logging in or signing up Waves and Atoms wpatcunningham64 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 51 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: April 18, 2010 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Waves and Atoms : Waves and Atoms A 3-d orbital The Birth of Modern Atomic Theory Models of the Atom : Models of the Atom Dalton: hard sphere Models of the Atom : Models of the Atom Dalton: hard sphere Thomson: raisin pudding Models of the Atom : Models of the Atom Dalton: hard sphere Thomson: raisin pudding Rutherford: nuclear, planetary model Models of the Atom : Models of the Atom Dalton: hard sphere Thomson: raisin pudding Rutherford: nuclear, planetary model Bohr: nuclear, orbiting electrons in distinct energy levels The Advantages : The Advantages The Bohr Atom Was a nuclear atom Left the electrons free to be given away or shared Did not collapse Because we just said “the electrons can only orbit at specific distances” Explained the emission spectra of atoms (changing energy levels, electrons emit specific frequencies of light) The Disadvantages : The Disadvantages The Bohr Atom No explanation of why or how the electrons could orbit only at specific distances or energy levels ? The Disadvantages : The Disadvantages The Bohr Atom No explanation of why or how the electrons could orbit only at specific distances or energy levels No explanation of how it is that molecules have a specific shape Electrons just ran around the nucleus, not in a specific place ? Benzene is flat and cyclical The Disadvantages : The Disadvantages The Bohr Atom No explanation of why or how the electrons could orbit only at specific distances or energy levels No explanation of how it is that molecules have a specific shape Electrons just ran around the nucleus, not in a specific place The math only worked for the hydrogen atom, not for anything with multiple electrons and protons! ? What is an electron? : What is an electron? We assume it is a particle Like a tiny hard sphere with a negative charge What is an electron? : What is an electron? We assume it is a particle Like a hard sphere But Einstein's study of the photoelectric effect stunned science What is an electron? : What is an electron? We assume it is a particle Like a hard sphere But Einstein's study of the photoelectric effect stunned science He showed that light, electromagnetic energy, can act like a particle, a packet of energy He called the packet a photon What is an electron? : What is an electron? We assume it is a particle Like a hard sphere But Einstein's study of the photoelectric effect stunned science He showed that light, electromagnetic energy, can act like a particle, a packet of energy So Louis de Broglie asked why a particle couldn't act like a wave Is the electron an energy wave? What is an electron? : What is an electron? Experiment shows that electrons can act like waves of light—very high energy, short wavelength light What is an electron? : What is an electron? Experiment shows that electrons can act like waves of light—very high energy, short wavelength light That's why we can use electrons to “light up” very small cellular structures in an electron microscope What is an electron? : What is an electron? Experiment shows that electrons can act like waves of light—very high energy, short wavelength light That's why we can use electrons to “light up” very small cellular structures in an electron microscope This is a fly's foot as imaged by an electron microscope Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Now h is Planck's constant, which is about 10 -33 J-s Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Now h is Planck's constant, which is about 10-33 J-s And m is the mass in kg And v is the velocity in meters per second Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv So just for fun, let's figure out your coach's wavelength Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = h mv In order of magnitude, coaches are about 102 kg and can move about 101 m/s So. . . Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = 10-33 102 x 101 = 10-36 m Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = 10-33 102 x 10 = 10-36 m If you think that's a short wavelength, you are right. The smallest atom is about 10-11 meters in size Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = 10-33 102 x 10 = 10-36 m So your coach's wavelength is too small to observe, even at top speed. Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = 10-33 107 x 10-30 (We'll assume that the velocity of these electrons is 10% of the speed of light, or 107 m/s and the electron mass is 10-30 kg) Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = 10-10 meters This wavelength is much longer than coach's, and could be used to light up a very small structure like a cell organelle. Electron as wave : Electron as wave So why did we take this trip into finding the electron's wave nature? Electron as wave : Electron as wave So why did we take this trip into finding the electron's wave nature? We wanted to find out how the electron behaves when close to the nucleus Electron as wave : Electron as wave So why did we take this trip into finding the electron's wave nature? We wanted to find out how the electron behaves when close to the nucleus Why can the electron only inhabit certain energy levels, and how can it get from a high energy level to a lower one without going anywhere in between? Waves on a string : Waves on a string This is a standing wave on a string The frequency is set so that there is a null spot or “node” in two places Waves on a string : Waves on a string This is a standing wave on a string The frequency is set so that there is a null spot or “node” in two places Union College website The waves generated at the end of the string vibrate at just the right frequency so that the parts of the string vibrate well in two or three spots, and not at all at the nodes Waves on a string : Waves on a string This can be demonstrated on a guitar or banjo string by plucking it in the middle and then holding the middle still while it is plucked halfway between the middle and the end. Waves on a string : Waves on a string This can be demonstrated on a guitar or banjo string by plucking it in the middle and then holding the middle still while