Get the free Lecture 35: Chapter 38 Friday 7 April 2006 1 Waves and Particles ...

Waves and Particles Today: 1. Photon: the elementary particle of light. 2. Electron waves 3. Wave-particle duality Photons Light is Quantized Einstein, 1905 Energy and momentum is carried by photons.

E an): q= in / n(q= 1 2 h) where n(q= 1 2 h) = Planck's constant: (E= 6.6 × 10 -34 S = 6.6 9.2×10 -34 J) h = 1.8 × 10 -16 J n = 1.2 × 10 -3 S Efforts to get an overall energy-momentum relation for light from quantum mechanics lead to different solutions, but all of these relations are wrong. The right-hand side (where n(q)=(1 2 q) is right!) holds with a tiny error, but the left-hand solution doesn't hold. This is an example of an argument that goes wrong when you try to deduce something about light energy from the Planck constant. The error occurs because the Planck constant changes as the speed of light increases. The error occurs mainly when you have to work with quantum mechanics and are attempting to work out the energy-momentum relation for light using quantum mechanics. When you have to work out something with quantum mechanics, you need accurate values of the Planck constant and, unfortunately, that requires you to work using quantum mechanics with the speed of light constant as a constraint. When this is done, it seems that the error from Planck constant uncertainty is always small, but in fact the error is small in only certain locations. In all other locations it is usually large. This is due to the fact that the probability of getting an energy result that is close to the value that you actually get depends on where this energy is measured. As you work through this exercise, you'll be able to work out which locations are most likely to contain errors and be able to use this knowledge to improve your understanding of photon energy and momentum calculations for light. You'll get an idea of how it works and then be able to look at the numbers of measurement errors produced by the Planck constant. Photon Energy, Momentum and Particles (and Everything Else) Today: 1. Particles and Waves Today: 2.

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