wave particle duality*
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/1.jpg)
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
![Page 2: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/2.jpg)
“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.
![Page 3: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/3.jpg)
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!
![Page 4: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/4.jpg)
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
![Page 5: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/5.jpg)
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.
![Page 6: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/6.jpg)
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
![Page 7: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/7.jpg)
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…
![Page 8: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/8.jpg)
Now for a little derivation =DE=mc2 The general equation for the
light-energy relationship
![Page 9: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/9.jpg)
Now for a little derivation =DE=mc2
E=hν For light, energy is proportional to Planck’s constant (h) times frequency (ν)
![Page 10: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/10.jpg)
Now for a little derivation =DE=mc2
E=hνhν=mνc2 Substitute hν for E
![Page 11: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/11.jpg)
Now for a little derivation =DE=mc2
E=hνhν=mνc2
mν= hν/c2 Rearrange for mν
So, now our thought progression looks like this:
![Page 12: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/12.jpg)
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?
![Page 13: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/13.jpg)
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
![Page 14: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/14.jpg)
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:
![Page 15: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/15.jpg)
Now, let’s play pool XP
𝑚1𝑣 1
𝑚2𝑣 2
𝑚1 𝑣
1 ′
p =
θ
φ p =
![Page 16: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/16.jpg)
…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.
![Page 17: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/17.jpg)
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:
![Page 18: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/18.jpg)
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?
![Page 19: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/19.jpg)
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
![Page 20: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/20.jpg)
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
![Page 21: Wave Particle Duality*](https://reader035.vdocuments.pub/reader035/viewer/2022062218/56816606550346895dd9366f/html5/thumbnails/21.jpg)
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!!!