it is plucked halfway between the middle and the end. A tone one octave higher is generated as both sides vibrate twice as fast. Waves on a string : Waves on a string This man is demonstrating how to set up higher and higher frequency standing waves on a string Light and matter.com Waves on a string : Waves on a string This man is demonstrating how to set up higher and higher frequency standing waves on a string It is obvious that only standing waves with a whole number of “lobes” and nodes will occur Waves on a string : Waves on a string This man is demonstrating how to set up higher and higher frequency standing waves on a string And if you try this yourself, you will see that the more lobes and nodes you have on the string, the more energy is needed to keep it going! Waves on a string : Waves on a string So if the electron is acting like a wave when it is near the nucleus, it can have only certain energies, and when it changes from a higher to a lower energy, there really is nothing in between. NASA website Waves on a string : Waves on a string Why? There's nothing in between because the electron is acting like a 3-D standing wave, and there are no energies between the allowed standing wave energies. NASA website The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. But it's not a planet revolving about the sun. The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. Think about what the standing wave below “looks like” The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. Think about what the standing wave below “looks like” It looks all “fuzzy” The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. Think about what the standing wave below “looks like” Only the nodes are clearly seen The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's talk in terms of probability There's zero probability of the wave at the nodes The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's talk in terms of probability And maximum probability of the wave here The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's think of a particle that we have to play probability games with Gnat in a box : Gnat in a box If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's think of a particle that we have to play probability games with It's a gnat flying around your head, or maybe a mosquito. Gnat in a box : Gnat in a box If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. But it's not a planet revolving about the sun. It's a gnat flying around your head, or maybe a mosquito. Does the mosquito fly in a predictable path? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Here's two seconds of a mosquito's life in a single picture Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Here's two seconds of a mosquito's life in a single picture Can you tell the path she took? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Here's two seconds of a mosquito's life in a single picture Can you tell the path she took? No. All you can tell is the probability of the mosquito being somewhere Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Where is the highest probability of finding the mosquito? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Where is the highest probability of finding the mosquito? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Where is the highest probability of finding the mosquito? Why do you think the mosquito spends so much time there? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them Or looking for food. . . Where is the highest probability of finding the mosquito? Why do you think the mosquito spends so much time there? Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths A mathematical equation is used to describe the probability of finding them in any given place Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths A mathematical equation is used to describe the probability of finding them in any given place This is a 2-D chart of such an equation, given n = 1. Such an equation was worked out by Erwin Schrödinger Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths The electron probability looks like a “cloud” of negative electricity Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths This spherical cloud is how the electron “looks” on the first energy level (n=1) Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths Without animation, this is one of the “orbitals” (electron clouds) on the second energy level. . . Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths Without animation, this is one of the “orbitals” (electron clouds) on the second energy level. . . You can see the space where there is no probability of finding the electron, a “node” www2.bwdsb.on.ca More orbitals : More orbitals This is one of three “p” orbitals in the 2nd energy level (2p) More orbitals : More orbitals This is one of three “p” orbitals in the 2nd energy level (2p) The gray figure represents the node where the probability of finding the electron is zero More orbitals : More orbitals This is one of three “p” orbitals in the 3rd energy level (3p) The gray figure represents the nodes where the probability of finding the electron is zero More orbitals : More orbitals This is one of five “d” orbitals in the 3rd energy level (3d) The gray figure represents the nodes where the probability of finding the electron is zero Next : Next We can better understand the periodic table now that we know where the electrons are and how they are added to atoms How Standing Waves are created : How Standing Waves are created Animation courtesy of Dr. Dan Russell, Kettering University If two sinusoidal waves having the same frequency (wavelength) and the same amplitude are travelling in opposite directions in the same medium then, using superposition, the net displacement of the medium is the sum of the two waves. As the movie shows, when the two waves are 180° out-of-phase with each other they cancel, and when they are in-phase with each other they add together. As the two waves pass through each other, the net result alternates between zero and some maximum amplitude. You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Waves and Atoms wpatcunningham64 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 51 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: April 18, 2010 