3 registered members (AndrewAMD, VoroneTZ, 1 invisible),
1,578
guests, and 7
spiders. |
Key:
Admin,
Global Mod,
Mod
|
|
|
Re: Perpetuum mobile
[Re: Joey]
#353276
01/09/11 00:20
01/09/11 00:20
|
Joined: Oct 2006
Posts: 1,245
AlbertoT
Serious User
|
Serious User
Joined: Oct 2006
Posts: 1,245
|
of course I meant mercury. Of course I understood that you meant mercury but you said that the Bohr's atom can predict its energy levels Sorry it is a nonsense I guess you made a confusion witn the Hertz experiment e... so where do you get your knowledge about quantum mechanics from? You seem to know very much about it. *hust* From university, at 14 years old my main interest was soccer The model by itself does not provide any explanation for the energy levels It does. No it doesn't Why did you not try to better support your opinion instead of making childish issues ? Anyway A mass of hydrogen , same as any other elements, can only absorbs or emit radiation having certains frequencies The set of fequencies being known as the spectrum of the elemet At the time it was also well known that : E = h * f whereas E is the energy of the photon of the radiation and f its frequency According to Rutherford's experiment , electrons should orbit about the nucleus Bohr put the above experimental evidences together He said Well there are some energy levels : e0 - e1 - e2 ...en which are stable despite classic electromagnetism Electrons can jump only from one of these state to an other one, absorbing or emitting a photon whose energy is the difference between the final and the initial energy level All the other energy levels are forbidden to the electron Why ? He did not provide any explanation The explanation came from the Schrödinger's equation The solutions of the equation for the atom of hydrogen prove that the energy levels associated with its spectrum are the only ones which allow a stable configuration However Schrödinger thought that electrons were waves If so, you can have an intuitive rappresentation of the stable configurations of the electrons Further experiments and theoratical analysis refuted such interpretation in favour of a probabilistic interpretation In conclusion Electrons are particles in perpetual motion about the nucleus even though they dont follow the Newtonian laws
Last edited by AlbertoT; 01/09/11 09:25.
|
|
|
Re: Perpetuum mobile
[Re: AlbertoT]
#353306
01/09/11 09:43
01/09/11 09:43
|
Joined: Jan 2003
Posts: 4,615 Cambridge
Joey
Expert
|
Expert
Joined: Jan 2003
Posts: 4,615
Cambridge
|
you said that the Bohr's atom can predict its energy levels Sorry it is a nonsense http://en.wikipedia.org/wiki/Bohr_model#Electron_energy_levelsFrom university, at 14 years old my main interest was soccer Hey I study physics. That 14 years old story was a joke (did nobody get that?). What do you study? No it doesn't Why did you not try to better support your opinion instead of making childish issues ? Okay, see the above link. It took me like five seconds to find it. I really don't get where you get that claim from. The Bohr model gives you the frequencies. Via E=hf you get the energy levels. You even explained that yourself o.O. But I'll try again: no matter how Bohr came to the conclusion, he sais that angular momentum is quantized. From that or alternatively from requesting a continuous wave circle (with the electron's de Broglie wavelength) you get discrete orbits. The frequency of these orbits give you the energy levels via E=hf. So the explanation for the discrete energy levels in the Bohr model is the quantized angular momentum or, alternatively, the continuous wave about the nucleus (standing wave). Of course you can say that Bohr derived the quantized angular momentum by looking at the discrete energy levels since they were known before. But that doens't matter. The Bohr model requires the quantized angular momentum to describe the energy levels. Whether or not this explanation is true does not matter. Neither does it matter how Bohr developed his ideas. Nowadays, the Bohr model is derived from the quantum rule for angular momentum, and that's where the discrete energy levels come from. All the others are forbidden Why ? He did not provide any explanation Again, to summarize: I don't know what Bohr did. The Bohr model though gives the explanation. It sais that all other orbits give no standing wave and thus are forbidden. The explanation came from the Schrödinger's equation In fact the Schrödinger equation is a postulate so it can hardly qualify as an explanation, if I follow your argumentation. For me, though, it gives an explanation (why does the Schrödinger equation give you an explanation while the Bohr model does not? Both are just theories...). The solutions of the equation for the atom of hydrogen prove that the above energy levels are the only ones which entail a stable configuration What do you mean with stable? Ok, time to use the knowledge from the book I read when I was fourteen. JOKEThe time-independent SE is a differential equation. If you plug in the hamiltonian for a Coulomb potential, which is spherically symmetric in the case of a hydrogen-like atom (which is the only one you can solve analytically anyway), you can factorize the wave function into a radial and an angular part. The angular solutions for all spherically symmetric potentials are the sperical harmonics Y_lm, where l is just the angular momentum quantum number and m its z-component (or, alternatively, its magnetic quantum number). For the radial part you get laguerre-polynomials P_nl, where n is the energy quantum number. The energy of this state now can be measured with the hamiltonian and are just its eigenvalues. However Schrödinger thought that electrons were waves Further experiments and theoratical analysis refuted such interpretation in favour of a probabilistic interpretation Of course electrons are waves. This does not conflict with the probabilistic interpretation. Electrons are particles in perpetual motion about the nucleus even though they dont follow the Newtonian laws No. Nothing is moving. Hydrogen wave functions are completely stationary, there is absolutely no time dependence involved (see my derivation above, you use the time-independent SE). Once again an interesting discussion =).
|
|
|
Re: Perpetuum mobile
[Re: Joey]
#353344
01/09/11 17:19
01/09/11 17:19
|
Joined: Oct 2006
Posts: 1,245
AlbertoT
Serious User
|
Serious User
Joined: Oct 2006
Posts: 1,245
|
I took a degree in nuclear engineering Of course you can say that Bohr derived the quantized angular momentum by looking at the discrete energy levels since they were known before. It is exactly what I say Not only The Bohr's model is more or less valid for the atom of hydrogen only and just a few others atoms ( including mercury) It is not even compatible with the atom of helium For this reason it must be understood as semi empirical model why does the Schrödinger equation give you an explanation while the Bohr model does not? You provided yourself the scientific explanation Let's translate it into a plain spaghetti English Generally speaking you can describe a physical model using a differential equation However it does not mean that all the solutions of the equations must have a physical meaning Having said that, let's write the Schrödinger's equation for the atom of hydrogen The equation contains the parameter "E" for energy If you assign to "E" an arbitrary value then the solutions of the equations do not have any physical meaning Only for some discrete values of E ( the eigenvalues ) the solution of the equation make sense from a physical point of view This set of E values comply with the the experimental values In other words for Bohr the quantization of the energy levels is an input for Schrödinger it is an ouput I suppose there is a difference Of course electrons are waves. This does not conflict with the probabilistic interpretation. If you mean some stuff such as the collapse of the wave form well there is still a minority of scientists who believe in this theory ( The great Roger Penrose for example ) but it has been refuted by the vast majority of scientists Electrons are supposed to be particles even though they dont behave same as the normal particle we are used to Right or wrong this is the state of art of modern quantum physics Once again an interesting discussion =). I agree, at least for us
Last edited by AlbertoT; 01/09/11 18:17.
|
|
|
Re: Perpetuum mobile
[Re: chrisp1]
#353378
01/09/11 19:18
01/09/11 19:18
|
Joined: Oct 2006
Posts: 1,245
AlbertoT
Serious User
|
Serious User
Joined: Oct 2006
Posts: 1,245
|
In fact the Schrödinger equation is a postulate so it can hardly qualify as an explanation, if I follow your argumentation. For me, though, it gives an explanation (why does the Schrödinger equation give you an explanation while the Bohr model does not? Both are just theories...). Just a few words more The Schrödinger equation is a postulate ...up to a certain extent The actual postulate is the duality particle / wave Once you accept this postulate, the equation can be derived by merging the D'Alambert equation ( wave) and the Hamilton equation (particles) via Debroglie The similarity between rays of light and material particles had already been noticed in the 18° century but nobody dared to draw the logical conclusion Apart from that the Schrödinger equation can be applied also to the study of the atom of hydrogen but it is not, so to speak, "Hydrogen " dependent On the contrary The postulate m*v * 2PI * r = nh It has been proposed by Bohr "ad hoc " for the atom of hydrogen due to the fact that Bohr knew in advance the results to be achieved For this reason the Schrödinger equation is a step forth in the study of the secret of atoms
Last edited by AlbertoT; 01/09/11 22:50.
|
|
|
Re: Perpetuum mobile
[Re: AlbertoT]
#353416
01/09/11 22:22
01/09/11 22:22
|
Joined: Feb 2008
Posts: 3,232 Australia
EvilSOB
Expert
|
Expert
Joined: Feb 2008
Posts: 3,232
Australia
|
As a side-note:: Speaking of Schrödinger always makes me think of being cruel to cats. So this is almost on topic... Take this Antigravity Machine... Add a spindle between the cat and the toast... Connect the spindle to a generator... Perpetual energy?
"There is no fate but what WE make." - CEO Cyberdyne Systems Corp. A8.30.5 Commercial
|
|
|
Re: Perpetuum mobile
[Re: AlbertoT]
#353755
01/12/11 17:54
01/12/11 17:54
|
Joined: Jan 2003
Posts: 4,615 Cambridge
Joey
Expert
|
Expert
Joined: Jan 2003
Posts: 4,615
Cambridge
|
In other words for Bohr the quantization of the energy levels is an input for Schrödinger it is an ouput I suppose there is a difference Yes, I see your point. But, as I said earlier, we no longer take the energy levels as input for the Bohr model, although Bohr himself might have done that once. What we do say, though, is that angular momentum is quantized. With this prerequisite, discrete energy levels are as well an output from the Bohr model. Electrons are supposed to be particles even though they dont behave same as the normal particle we are used to Of course electrons are particles. But they're waves, too, in every sense. In quantum field theory, which is the most successful theory so far for the whole matter, electrons are nothing but filled modes in momentum space. I don't know exactly what you meant with Penrose, but I don't know a physicicst who sais that electrons cannot be described as waves. Once again an interesting discussion =). I agree, at least for us Maybe I should stop looking for physical discussions around here. Seems to kill topics
|
|
|
Re: Perpetuum mobile
[Re: Joey]
#353763
01/12/11 18:48
01/12/11 18:48
|
Joined: Oct 2006
Posts: 1,245
AlbertoT
Serious User
|
Serious User
Joined: Oct 2006
Posts: 1,245
|
Ok I agree , this is my last post on this topic we no longer take the energy levels as input for the Bohr model, although Bohr himself might have done that once. What we do say, though, is that angular momentum is quantized. With this prerequisite, discrete energy levels are as well an output from the Bohr model. Maybe I am rusty, I studied this stuff may years ago, but honestly I dont think that you are right Both the Bohr's and the Schrödinge's model make use of the duality particle / wave but there is a huge difference The Bohr's model lacks the equation ! it can not be an exhaustive model, more inputs are needed The Bohr's model is , relatively speaking, quite a rough one You even need to introduce empirical parameters taken from the Balmer equation You can imagine Unless for Bohr's model you mean some further development which I am not aware of The original one is not for sure what you have been talking about It may have an hystorical interest, nothing more Of course electrons are particles. But they're waves In the past most of the scientists believed that electrons were really both particles and waves Nowadays the associated "wave" must be understood just as a mathematical entity
Last edited by AlbertoT; 01/12/11 22:36.
|
|
|
|