Quantum Theory Chapter 5

1. Quantum TheoryChapter 5

2. Indicate what is meant by the duality of matter. Discuss the wavelike nature of matter as proposed by De Broglie’s Theory. List one way that matter acts in a manner that reveals its wavelike nature. State Heisenberg’s Uncertainty Principle as it relates to atoms. Indicate what information Schroedinger’s Wave Equation gives us about the electron. Lecture Objectives

3. Wave-Particle Duality • Recall the Bohr’s model only accurately predicted the emission spectrum of hydrogen. • In the 1920s, De Broglie proposed 2 radical ideas: • The possible circular orbits of an electron are limited to whole numbers of complete wavelengths. • If light, a wave, could also take on particle-like properties, couldn’t the electron, a particle, also take on wave-like properties?

4. The Standing Waves Caused by the Vibration of a Guitar String Fastened at Both Ends

5. The Hydrogen Electron Visualized as a Standing Wave Around the Nucleus

6. Wave-Particle Duality • For these ideas to be true, the electron is therefore allowed only certain possible wavelengths, frequencies, and energies. • De Broglie’s Equation: • l= h mv • This equation predicts the wavlength of a particle of mass (m) moving at velocity (v).

7. Wave-Particle Duality • i.e., all moving particles have wave characteristics. • N.B. Normal objects don’t have waves detectable with even very sensitive objects, but an electron has a wavelength of 2.9 x 10-5 m, which is easily measurable by experimentation.

8. Electron Interference • Richard Feynman liked to talk about wave-particle duality with the following analogy: • Imagine shooting a machine gun at an iron plate with two slots in it. If there were a concrete wall behind the iron plate, what kind of pattern do you think the bullets would make? • Electron Gun Experiment • http://www.colorado.edu/physics/2000/schroedinger/two-slit3.html

9. G. P. Thomson • Also in 1927, G. P. Thomson, the son of J. J. Thomson, reported his experiments, in which a beam of energetic electrons was diffracted by a thin foil. • This is constructive-destructive interference, just like we saw with light!

10. Getting the Prize • Experiments by Davisson, Germer, and Thomson proved that de Broglie's waves are not simply mathematical conveniences, but have observable physical effects. They got the 1937 Nobel Prize in Physics for their pioneering work.

11. The Heisenburg Uncertainty Principle • “It is fundamentally impossible to know precisely both the velocity and the position of a particle at the same time.” • x= position • mv = momentum • h = Planck’s constant • The more accurately we know a particle’s position, the less accurately we can know its momentum.

12. The Heisenburg Uncertainty Principle • For large objects, the change in velocity produced by determining the position is so small that we can ignore it. • This is why scientists, in the 1920s, found Heisenburg’s idea so difficult to accept.

13. The Heisenburg Uncertainty Principle • For atomic particles, however, it is profound, as the uncertainty produced is on the order of 10-9 m, an uncertainty one order of magnitude greater than the diameter of the entire atom. • E.g. Using a photon to “bump” an electron in order to determine its location will cause an excitation of the electron that, according to quantum mechanics, will change its orbit and, therefore, both its wavelenth, velocity, and position.

14. The Shroedinger Wave Equation • In 1926, the Austrian physicist Erwin Schroedinger derived Bohr’s equation for hydrogen’s electron by assuming it is a wave. • It accurately predicted hydrogen’s energy levels! • The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wavefunction gives the probability of finding the particle at a certain position.

16. The Quantum Model • This works because, while matter has duality, just like light, if you perform an experiment to see where a particle is, then you find something particle-like. But otherwise it's a wave that carries information about where the electron probably is.

17. The Quantum Model • Until you check where the electron is, it's really just a wave. • Not only that, but Schrödinger showed that these electrons don't even move. The waves are stationary. • Each time you check where an electron is you will find it in a different place, but that doesn't mean it's moving in between checks. • For some energy levels, if you check position enough times you may see an "orbit-like" pattern, but the electron isn’t actually moving in little circles.

18. The Quantum Model • An electron isn't in any particular place when you aren't looking because then it is a wave. • Generally, for most physics we only care about how much energy it has, not where it is. • Orbits, while misleading about where the electron is, do tell us how much energy it has.

19. The Quantum Model • We call this the Energy Level of the electron. Because the idea of orbits is so misleading, physicists started using a picture of the atom which just showed energy levels as relative heights. • And we called this the "Schrödinger Model," of course. • Born, a German-born Jewish physicist, coined the term “quantum mechanics”, which replaces Newtonian “classical mechanics” in explaining the behavior of matter at the atomic level. • He was the person who discovered that the wavefunction in Schroedinger’s equation was a probability density function for the electron