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Waves and Atoms : Waves and Atoms A 3-d orbital The Birth of Modern Atomic Theory Models of the Atom : Models of the Atom Dalton: hard sphere Models of the Atom : Models of the Atom Dalton: hard sphere Thomson: raisin pudding Models of the Atom : Models of the Atom Dalton: hard sphere Thomson: raisin pudding Rutherford: nuclear, planetary model Models of the Atom : Models of the Atom Dalton: hard sphere Thomson: raisin pudding Rutherford: nuclear, planetary model Bohr: nuclear, orbiting electrons in distinct energy levels The Advantages : The Advantages The Bohr Atom Was a nuclear atom Left the electrons free to be given away or shared Did not collapse Because we just said “the electrons can only orbit at specific distances” Explained the emission spectra of atoms (changing energy levels, electrons emit specific frequencies of light) The Disadvantages : The Disadvantages The Bohr Atom No explanation of why or how the electrons could orbit only at specific distances or energy levels ? The Disadvantages : The Disadvantages The Bohr Atom No explanation of why or how the electrons could orbit only at specific distances or energy levels No explanation of how it is that molecules have a specific shape Electrons just ran around the nucleus, not in a specific place ? Benzene is flat and cyclical The Disadvantages : The Disadvantages The Bohr Atom No explanation of why or how the electrons could orbit only at specific distances or energy levels No explanation of how it is that molecules have a specific shape Electrons just ran around the nucleus, not in a specific place The math only worked for the hydrogen atom, not for anything with multiple electrons and protons! ? What is an electron? : What is an electron? We assume it is a particle Like a tiny hard sphere with a negative charge What is an electron? : What is an electron? We assume it is a particle Like a hard sphere But Einstein's study of the photoelectric effect stunned science What is an electron? : What is an electron? We assume it is a particle Like a hard sphere But Einstein's study of the photoelectric effect stunned science He showed that light, electromagnetic energy, can act like a particle, a packet of energy He called the packet a photon What is an electron? : What is an electron? We assume it is a particle Like a hard sphere But Einstein's study of the photoelectric effect stunned science He showed that light, electromagnetic energy, can act like a particle, a packet of energy So Louis de Broglie asked why a particle couldn't act like a wave Is the electron an energy wave? What is an electron? : What is an electron? Experiment shows that electrons can act like waves of light—very high energy, short wavelength light What is an electron? : What is an electron? Experiment shows that electrons can act like waves of light—very high energy, short wavelength light That's why we can use electrons to “light up” very small cellular structures in an electron microscope What is an electron? : What is an electron? Experiment shows that electrons can act like waves of light—very high energy, short wavelength light That's why we can use electrons to “light up” very small cellular structures in an electron microscope This is a fly's foot as imaged by an electron microscope Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Now h is Planck's constant, which is about 10 -33 J-s Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Now h is Planck's constant, which is about 10-33 J-s And m is the mass in kg And v is the velocity in meters per second Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv So just for fun, let's figure out your coach's wavelength Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = h mv In order of magnitude, coaches are about 102 kg and can move about 101 m/s So. . . Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = 10-33 102 x 101 = 10-36 m Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = 10-33 102 x 10 = 10-36 m If you think that's a short wavelength, you are right. The smallest atom is about 10-11 meters in size Coach's Wavelength : Coach's Wavelength What is coach's wavelength? Depends upon his/her velocity: λ = 10-33 102 x 10 = 10-36 m So your coach's wavelength is too small to observe, even at top speed. Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = h mv Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = 10-33 107 x 10-30 (We'll assume that the velocity of these electrons is 10% of the speed of light, or 107 m/s and the electron mass is 10-30 kg) Electron Wavelength : Electron Wavelength What is the electron's wavelength? Depends upon its velocity: λ = 10-10 meters This wavelength is much longer than coach's, and could be used to light up a very small structure like a cell organelle. Electron as wave : Electron as wave So why did we take this trip into finding the electron's wave nature? Electron as wave : Electron as wave So why did we take this trip into finding the electron's wave nature? We wanted to find out how the electron behaves when close to the nucleus Electron as wave : Electron as wave So why did we take this trip into finding the electron's wave nature? We wanted to find out how the electron behaves when close to the nucleus Why can the electron only inhabit certain energy levels, and how can it get from a high energy level to a lower one without going anywhere in between? Waves on a string : Waves on a string This is a standing wave on a string The frequency is set so that there is a null spot or “node” in two places Waves on a string : Waves on a string This is a standing wave on a string The frequency is set so that there is a null spot or “node” in two places Union College website The waves generated at the end of the string vibrate at just the right frequency so that the parts of the string vibrate well in two or three spots, and not at all at the nodes Waves on a string : Waves on a string This can be demonstrated on a guitar or banjo string by plucking it in the middle and then holding the middle still while it is plucked halfway between the middle and the end. Waves on a string : Waves on a string This can be demonstrated on a guitar or banjo string by plucking it in the middle and then holding the middle still while it is plucked halfway between the