamental particles: force particles and matter particles. Force particles are always bosons. The overall spin of atoms and nuclei will be the sum of the spins of the component particles; therefore, any nucleus with an even number of protons and neutrons will be a boson.

 Freda Fermion had berated Ernie for enjoying life in a helium atom, a boson. "Why shouldn't I like it?" countered Ernie defensively. I like stable nuclei. I like being inert." "You would," said Freda scathingly. "But I don't. I want to fly free in the ether. I crave adventure. I want to explore. I want to be fired through the slits of doom!" Ernie would have shivered, if electrons had skin. Is it true that helium is chemically the least reactive element, that the amount of energy required to ionize a first helium electron is the highest of any atom?
y. The amount of energy required to ionize the first electron of an atom varies predictably in the periodic table. Inert or noble gases are the farthest to the right in the table and have higher first ionization energies than elements to the left of them in the table. Ionization energies also increase going up the periodic table. Helium, located at the top right hand corner, has the highest ionization energy.

 Freda Fermion's desire to brave the perilous slits of doom dismayed her friend Ernie, but Ernie was still smarting from Freda's rebuke. "Say what you will, Freda," Ernie said stiffly, "Helium is a noble gas." Freda groaned (although perhaps not as loudly as the reader) at this terrible pun. Abruptly Freda's gasp followed the groan, a gasp that Ernie echoed. "Oh yes, yes!" Freda exulted. "Oh, no, no!" Ernie wailed. "Please, not a 530 electron volt photon. Not double ionization!" The energy required to produce double ionization of the helium atom is 530 ev. What is double IONization?
The abrupt ejection of both electrons from the helium orbital producing a He +2 ion.. The energy required to ionize two electrons is the "double ionization" energy. It is typically expressed in electron volts. A 530 ev photon is very energetic indeed, being in the "x-ray" portion of the electromagnetic spectrum.

 Freda and Ernie had a simultaneous premonition that a 530 ev photon was about to strike their helium atom. Nothing can exceed the speed of light, and the photon is already traveling at that speed. For Freda and Ernie to have advanced warning, it would have to be possible for a particle to affect them from a distance and for this effect to be transmitted faster than the speed of light. Is there any experimental evidence of a "nonlocality" phenomenon that implies instantaneous interaction at a distance between particles obeying quantum mechanical laws? (Would this be a pointless question if there wasn't?)
y. There are a number of predictions of quantum theory that would seem to require particles to "know" instantaneously what has happened to another particle at a distance from them. This has now gone beyond the realm of "thought experiment". In the "Scientific American" of August 1993, a series of experiments is described in which "information" must have been passed from particle to particle instantaneously.

 There was a blinding flash, and Freda Fermion, the adventurous electron, found herself streaking toward an apparatus with a frayed wire. She tumbled into the wire and was immediately carried along in an electrical current. Freda slammed into a tungsten molecule and found herself in an outer orbital shell. She squealed with delight. She was looking from the inside of an electron gun, out the barrel; and in the distance she could see...(drum roll)... the Slits of Doom. What modern device(s) utilize electron guns?
All of these (Color Televisions, Electron Microscopes, CRT computer monitors). If you have an old fashioned CRT monitor, the image you see on your computer screen is the result of electrons being fired from and electron gun and activating colored, phosphorus dots. The gun tracks across the screen, line by line, until an entire screen is painted. A typical computer monitor repaints the screen 85 times per second or more.

 Outside the electron gun Freda could hear the voices of Dr. Max Plankton and the evil wizard physicist, Dr. J Robert Atomhammer. "I have carefully worked through Schroedinger's equation and Heisenberg's matrices," Freda heard Plankton say. "I am certain that if we fire electrons from our gun, through the slits, the electrons will interfere with one another just as if they were waves." "If you are correct, Herr Plankton," opined Atomhammer, "then, on the screen on the other side of the slits, we should see an interference pattern, not the pattern that particles would make." Freda felt the tug of a powerful electrical field. All around her electrons were being pulled through the maw of the gun to be sent streaming through the two slits. Most were screaming in terror as they swirled through the slits. Abruptly the electrical field shut down. A disappointed Freda remained stuck in her orbital. Will Plankton and Atomhammer see an interference pattern, characteristic of waves on the phosphorus screen?
y. Behaving as waves, the particles produce a pattern of bright and dark bands on the detector. The pattern of light and dark would be similar to the peaks and valleys that which would be produced if two rocks were dropped into a still pool. At some points the waves reinforce (add) to one another, while at others they interfere (subtract) from one another.

 "You are no doubt feeling smug now, Plankton." Freda heard Atomhammer say. "But if we fire electrons through the slit one at a time, there will be no "interference" pattern. A single electron fired through two slits couldn't very well split itself so as to go through both slits and interfere with itself." "I do not pretend to understand how they will do it," Plankton responded, "but the theory says they will act like waves, regardless. I expect quantum theory to be confirmed." Freda began feeling repeated tugs from an electrical field. Each time a single electron would be pulled out of a tungsten orbital and fired at the slits. When the electrons are fired at the slits individually, will they behave as particles or somehow manage to obey quantum theory and behave as waves?
Waves. Quantum theory predicts that electrons, even if fired individually at the two slits, will still produce an interference pattern characteristic of waves. They behave is if they can split into to "half" electrons and then interfere with themselves. Equivalent experiments have documented that the predicted behavior does, in fact, occur.

 Freda was becoming frustrated. So many other electrons had had their opportunity to brave the "Slits of Doom", but she remained stuck in her orbital shell. Once again she heard Atomhammer and Plankton discussing the experiment. "It is simply not possible to explain these results," huffed Atomhammer. "The results agree with quantum theory," Plankton countered. "It is the electrons," Atomhammer stated. "They conspire with one another. They communicate with one another, somehow." "That is preposterous," Plankton said. "Oh is it?" Atomhammer retorted. "We shall see. We will place detectors on the slits. The electrons will have to go through one slit or the other because we will be watching. That cursed interference pattern will disappear." "You are mad Atomhammer," Plankton stated flatly, "if you expect electrons to behave differently because we watch them." Will the pattern change to one characteristic of particles if detectors are place that allow the experimenter to determine through which slit an electron passes?
y. Again, theory predicts and experiments confirm that the "watched" electrons will produce the "non-interference" pattern characteristic of particles.

 Freda again felt a tug from an electrical field. She broke out of her orbital and accelerated down the barrel of the electron gun. She hurtled toward the two slits. In an instant she was past them and plowed into a phosphorus molecule on the screen, exciting it to emit a photon. As she careened happily above the two scientists, she saw Plankton scratching his head. "The question is," she heard Atomhammer say, "how do they communicate?" Quantum "transactions" arbitrarily assume that particles are moving forward in time. If you have an electron traveling forward in time, would quantum electrodynamics allow you to substitute a positron moving back in time in certain situations?
y. One explanation that has been put forward to explain the phenomenon of particles seeming to "know" what other particles are doing is just that: viewing quantum transactions as involving anti-matter particles moving back in time.

 Freda sped contently through the ether, a free fermion. There was a sudden disturbance in the empty space in front of her. A positron and electron pair seemed to erupt out of nothing and annihilate one another. What topic of a future physics quiz had Freda just witnessed? (Hint: Physicists don't always have to use inherently confusing terminology.)
Zero point energy. One consequence of quantum theory is that we should not expect "nothing" to just stay that way. Quantum theory predicts that particles will occasionally erupt out of empty space, sometimes "leaking" energy in the process of annihilating themselves. This "zero point energy" has been detected, confirming the prediction.

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