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PH 103

PH 103. Dr. Cecilia Vogel Lecture 19. Review. Matter Waves. Uncertainty Principle Tunneling Atomic model Nucleus and electrons The quantum model quantum numbers. Outline. Position Uncertainty. A wave is not at one place. D x = uncertainty in position

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PH 103

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  1. PH 103 Dr. Cecilia Vogel Lecture 19

  2. Review • Matter Waves • Uncertainty Principle • Tunneling • Atomic model • Nucleus and electrons • The quantum model • quantum numbers Outline

  3. Position Uncertainty A wave is not at one place. Dx = uncertainty in position = spread in positions where the wave is. Dx

  4. Momentum Uncertainty A wave is not moving in just one way. Dp • Dp = uncertainty in momentum • = spread in ways the wave moves.

  5. Heisenberg Uncertainty Principle What it means: You cannot know position and momentum both very precisely at the same time If you measure momentum, you disturb the position, so you no longer know the position accurately -- and vice versa This disturbance is random, indeterminate (unlike letting a little air out when you measure the tire pressure)

  6. Heisenberg Uncertainty Principle

  7. Heisenberg Uncertainty Principle Zero-point motion: Any confined particle cannot have a definite momentum in particular, it cannot have zero momentum any confined particle will have some kinetic energy -- some “zero-point motion”

  8. Heisenberg Uncertainty Principle What it does not mean: It does not mean you can’t measure position (or momentum) very precisely. It does not mean you need better measuring instruments. It does NOT just a matter of not knowing: If Dx is large enough, an electron will pass thru both of two slits and interfere with itself

  9. Another Uncertainty Principle What it means If you only have a small time Dt to measure energy, you can’t accurately measure energy. If a particle only lives for a short timeDt, you can’t accurately measure its energy. Since E=mc2, you can’t accurately measure its mass! Unstable particles have uncertain mass.

  10. Another Uncertainty Principle For a short enough period of time Dt, you can violate conservation of energy by DE. means you can measure DE in time Dt for these times, energy conservation cannot be violated means you can’t measure DE in time Dt so the universe can violate energy conservation for shorter times and “get away with it”

  11. Classically, potential energy cannot be greater than the total energy • Otherwise the kinetic energy would be negative! K = E - U • Places where U>E are classically forbidden

  12. Tunneling Waves can tunnel into regions where they “shouldn’t” be -- if region is small enough. Light waves tunnel through region, even when they “should” have totally reflected, if region is very narrow. Matter waves tunnel through “classically forbidden regions”

  13. Tunneling • Wait, did you say a particle can tunnel into classically forbidden region • where the kinetic energy would be negative?!!? YUP Another example of violating conservation of energy for short enough time - HUP

  14. Examples of Quantum Tunneling

  15. One type of Scanning Tunneling Microscope = STM • A small, metal needle passes very near a material. • Electrons from the needle can tunnel through the small gap and into the material. • The smaller the gap, the more likely the tunneling. • The more tunneling happens, the stronger the current of electrons. • As the needle scans across the surface • the tunneling current gives an outline of the material.

  16. Early Atomic Models • You’ve learned about many physics models (theories) that are “wrong.” • So far, these models have been useful. • F=ma & K=½mv2 are good when v<<c. • The ray model of light is good for short wavelength. • etc • WARNING: • The early atomic models are not useful, except to see how we disprove theories.

  17. Nuclear Model of Atom • a tiny, massive, dense nucleus • at the center of the atom • surrounded by electrons • very little of the mass of the atom is electrons • most of the volume of the atom is electrons

  18. Orbits • Where are the electrons? • Electrons do NOT orbit the nucleus, like planets orbit Sun • Although it seems reasonable, since the electric force and the gravitational force are very similar: • but…

  19. Two Problems with Orbits 1) An orbiting electron is an accelerating charge, and • accelerating charges give off EM radiation (like an antenna), • thus giving off energy. • The electron would gradually lose all its energy. • That doesn’t happen -- atoms are stable.

  20. Second Problem with Orbits 2) Quantization • A planet can be in any size orbit with any orbital energy, • but electrons in atoms have only certain -- quantized -- energy levels. • Orbit model can’t explain why.

  21. Current Model of Orbit • Electron “cloud” is wavefunction • describes the probability of electron being at various points around the nucleus. • Electron wave behavior based on Schroedinger equation. • The electron states are quantized • 3 quantum numbers for spatial state: • n, ℓ, mℓ. • http://www.falstad.com/qmatom/directions.html

  22. Principle Quantum Number • Principle quantum number, n, • n = 1, 2, 3, 4, 5, .... • tells what “shell” the electron is in. • n=1 is called the K-shell, • n=2 is the L-shell, etc • tells a lot about the electron’s energy • for hydrogen atom, it determines the electron’s energy • for hydrogen atom:

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