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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. - PowerPoint PPT Presentation
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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!!!