lemur Posted April 6, 2011 Share Posted April 6, 2011 Since (intuitive) classical mechanics no longer seems to apply at the sub-atomic level, what would you say the smallest scale is at which phenomena can be described and analyzed in terms of classical mechanics? Link to comment Share on other sites More sharing options...
ajb Posted April 6, 2011 Share Posted April 6, 2011 (edited) When the size of the system is comparable to the de Broglie wavelength of the particles then classical mechanics breaks down. The wavelength is given by [math]\lambda = \frac{h}{m v}[/math], (nonrelativistic) where [math]m[/math] is the particle's mass and [math]v[/math] is the speed of the particle. [math]h[/math] is Planck's constant. As long as you are considering things on a length scale much larger than [math]\lambda[/math] classical mechanics will be ok. Edited April 6, 2011 by ajb Link to comment Share on other sites More sharing options...
lemur Posted April 7, 2011 Author Share Posted April 7, 2011 When the size of the system is comparable to the de Broglie wavelength of the particles then classical mechanics breaks down. The wavelength is given by [math]\lambda = \frac{h}{m v}[/math], (nonrelativistic) where [math]m[/math] is the particle's mass and [math]v[/math] is the speed of the particle. [math]h[/math] is Planck's constant. As long as you are considering things on a length scale much larger than [math]\lambda[/math] classical mechanics will be ok. Could you maybe give examples for reference since I am somewhat math illiterate? When the size of the system is comparable to the de Broglie wavelength of the particles then classical mechanics breaks down. The wavelength is given by [math]\lambda = \frac{h}{m v}[/math], (nonrelativistic) where [math]m[/math] is the particle's mass and [math]v[/math] is the speed of the particle. [math]h[/math] is Planck's constant. As long as you are considering things on a length scale much larger than [math]\lambda[/math] classical mechanics will be ok. Could you maybe give examples for reference since I am somewhat math illiterate? Link to comment Share on other sites More sharing options...
StringJunky Posted April 7, 2011 Share Posted April 7, 2011 I think AJB means sizes larger than an atom are valid in classical mechanics. http://www.stanford.edu/group/fayer/Wonderfest11-6-05.pdf The link also tersely contrasts the effects of measurement (observation) between quantum and classical systems. Link to comment Share on other sites More sharing options...
ajb Posted April 7, 2011 Share Posted April 7, 2011 It will depend on the mass of particle and its velocity. So, [math]10^{-10}[/math] meters tells us that we cannot ignore quantum effects when dealing with atomic physics. Link to comment Share on other sites More sharing options...
StringJunky Posted April 7, 2011 Share Posted April 7, 2011 (edited) It will depend on the mass of particle and its velocity. So, [math]10^{-10}[/math] meters tells us that we cannot ignore quantum effects when dealing with atomic physics. That appears smaller than the bound of an atom; is the calculation I pasted wrong? If you look at your post it is non sequiter...how can you follow an indefinite with a definite? You say it depends... and then give a fixed numeric answer!? Edited April 7, 2011 by StringJunky Link to comment Share on other sites More sharing options...
swansont Posted April 7, 2011 Share Posted April 7, 2011 That appears smaller than the bound of an atom; is the calculation I pasted wrong? If you look at your post it is non sequiter...how can you follow an indefinite with a definite? You say it depends... and then give a fixed numeric answer!? Atomic size runs from a few tenths of an angstrom to a few angstroms. It will be different should you use another particle and you will have to re-evaluate, but for an electron in an atom (you gave the fixed numeric answer), you can see that have to use QM. 1 Link to comment Share on other sites More sharing options...
ajb Posted April 7, 2011 Share Posted April 7, 2011 If you look at your post it is non sequiter...how can you follow an indefinite with a definite? You say it depends... and then give a fixed numeric answer!? You gave a numerical value of the wavelength for an electron "whizzing around" an atom. It turns out to be about an angstrom, which is comparable to the size of atoms. Like swansont says, angstroms are the natural scale of atoms. This means that atomic physics is inherently quantum mechanical in nature. 1 Link to comment Share on other sites More sharing options...
StringJunky Posted April 7, 2011 Share Posted April 7, 2011 (edited) Thanks for the clarification Swansont and AJB. Edited April 7, 2011 by StringJunky Link to comment Share on other sites More sharing options...
lemur Posted April 7, 2011 Author Share Posted April 7, 2011 This means that atomic physics is inherently quantum mechanical in nature. Ok, what about inter-atomic physics? I.e. physical interactions among atoms? Link to comment Share on other sites More sharing options...
ajb Posted April 7, 2011 Share Posted April 7, 2011 Ok, what about inter-atomic physics? I.e. physical interactions among atoms? Molecular physics, condensed matter physics and many aspects of chemistry rely on quantum mechanics. Link to comment Share on other sites More sharing options...
mississippichem Posted April 7, 2011 Share Posted April 7, 2011 (edited) Molecular physics, condensed matter physics and many aspects of chemistry rely on quantum mechanics. Yep, you can treat a molecule as a classical body as long you are only worried about molecular dynamics/statistical mechanics. If you want to look at things like individual bond movements or energy level stuff, you are back to QM for obvious reasons. Edited April 7, 2011 by mississippichem Link to comment Share on other sites More sharing options...
lemur Posted April 7, 2011 Author Share Posted April 7, 2011 Molecular physics, condensed matter physics and many aspects of chemistry rely on quantum mechanics. Yep, you can treat a molecule as a classical body as long you are only worried about molecular dynamics/statistical mechanics. If you want to look at things like individual bond movements or energy level stuff, you are back to QM for obvious reasons. What about things like how substances behave in various materials, mixtures, etc? E.g. I am guessing that the malleability/ductility of metals have to do with their electron abundance, but is this effect of the atoms interacting with each other explained by QM aspects or does it have to do with how the atoms interact at the inter-atomic level? Link to comment Share on other sites More sharing options...
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