PH 103 Dr. Cecilia Vogel Lecture 19
Review Outline Uncertainty Principle Tunneling Atomic model Nucleus and electrons The quantum model quantum numbers Matter Waves
Position Uncertainty A wave is not at one place. x = uncertainty in position = spread in positions where the wave is. xx
Momentum Uncertainty A wave is not moving in just one way. p = uncertainty in momentum = spread in ways the wave moves. pp
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)
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”
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 x is large enough, an electron will pass thru both of two slits and interfere with itself
Another Uncertainty Principle What it means If you only have a small time t to measure energy, you can’t accurately measure energy. If a particle only lives for a short time t, you can’t accurately measure its energy. Since E=mc 2, you can’t accurately measure its mass! Unstable particles have uncertain mass.
Another Uncertainty Principle For a short enough period of time t, you can violate conservation of energy by E. means you can measure E in time t for these times, energy conservation cannot be violated means you can’t measure E in time t so the universe can violate energy conservation for shorter times and “get away with it”
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
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”
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
Examples of Quantum Tunneling
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.
Early Atomic Models You’ve learned about many physics models (theories) that are “wrong.” So far, these models have been useful. F=ma & K=½mv 2 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.
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
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…
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.
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.
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, m ℓ.
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: