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=mc2Energy 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=mc2Energy has mass Mass is energy

Light from a hot source is continuous

and

• Blackbody radiation shows a continuous spectrum

• Radiation intensity from a given source changes with temperature

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

andand

Smaller and smaller pieces of a type of stuff look the same.

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

andand

Atomic theory requires matter to be particulate

but

While matter looks continuous, its properties are explained with a particulate model

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

and

but

Is light also particulate?

so

Now, we must confront the essential

question…

Now for a little derivation =DE=mc2 The general equation for the

light-energy relationship

Now for a little derivation =DE=mc2

E=hν For light, energy is proportional to Planck’s constant (h) times frequency (ν)

Now for a little derivation =DE=mc2

E=hνhν=mνc2 Substitute hν for E

Now for a little derivation =DE=mc2

E=hνhν=mνc2

mν= hν/c2 Rearrange for mν

So, now our thought progression looks like this:

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

Light is particulatemass:

and

but

and

But what about momentum?

This calls for another derivation ^.^𝑝=𝑚𝑣 Momentum = mass (velocity)𝑝𝑣=𝑚𝑣𝑐 c is the speed of light

= Because =

= Erase middle term, cancels

= …since

So let’s add that to the thought progression

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

Light is particulatemass:

and

but

andmomentum:

Now, let’s play pool XP

𝑚1𝑣 1

𝑚2𝑣 2

𝑚1 𝑣

1 ′

p =

θ

φ p =

…and parallel that to the scattering of light

θ

φ

𝑣

𝜈=𝑐𝜆

𝑣 ′= 𝑐𝜆′

p =

p =

λ

e

e

λ’Incident light ray has a certain wavelength and a certain frequency

reflected light ray has a different wavelength and a different frequency

A.H. Compton proved that when electrons scatter x-rays, there is a momentum change.

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

Light is particulatemass:

momentum:

and

but

and

and

Light has wave propertiesfrequency:

wavelength:

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

Light is particulatemass:

momentum:

and

but

and

and

Light has wave propertiesfrequency:

wavelength: so

Does matter have wave 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=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

Light is particulatemass:

momentum:

and

but

and

and

Light has wave propertiesfrequency:

wavelength: and

Matter has wave propertieswavelength

E=mc2Energy has mass Mass is energy

Light from a hot source is continuous

Matter appears to be continuous

and

Atomic theory requires matter to be particulate

Light is particulatemass:

momentum:

and

but

and

and

Light has wave propertiesfrequency:

wavelength: and

Matter has wave propertieswavelength

Enter

Quantum

Mechanics!!!