middle and the end. A tone one octave higher is generated as both sides vibrate twice as fast. Waves on a string : Waves on a string This man is demonstrating how to set up higher and higher frequency standing waves on a string Light and matter.com Waves on a string : Waves on a string This man is demonstrating how to set up higher and higher frequency standing waves on a string It is obvious that only standing waves with a whole number of “lobes” and nodes will occur Waves on a string : Waves on a string This man is demonstrating how to set up higher and higher frequency standing waves on a string And if you try this yourself, you will see that the more lobes and nodes you have on the string, the more energy is needed to keep it going! Waves on a string : Waves on a string So if the electron is acting like a wave when it is near the nucleus, it can have only certain energies, and when it changes from a higher to a lower energy, there really is nothing in between. NASA website Waves on a string : Waves on a string Why? There's nothing in between because the electron is acting like a 3-D standing wave, and there are no energies between the allowed standing wave energies. NASA website The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. But it's not a planet revolving about the sun. The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. Think about what the standing wave below “looks like” The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. Think about what the standing wave below “looks like” It looks all “fuzzy” The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. Think about what the standing wave below “looks like” Only the nodes are clearly seen The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's talk in terms of probability There's zero probability of the wave at the nodes The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's talk in terms of probability And maximum probability of the wave here The Particle Analogy : The Particle Analogy If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's think of a particle that we have to play probability games with Gnat in a box : Gnat in a box If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. So let's think of a particle that we have to play probability games with It's a gnat flying around your head, or maybe a mosquito. Gnat in a box : Gnat in a box If you still want to look at the electron as a particle, quantum mechanics has a model for you to think about. But it's not a planet revolving about the sun. It's a gnat flying around your head, or maybe a mosquito. Does the mosquito fly in a predictable path? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Here's two seconds of a mosquito's life in a single picture Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Here's two seconds of a mosquito's life in a single picture Can you tell the path she took? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Here's two seconds of a mosquito's life in a single picture Can you tell the path she took? No. All you can tell is the probability of the mosquito being somewhere Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Where is the highest probability of finding the mosquito? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Where is the highest probability of finding the mosquito? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them They are trying to avoid getting killed Where is the highest probability of finding the mosquito? Why do you think the mosquito spends so much time there? Gnat in a box : Gnat in a box Tiny insects fly in unpredictable paths that “make sense” only to them Or looking for food. . . Where is the highest probability of finding the mosquito? Why do you think the mosquito spends so much time there? Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths A mathematical equation is used to describe the probability of finding them in any given place Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths A mathematical equation is used to describe the probability of finding them in any given place This is a 2-D chart of such an equation, given n = 1. Such an equation was worked out by Erwin Schrödinger Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths The electron probability looks like a “cloud” of negative electricity Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths This spherical cloud is how the electron “looks” on the first energy level (n=1) Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths Without animation, this is one of the “orbitals” (electron clouds) on the second energy level. . . Electron as “bug” : Electron as “bug” Electrons around the nucleus can also be considered as particles without knowing their paths Without animation, this is one of the “orbitals” (electron clouds) on the second energy level. . . You can see the space where there is no probability of finding the electron, a “node” www2.bwdsb.on.ca More orbitals : More orbitals This is one of three “p” orbitals in the 2nd energy level (2p) More orbitals : More orbitals This is one of three “p” orbitals in the 2nd energy level (2p) The gray figure represents the node where the probability of finding the electron is zero More orbitals : More orbitals This is one of three “p” orbitals in the 3rd energy level (3p) The gray figure represents the nodes where the probability of finding the electron is zero More orbitals : More orbitals This is one of five “d” orbitals in the 3rd energy level (3d) The gray figure represents the nodes where the probability of finding the electron is zero Next : Next We can better understand the periodic table now that we know where the electrons are and how they are added to atoms How Standing Waves are created : How Standing Waves are created Animation courtesy of Dr. Dan Russell, Kettering University If two sinusoidal waves having the same frequency (wavelength) and the same amplitude are travelling in opposite directions in the same medium then, using superposition, the net displacement of the medium is the sum of the two waves. As the movie shows, when the two waves are 180° out-of-phase with each other they cancel, and when they are in-phase with each other they add together. As the two waves pass through each other, the net result alternates between zero and some maximum amplitude.