View
221
Download
0
Tags:
Embed Size (px)
Citation preview
P2-13: ELECTRON DIFFRACTIONP3-51: BALMER SERIES
P2-15: WAVE PACKETS – OSCILLATORSP2-12: X-RAY DIFFRACTION MODELP2-11: INTERFERENCE OF PHOTONS
Lecture Demos
Where: Chemistry building (attached to Physics building)Room # 1402
When:October: 20, 27, and 29
Change of Class room: See schedule on website
Quantum means “a discrete amount”. Energy only exists in lumps, and these lumps have a minimum lump size (for a confined particle & photons).
Matter (like electrons, protons, neutrons, atoms, etc.) and light travel as waves. When detected, they transfer their energy to a detector (like a particle collision).
This is quantum mechanics.
We will investigate the phenomenology of matter interference and diffraction, and the phenomenology of detecting light and matter.
Before starting, here is what will be emphasized in the chapter:
1.Electrons, neutrons, atoms, etc. exhibit the properties of interference and diffraction.
2. The wavelength of matter waves is related to momentum:
3. E&M radiation can be thought of as composed of photons, or ‘wave packets’. Matter can be thought of as composed of wave packets as well.
4. The energy of a photon is related to it’s frequency:
5. Particles which are confined in space (i.e. a small box) form standing waves --- only discrete amounts of momentum and energy are allowed.
“particle/wave duality”:Matter and light (photons) travel as waves or wave packets. They are individually detected as discrete “lumps”.
Fourier analysis of the wave packet yields Heisenberg uncertainty principle.
Arbitrary wave packet – the more spread out it is in x, the smaller the range of frequencies required to make it:
Wave packets – understanding Heisenberg Uncertainty principle
Arbitrary wave packet – the more spread out it is in x, the less spread in frequencies required to make it:
Heisenberg uncertainty relation:Momentum p ~ k, so
Wave packets – understanding Heisenberg Uncertainty principle
X-rays
X-rays are E&M radiation of high frequency (short wavelength ~0.01 to 10 nm). Recall that light ~500nm
Can use X-rays to probe crystal structures of matter, where the regularly repeating grid of atoms act like a “3-D” diffraction grating where atoms are ~0.5 nm apart.
Many Planes Many Bragg peaks in X-ray spectrum
From X-ray spectrum Bragg peaks, the complete 3-D crystal structure can be surmised for completely unknown crystal structures.
Also used to analyze the quality of crystals (poor quality broad peaks) or if there exists twinning.
A SINGLE photon incident on double slit at a time.
The “photon” interferes with itself. That is, the wave packet is sufficiently spread out enough in space to go through both slits.
When detected, each photon is detected as a single lump somewhere on the screen, but the probability of where it is detected obeys the double slit interference pattern.
A classical particle would travel in a straight line and impact the screen, traveling through one hole or another --- no interference and no diffraction.
Photons – phenomenology: Double slit interference
Electrons travel as a wave!!
Wavelength found from Bragg peaks assuming the same lattice spacing (d) as found from x-rays:
Electron Interference existence of some kind of wave with a specific wavelength.
Wavelength directly related to K.E. of electrons: K.E. ~ 1/wavelength ~ f
But what exactly is waving?
Experiment: Electron beam (of some specific kinetic energy) aimed at a crystal displays same behavior as x-ray patterns/Bragg peaks
Matter waves – Bragg peaks
Spectroscopy --- Continuous and Discrete spectrums
Hot objects emit light at all frequencies (sun, light bulbs). Called “Planck’s Black Body” radiation spectrum --- more about this later.
Gas discharge tube --- different elements emit different discrete spectrum
Classical Newtonian mechanics can not explain discrete spectrum!
Matter wave confined --- particle in a box
Matter travels as some kind of wave, therefore if it is confined matter will form standing waves.
What we will see is that this confinement will have profound consequences which lead to quantization of energy and momentum.
Hydrogen atom confines the electron to some region of space. This produces the Energy levels of the atoms and ultimately explains the discrete spectrums of the atoms.The confinement area changes with KE of particle, so solutions differ from simple particle in a box: