Wave Particle Duality*

Wave Particle Duality* *Information for this presentation was taken from ASU PHY 540 and “Chemical Bonding Clarified Through Quantum Mechanics” by George C. Pimemtel and Richard D. Spratley

“Energy transfer is accompanied by a mass transfer and every mass, whether moving or not, represents a store of energy” E α m The proportionality constant between these units is c2 E = mc2 Einstein proposed this in 1905 as a model to explain how energy and mass are simply different materializations of the same thing.

E=mc2 Energy has mass Mass is energy Since energy and mass are the same thing, the conservation laws of the two are now bonded Physics and chemistry got married!

E=mc2 Energy has mass Mass is energy • Blackbody radiation shows a continuous spectrum Light from a hot source is continuous and • Radiation intensity from a given source changes with temperature

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and Smaller and smaller pieces of a type of stuff look the same.

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and but While matter looks continuous, its properties are explained with a particulate model Atomic theory requires matter to be particulate

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous so and and but Is light also particulate? Atomic theory requires matter to be particulate Now, we must confront the essential question…

Now for a little derivation =D E=mc2 The general equation for the light-energy relationship

Now for a little derivation =D E=mc2 For light, energy is proportional to Planck’s constant (h) times frequency (ν) E=hν

Now for a little derivation =D E=mc2 E=hν hν=mνc2 Substitute hν for E

Now for a little derivation =D E=mc2 E=hν hν=mνc2 mν= hν/c2 Rearrange for mν So, now our thought progression looks like this:

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and and but Light is particulate mass: Atomic theory requires matter to be particulate But what about momentum?

This calls for another derivation ^.^ Momentum = mass (velocity) = c is the speed of light Because = = = Erase middle term, cancels …since So let’s add that to the thought progression

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and and but Light is particulate mass: Atomic theory requires matter to be particulate momentum:

Now, let’s play pool XP p = θ p = φ

…and parallel that to the scattering of light A.H. Compton proved that when electrons scatter x-rays, there is a momentum change. e p = θ e φ λ p = λ’ Incident light ray has a certain wavelength and a certain frequency reflected light ray has a different wavelength and a different frequency

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and and but and Light is particulate mass: momentum: Atomic theory requires matter to be particulate Light has wave properties frequency: wavelength:

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and so and and but and Light is particulate mass: momentum: Atomic theory requires matter to be particulate Light has wave properties frequency: wavelength: Does matter havewave properties?

Let’s make sure we define the matter-wave property relationship :-] = Momentum is connected to wavelength for light Let’s assume the same for mass = = And rearrange for wavelength The wave behavior of light can be proven using diffraction grating or crystals

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and and and but and Light is particulate mass: momentum: Atomic theory requires matter to be particulate Light has wave properties frequency: wavelength: Matter has wave properties wavelength

E=mc2 Energy has mass Mass is energy Light from a hot source is continuous Matter appears to be continuous and and and and but and Enter Quantum Mechanics!!! Light is particulate mass: momentum: Atomic theory requires matter to be particulate Light has wave properties frequency: wavelength: Matter has wave properties wavelength

Wave Particle Duality*