AS Physics Unit 3Matter Waves Extension

KS5 AS PHYSICS AQA 2450Mr D Powell

Mr Powell 2008Index

Summary• We can think of electrons as waves

• We can think of electrons as particles

• Newtonian Mechanics works in certain cases (simple stuff)

• If we think of electrons in a quantum way (as waves) the maths always works out but the calculations are more complex

To build the structure, the scientists used a scanning tunneling microscope (STM) to individually place 48 iron atoms on a copper surface in a circle roughly 143 angstroms across. Then, using the STM again to sense electron behavior inside the corral, they detected "local densities," which appear as waves, at the very intervals predicted by quantum mechanics -- specifically, the Schrodinger equation for a particle in a hard-wall enclosure. The standing waves appear when iron atoms scatter the copper's superface electrons.

Mr Powell 2008Index

Wave nature of the electronExtension

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DeBroglie Hypothesis – Mathematical Proof As a young student at the University of Paris, Louis DeBroglie had been impacted by relativity and the photoelectric effect, both of which had been introduced in his lifetime. The photoelectric effect pointed to the particle properties of light, which had been considered to be a wave phenomenon. He wondered if electrons and other "particles" might exhibit wave properties. The application of these two new ideas to light pointed to an interesting possibility:

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Mr Powell 2008Index

DeBroglie Hypothesis - Summary • Suggested by De Broglie in about 1923, the

path to the wavelength expression for a particle is by analogy to the momentum of a photon.

• Starting with the Einstein formula:

• Another way of expressing this is

• Therefore, for a particle of zero rest mass

• For a photon:

• The momentum-wavelength relationship for a photon can then be derived and this DeBroglie wavelength relationship applies to other particles as well.

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