Oscillating Molecule and Revolving Electron

[cire]

I found the problem of the ocsillating molecule interesting as well as the electron revolving around the nucleus, in both cases there is energy loss due to radiation and eventually the molecule will stop ocsilating and the electron will be together with the nucleos. the times when this happen are really low we got 10^-5 s for the molecule and 10^-38 seconds for the electron. If we get something like the age of the universe make sense, but those times are really fast!
How to explain why the molecule doesn't stop oscilating? it actually oscialting??
I think that doesn't happen due to the uncertainty principle, that gives kinetic energy 0.5m(h/x)^2 when the position is localized, that could compensates the energy loss due to radiation?. but it actually radiates by the ocsilation (I now the QM description... homework and selections rules...) but what are the asumtions or facts that make classical electrodynamics fail a low scale?

 

[dextercioby]

I found the problem of the ocsillating molecule interesting as well as the electron revolving around the nucleus, in both cases there is energy loss due to radiation and eventually the molecule will stop ocsilating and the electron will be together with the nucleos.

What do you mean...?

the times when this happen are really low we got 10^-5 s for the molecule and 10^-38 seconds for the electron.

How did u come up with these numbers...?

If we get something like the age of the universe make sense, but those times are really fast!

Well,they look fast...Show me if they are correct...

How to explain why the molecule doesn't stop oscilating? it actually oscialting??

Yes,and its energy levels are quantized...

I think that doesn't happen due to the uncertainty principle, that gives kinetic energy 0.5m(h/x)^2 when the position is localized, that could compensates the energy loss due to radiation?.

Again,what loss of energy...?

but it actually radiates by the ocsilation (I now the QM description... homework and selections rules...) but what are the asumtions or facts that make classical electrodynamics fail a low scale?

I don't know who and under what conditions radiates (what...?),but the first historical example what the quantum-based explanation of the photoelectric effect due to A.Einstein 100 years ago...

Daniel.

 

[ZapperZ]

I found the problem of the ocsillating molecule interesting as well as the electron revolving around the nucleus, in both cases there is energy loss due to radiation and eventually the molecule will stop ocsilating and the electron will be together with the nucleos. the times when this happen are really low we got 10^-5 s for the molecule and 10^-38 seconds for the electron. If we get something like the age of the universe make sense, but those times are really fast!
How to explain why the molecule doesn't stop oscilating? it actually oscialting??
I think that doesn't happen due to the uncertainty principle, that gives kinetic energy 0.5m(h/x)^2 when the position is localized, that could compensates the energy loss due to radiation?. but it actually radiates by the ocsilation (I now the QM description... homework and selections rules...) but what are the asumtions or facts that make classical electrodynamics fail a low scale?

There are several errors/flaw/misunderstanding in here:

1. Molecules are often made up of NEUTRAL atoms. So their oscillations do not produce EM radiation;

2. Molecular vibrations are often attributed due to finite temperature, i.e. their are thermal vibrations. Classically, one expects none to very little vibrations at T approaches zero. Quantum mechanically, it's a different matter (refer to the deBoer effect).

3. It fallacy of "electron revolving around the nucleus" has been addressed ad nauseum on here, it is best for you to a search of that and see why, after you learn a bit of QM, that this picture is wrong. That should sufficiently address why an atom in its ground state does not radiate.

Zz.

 

[cire]

Classically an acelarating charge radiates, the power radiated is P=(2e^2|a|^2)/(3c^3 ) (1)
a is the acelaration that is e^2/mr^2, Eo vacuum permittivity, c speed of light.
For an electron revolving around a nucleus Total energy E=KE +PE=-0.5e^2/r
dE/dt=e^2/r^2 dr/dt (2)
(2)=-(1) and integrating from R to 0 I get
time=(m^2c^3 R^3)/(4e^4) R is the initial radius
I get 10^-38 s,
so classically the electron radiates energy due that is has an acelaration and cosenquently falls to the nucleous, and the time is fast, not the age of the unieverse or some big number.

similarly a classical harmonic charged oscilator radiates and evetually lost all the enegy, I got a homework problem and the time was 10^-5s

that is what I mean

 

[dextercioby]

Incorrect calculus...The numbers u should be getting is much bigger...

Daniel.

P.S.Pay attention with the integration.

 

[cire]

what is incorrect?
I forgot to say that the formula for the radiated power is the dipole approximation

 

[ZapperZ]

Classically an acelarating charge radiates, the power radiated is P=(2e^2|a|^2)/(3c^3 ) (1)
a is the acelaration that is e^2/mr^2, Eo vacuum permittivity, c speed of light.
For an electron revolving around a nucleus Total energy E=KE +PE=-0.5e^2/r
dE/dt=e^2/r^2 dr/dt (2)
(2)=-(1) and integrating from R to 0 I get
time=(m^2c^3 R^3)/(4e^4) R is the initial radius
I get 10^-38 s,
so classically the electron radiates energy due that is has an acelaration and cosenquently falls to the nucleous, and the time is fast, not the age of the unieverse or some big number.

similarly a classical harmonic charged oscilator radiates and evetually lost all the enegy, I got a homework problem and the time was 10^-5s

that is what I mean

But you should have known by now that the situations you were asking are NOT "classically" relevant. A molecule's oscillation isn't a charged particle in a classical harmonic oscillator. In fact, it isn't even a charged particle, but rather neutral particles. And an electron in an atom is NOT orbiting the nucleus like a planetary model!

Zz.

 

[cire]

I heteronuclear molecule have a permanent dipole moment that ocsillates as the molecule oscilates
but let's focus in the electron case:
I know that the electron in a atom is not orbiting the nucleus like a planetary model, I now QM description
but my question is what classical electrodynamics assumtion make it fail?

 

[marlon]

Here is how you should look at the fact that there is no radiation of electrons in an atom. The electrons move indeed in orbitals with a certain velocity (no acceleration). No the fact that electrons do not fall into the nucleus due to the Coulombic interaction has to do with the fact that there is an equilibrium in both potential and kinetic energy. Electrons that are "closest" to the nucleus have a lower potential energy (more negative) but they move in the orbitals with higher speed (higher kinetic energy). Once you look at electrons further waway from the nucleus, the potential energy rises and the velocity (and therefore the kinetic energy) lowers. In the end there is an equilibrium between those too.

marlon

 

[ZapperZ]

but let's focus in the electron case:
I know that the electron in a atom is not orbiting the nucleus like a planetary model, I now QM description
but my question is what classical electrodynamics assumtion make it fail?

Didn't you just answer this yourself in the very first posting of this thread? If not, how in the world did you calculate what you obtained?

Zz.

 

[marlon]

ps keep in mind that accelerated charged particles will radiate because of energy conservation. However this condition is already respected by the "stable orbital structure" of atoms because of the reason written down in my previous post. So , keeping that in mind, the question should really be : why would atoms radiate or why would electrons "collapse" onto the atomic nucleus...

marlon

 

[dextercioby]

I remember dong that specific calculation while i was in the 12-th grade.A problem simply provided the Larmor formula and asked for this "time".It's about 10^{-11}s for the H atom.

As the previous posters hinted,it means nothing...

Daniel.