particle wave duality Particle Wave Duality 1 particle

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particle wave duality Particle - Wave Duality 1

particle wave duality Particle - Wave Duality 1

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Einstein knew that energy is involved: 1. when things move - the kinetic energy concept. (for example, water falling over the spillway of a dam) 2. when things are not moving- potential energy concept. (for example, water at the top of dam spillway before the spillway gage opens) 2

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Einstein believed that energy • and mass must be interchangeable. • possessed by a nonmoving object is associated with its mass. • possessed by a moving object is greater than when the object is not moving. (The extra energy coming from objects momentum. ) 3

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Einstein did NOT know: • the structure of atoms and molecules that made up objects. • that the atoms and/or molecules in a nonmoving object are always moving. 4

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Einstein developed a mass-energy theory (idea) that he described succinctly using an equation that connected the energy of an object with two distinct but related mass-energy terms. 2 2 2 Eobject= (m x c ) + 5 (p x c) 2

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) + (p x c) 2 Consider this ball to represent any object with mass. 6

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) + (p x c) 2 Consider this ball to represent any object with mass. Einstein believed there was an amount of energy, E , that defined the object existence of that ball. 7

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) + (p x c) 2 Consider this ball to represent any object with mass. Einstein believed: there was an amount of energy, E , that defined the object existence of that ball. this total energy was the sum of the energy when the ball is not moving plus extra energy, (pxc), if the ball is moving. 8

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) + (p x c) 2 Since momentum, p, is the product of the object’s mass, m, with the object’s velocity, c, p=mxc Einstein knew he could, if he wished, expand his equation to be: 2 2 2 Eobject= (m x c ) + (m x c) 9 2

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) 2 + (p x c) + (m x c) or 2 2 2 Eobject= (m x c ) 2 Einstein consider many situations where his model (equation) might be used. Let’s just look at two of those situations. 10

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) 2 + (p x c) + (m x c) or 2 2 2 Eobject= (m x c ) 2 Case 1: Particle with mass that is not moving. Case 2: “Particle” without mass that is moving. Let’s do the easy case first! 11

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) 2 2 2 Eobject= (m x c ) + (m x c) 2 or 2 2 2 = Eobject (m x c ) + (p x c) 2 Case 1: Particle with mass that is not moving. Since the particle is not moving it does not have any momentum. 2 2 2 = Eobject (m x c ) + 12 2 0 (momentum) (p x c)

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 1: Particle with mass that is not moving. 2 2 2 = Eobject (m x c ) + (p x c) 2 Eobject 2 = (m x c 2 ) 2 Eobject = (m x c 2) thus when an object is not moving the equation of Einstein’s idea reduces to the “Tee Shirt” equation. 13

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 1 = E 2 c m 14

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without mass that is moving. (This situation is what really make’s Einstein’s genius so obvious. ) Einstein considered the possibility that there might be something, a photon of light, that exists but does not have mass. (For someone living in 1905 who understood the physics that was being taught in school then, this was then (and is today) a brilliant thought!! ) 15

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without mass that is moving. Einstein considered the possibility that there might be something, a photon of light, that exists but does not have mass. Einstein then reasoned that if a photon exists it has an energy associated with it and his model (equation) would let him calculate that energy. 2 2 2 Eobject= (m x c ) + 2 (p x c) 16

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without mass that is moving. 2 2 2 = Eobject (m x c ) + (p x c) 2 Since the particle (photon) exists but has no mass, it can not be at rest. 2 2 2 Eobject= (m x c ) + (p x c) 2 2 2 Eobject= (m x 0 c ) + (p x c) When the rest mass, m 17 rest 2 2 , equals 0

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without mass that is moving. 2 Eobject= (m Eobject 2 = rest 0 x c ) 2 2 + (p x c ) (p x c) 2 Eobject = ( p x c ) Now the really clever part! 18 2

