Lec34 - so that the Compton wavelength is always shorter...

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Unformatted text preview: so that the Compton wavelength is always shorter then the de Broglie wavelength. When we do an experiment whose typical size D dB the particles wavelength is very short, such that it would behave according to the geometrical optics approximation, i.e., will behave like a particle does. When D dB , the particle will exhibit wavelike phenomena such as interference and diffraction, and will behave according to the physical optics approxima- tion. When we reduce the size of the experiment even further, so that D C , the particle exhibits both physical optics and special relativistic behavior: it is the realm of relativistic quantum mechanics. As as example, consider the de Broglie wavelength of an electron. As a typical speed of an electron we take v/c = 1 / 137. (As we shall see below, this speed is typical of atomic electrons.) This speed is slow enough for us to use the Newtonian momentum as a good approximation, so that dB = h mv = hc mc 2 ( v c ) 1 , 240 eV nm . 511 10 6 eV 1 137 = 0 . 33 nm which is on the typical length scale of atoms. Therefore, in atoms electrons behave like waves. But when the size of the experiment is much longer than a nm, electrons behave like particles do. As another exmple consider a speck of dust of mass 10- 4 g moving at a typical speed of 1 m / s. The de Broglie wavelength is dB = h mv = 6 . 6 10- 34 J s 10- 7 kg 1 m / s = 6 . 6 10- 27 m . This is a ridiculously short wavelength! It is shorter by 12 orders of magnitude than the typical size of the atomic nucleus. It is certainly not practical (and in all likelihood plain impossible) to design an experiment whose typical size is so short. Therefore, specks of dust always behave like particles do, and they do not exhibit wavelike features. To see physical optics effects with everyday objects, the de Broglie wavelength would have to be on the scale of 1m. For objects of typical mass of 1kg and speed of 1 m/s, the Planck constant would have to be 1 J...
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This note was uploaded on 07/19/2011 for the course PH 113 taught by Professor Liorburko during the Spring '09 term at University of Alabama - Huntsville.

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Lec34 - so that the Compton wavelength is always shorter...

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