particle wave duality 1 Particle - Wave Duality

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

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

particle wave duality 4 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. Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 5 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. E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 6 Consider this ball to represent any object with mass. E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 7 Einstein believed object there was an amount of energy, E, that defined the existence of that ball. Consider this ball to represent any object with mass. E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 8 Einstein believed: this total energy was the sum of the energy when the ball is not moving object there was an amount of energy, E, that defined the existence of that ball. Consider this ball to represent any object with mass. this total energy was the sum of the energy when the ball is not moving plus extra energy, (p x c), if the ball is moving. E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 9 E object = (m x c ) 22 + (m x c x c) 2 2 Since momentum, p, is the product of Einstein knew he could, if he wished, expand his equation to be: p = m x c the object’s mass, m, with the object’s velocity, c, E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 10 Einstein consider many situations where his model (equation) might be used. or Let’s just look at two of those situations. E object = (m x c ) 22 + (m x c x c) 2 2 E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 11 Case 1: Particle with mass that is not moving. Case 2: “Particle” without mass that is moving. Let’s do the easy case first! or E object = (m x c ) 22 + (m x c x c) 2 2 E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 12 or Case 1: Particle with mass that is not moving. Since the particle is not moving it does not have any momentum. E object = (m x c ) 22 + (p x c) 2 2 E object = (m x c ) 22 + (p x c) (momentum) E object = (m x c ) 22 + (m x c x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 13 Case 1: Particle with mass that is not moving. E object 2 = (m x c ) 22 thus when an object is not moving the equation of Einstein’s idea reduces to the “Tee Shirt” equation. E object = (m x c ) 2 Case 1: Particle with mass that is not moving. E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

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

particle wave duality 15 Einstein considered the possibility that there might be something, a photon of light, that exists but does not have mass. (This situation is what really make’s Einstein’s genius so obvious.) (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!! ) Case 2: “Particle” without mass that is moving. Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 16 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. Case 2: “Particle” without mass that is moving. E object = (m x c ) 22 + (p x c) 2 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 17 Since the particle (photon) exists but has no mass, it can not be at rest. Case 2: “Particle” without mass that is moving. E object = (m x c ) 22 + (p x c) 2 2 E object = (m x c ) 22 + (p x c) 2 2 E object = (m x c ) 22 + (p x c) When the rest mass,m rest, equals 0 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 18 Case 2: “Particle” without mass that is moving. E object 2 = E = ( p x c ) Now the really clever part! (p x c ) 2 E object = (m x c ) 22 + (p x c) 22 rest 0 Case 2: “Particle” without mass that is moving. Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

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

particle wave duality 20 To help people understand this new view of mass, 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. Case 2: “Particle” without rest mass that is moving. Einstein introduced two terms. Two brand new ideas, at the time, that did not go over very well at first! Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

particle wave duality 21 Rest mass = 0 Relative mass = the value for the mass term that is in the model equation when the first term in the equation is equal to zero. E object = ( p x c ) p = (m x c ) ( m x c x c ) Case 2: “Particle” without rest mass that is moving. E object = (m x c ) 222 rest 0 E object = + (p x c) 2 Einstein’s Famous Idea in Equation Form (light is a little more than meets the eye)

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

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

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

particle wave duality 25 In 1923, (m ) object (v ) velocity h object = De Broglie’s Contribution By 1923, the world understood the idea that light is a mass less particle. (photons) By 1900, the world understood the idea that light is a mass less wave. (a light ray) } light is a wave; 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. } electrons are particles; electrons are waves the duality of light the duality of particles light is a particle

particle wave duality 26 (m ) object (v ) velocity h object = What is the wavelength value associated with a 0.15 kg baseball moving with a velocity of 30 meters/second. De Broglie’s Contribution – particles have wavelengths What is the wavelength associated with a 9.11 x10 kg electron -31 moving with a velocity of 1.47 x 10 meters/second. 7 (Example calculations for two extremely different types of particles.) 1.) 2.) In both cases; “De Broglie’s wavelength” is calculated the same way:

particle wave duality 27 “Debroglie’s wavelength for a moving baseball and electron. Knowns: Unknowns: Equations: (m ) object (v ) velocity h object = Mass of baseball = 1.5 x 10 kg - 1 Mass of electron = 9.11 x 10 kg -31 Planck’s constant = h = 6.64 x 10 Js -34 Speed of electron = v = 1.47 x 10 m/s 7 Speed of baseball = v = 3.0 x 10 m/s 1 “Debroglie’s wavelength for baseball =in meters “Debroglie’s wavelength for electron =in meters

particle wave duality 28 h = 6.64 x 10 Js -34 m = 1.5 x 10 kg - 1 baseball m = 9.11 x 10 kg -31 electron v = 3.0 x 10 m/s 1 baseball Knowns: v = 1.4 x 10 m/s 7 electron (m ) ball (v ) ball h ball = Equations: (m ) electron (v ) h electron = meters ball = 6.64 x 10 Js -34 (1.5 x 10 kg) - 1 (3.0 x 10 m/s ) 1 meters e = 6.64 x 10 Js -34 (9.11 x 10 kg) - 31 (3.4 x 10 m/s ) 7

particle wave duality 29