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without mass that is moving. Eobject = ( p x c ) Of course Einstein knew that: momentum is the product of mass and velocity p = (m x c ) Therefore, the mass, m, in this momentum equation represented something very special that no one had ever dealt with before. 19

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without rest mass that is moving. To help people understand this new view of mass, Einstein introduced two terms. Rest mass – the mass an object has when it is not moving. Relative mass – the mass an object with no mass can be thought to have when it is moving. Two brand new ideas, at the time, that did not go over very well at first! 20

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without rest mass that is moving. Rest mass = 0 the value for the mass term that is in Relative mass = the model equation when the first term in the equation is equal to zero. 2 2 = + 0 Eobject (m xc ) (p x c) rest Eobject = ( p x c ) p = (m x c ) Eobject = ( m x c ) 21

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2: “Particle” without rest mass that is moving. Eobject = ( m x c ) Eobject 2) (m x c = Therefore: when an object with no mass is moving, the equation of Einstein’s idea reduces to the “Tee Shirt” equation. 22

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) Case 2 E= mc 2 23

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more

particle wave duality Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye) BUT this is NOT the same “Tee Shirt” equation we saw before. 2 E = MC Resting mass “Tee Shirt” Relative mass “Tee Shirt” Case 1: Particle with mass that is not moving. For a baseball: Speed = 0 meters/sec ( in the catcher’s mitt) Case 2: “Particle” without mass that is moving. For a photon: Speed ( in a vacuum) 24 8 = 3 x 10 meters/sec

particle wave duality De Broglie’s Contribution By 1900, the world understood the idea that

particle wave duality De Broglie’s Contribution By 1900, the world understood the idea that light is a mass less wave. (a light ray) By 1923, the world understood the idea that light is a mass less particle. (photons) the duality of light In 1923, } light is a wave; light is a particle De Broglie introduced to the world the idea that a particle with mass also behaved like a wave by connecting the mass and speed of a moving object (its momentum) to a wavelength. l object = the duality of particles h (m object ) (vvelocity ) } electrons are particles; electrons are waves 25

particle wave duality De Broglie’s Contribution – particles have wavelengths (Example calculations for two

particle wave duality De Broglie’s Contribution – particles have wavelengths (Example calculations for two extremely different types of particles. ) 1. ) What is the wavelength value associated with a 0. 15 kg baseball moving with a velocity of 30 meters/second. -31 What is the wavelength associated with a 9. 11 x 10 kg electron 2. ) moving with a velocity of 1. 47 x 10 7 meters/second. In both cases; “De Broglie’s wavelength” is calculated the same way: l object= h (mobject )(vvelocity ) 26

particle wave duality “Debroglie’s wavelength for a moving baseball and electron. Knowns: Planck’s constant

particle wave duality “Debroglie’s wavelength for a moving baseball and electron. Knowns: Planck’s constant = h = 6. 64 x 10 -34 Mass of baseball = 1. 5 x 10 Mass of electron = 9. 11 x 10 -1 -31 Js kg kg Speed of baseball = v = 3. 0 x 10 1 Speed of electron = v = 1. 47 x 10 Unknowns: “Debroglie’s wavelength for baseball = “Debroglie’s wavelength for electron = Equations: l object = h (m object) (vvelocity ) 27 m/s in meters

particle wave duality Knowns: h = 6. 64 x 10 -34 m baseball =

particle wave duality Knowns: h = 6. 64 x 10 -34 m baseball = 1. 5 x 10 m electron = 9. 11 x 10 Equations: l ball = le = Js -1 -31 1 kg v baseball = 3. 0 x 10 m/s kg v electron = 1. 4 x 10 m/s 7 h (m ball ) (vball l electron = ) 6. 64 x 10 -34 Js (1. 5 x 10 -1 1 (9. 11 x 10 (m electron ) (v ) meters kg) (3. 0 x 10 m/s ) 6. 64 x 10 -34 Js - 31 h 7 kg) (3. 4 x 10 m/s ) 28 meters

particle wave duality 29

particle wave duality 29