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?

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, 201114 yr by ajb

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?

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.

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.

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, 201114 yr by StringJunky

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.

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.

Thanks for the clarification Swansont and AJB.

Edited April 7, 201114 yr by StringJunky

This means that atomic physics is inherently quantum mechanical in nature.

Ok, what about inter-atomic physics? I.e. physical interactions among atoms?

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.

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, 201114 yr by mississippichem

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?