1. PH 103 Dr. Cecilia Vogel Lecture 19

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

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

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

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. 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  x 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  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.

10. 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”

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=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.

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, m ℓ.  http://www.falstad.com/qmatom/directions.html 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: