P2-13: ELECTRON DIFFRACTION P3-51: BALMER SERIES P2-15: WAVE PACKETS – OSCILLATORS P2-12: X-RAY DIFFRACTION MODEL P2-11: 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.

X-ray Diffraction Each atom acts like a “point source”, much like a diffraction grating

Bragg condition: Constructive interference X-ray Diffraction by Crystal – Bragg Condition

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.

Photons – phenomenology and postulate

Photons –postulates

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

Matter waves – De Broglie wavelength

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!

Spectroscopy --- The Discrete Hydrogen 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.

Matter waves confined --- Quantum Corral (particle(s) in a box)

Matter wave confined --- Review of standing waves Chapter 21

Matter wave confined --- particle in a box

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:

Producing and Receiving EM waves At large distances, E becomes ‘flat’  Plane waves