I still think this belongs in Chemistry: When I say “model an atom” in a given configuration, I mean identify the atom’s internal characteristics, i.e. the mass and energy of the atomic particles, their distances from each other, and their relative motions to each other while in a specific energy state and while that specific energy state remains unchanged (no other absorption or emission takes place). Do we know enough about the nature and configuration of the atomic particles within the atom to model an atom in a given energy state that will absorb photon energy of a predictable frequency and thus increase the energy state of an electron or electrons one discrete jump? If we then take the configuration of that atom at the new energy level after it has absorbed that specific amount of photon energy, do we know enough about its new configuration to say what changes have taken place in each of the characteristics of the configuration that we started with? Do we know if there is a time delay while the atom is preparing to make a jump up or down in energy or does the jump coincide precisely with the arrival or the emission of the photon energy? I ask about the time delay because, from what I can get out of the text, the frequency of the photon energy emitted from a blackbody changes in increments (multiples of Planck’s constant). If the highest frequency emitted in the blackbody spectrum is to increase to the next higher wavelength then the blackbody must absorb more energy; fill the next bigger bucket so to speak. On the theory that in order for the blackbody to fill the new bigger bucket and absorb enough energy to emit higher energy photons than before, would there be a finite amount of time between the absorption and the emission of that incremental energy? During that time delay, if there is one, the blackbody would be absorbing energy that forces the emission of the next higher frequency, but it would seem obvious that the next higher frequency emitted would not be the same frequency of the photon energy being absorbed to fill that new bucket. Does anyone understand what I’m asking, i.e. is the frequency of the photon emitted different from the frequency absorbed to provide the energy that will be emitted? If so, would it stand to reason that the energy absorbed by the electrons would be stored in non-discrete amounts (not quantum), and the discrete part or quantized amount is controlled at the instant of absorption and emission? Clear as mud, right.
Don't know if anyone here at SciForums will respond, but a little self-study reveals that the answer is no, we cannot model an atom with sufficient precision to be able predict the the frequency of a photon that can be absorbed. Experimental evidence might be available for specific photon frequencies that can be absorbed by a simple hydrogen atom that is at various levels of excitement, but to model the hydrogen atom in such exact detail as to be able to derive those few frequencies from the model is not yet possible, or at least is not evident in the first year college level text, or in the Internet searches for "modeling of the atom". There are many interesting links in that search though, so if anyone thinks it is possible, just say so. Same answer. We don't yet have a model of the atom that can reflect all of the specific changes to all of the aspects of its configuration from one energy state to another, or at least one that can be relied upon to allow input of the particulars for each particle and then from which the frequencies of the possible abosortions and emissions can be derived. Does anyone think otherwise? There certainly must be a time delay between the build up of energy in a blackbody, and the emission of the next higher frequency photon at the ultraviolet end of the spectrum, since the energy transferred to the blackbody is due to a temperature difference between the blackbody and it surroundings, from what I can tell. Heat energy is transferred in calories which are measured in joules, and photon energy (e=hf) can be transferable to joules, but is there actual photon energy involved in thermal conductivity?
I'm posting this from my iPad but all of the content is not visible because it is Apple. I have to view it on my PC to see it all, so I'll have to look at it later, but here is the link for future reverence: http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/Blackbody_Radiation But to answer my own question, photon energy is the means of heat transfer into and out of a blackbody. This link is interesting and I will have to come back to it later also, but the non-thermal radiation brings up some interesting questions, http://www.grandunification.com/hypertext/NonthermalThermalRadiation.html: Nonthermal Radiation Some of the more unusual objects in space such as supernovas, pulsars, radio galaxies, Seyfert galaxies, BL Lacertae objects, GRBs, and others, produce copious amounts of photons that can not be described as "blackbody radiation" or "thermal radiation." These photons almost certainly were not made by electrons changing their orbit. This process is not as well understood by scientists, and what is known may be incomplete. Scientists know of two techniques that can be used to create nonthermal radiation: the Synchrotron Process and the Inverse Compton Process. The Ball-of-Light Particle Model describes a new -- third -- process that can produce nonthermal radiation. This particle model describes "elementary" particles as: standing, spherical waves of electric, magnetic, and gravitational fields -- in essence as balls of light. According to this particle model, when these "elementary" particles decay, they create nonthermal radiation. The Ball-of-Light Particle Model also predicts nonthermal radiation can be created by the electromagnetic fields on the surface of a ball-of-light.
I can speak from personal experience of having worked on precisely the problem of modelling energy levels and photon absorption/emissions frequencies in molecules. It is a highly non-trivial task which requires a lot of simplifications, restructuring and enough computing power to kill a rhino at 50 paces. Ignoring issues of how you actually solve the problem computationally in principle quantum mechanics does it by modelling the nuclei as particles (ie don't model individual protons and neutrons) along with the electrons. The frequencies of photons are defined by the differences in the energies of the different molecular states, ie the eigenvalues I told you about in the other thread. So you convert the time dependent Schrodinger equation describing the nuclei and electrons into the associated time independent eigenvalue problems. This is an enormously complex problem and all sorts of methods exist to do it but they aren't relevant to the fact you want the energy levels.
The particles in an atom have no specific positions, so their relative distances from one another at any given time cannot be determined. Likewise, their relative motions cannot be determined. Both position and momentum are subject to the Heisenberg uncertainty principle. Having said that, there are a number of "internal characteristics" of an atom that can be measured. And we have quite good mathematical models of atoms that allow various predictions to be made about atomic behaviour. Yes. That was one of the main problems that people like Neils Bohr set out to solve in the early 20th century - predicting the emission and absorption characteristics of different atoms. Yes. Atoms in excited states take a short time to decay back to their ground states. We know enough to calculate the average lifetimes of each energy state. Only an average calculation is possible due to quantum uncertainties, again. Black bodies essentially emit at all frequencies. Such sources are "thermalised" and consist of millions of atoms. They are quite different from single atoms.
Reminds me of a question someone recently asked me... ''where is an electron inside the atom.'' I replied ''you can take your choice... either it is no where or everywhere.''
I do like that particular simplification. The mass of the sum of the nucleons is smaller than the sum of their physical constants due to energy lost as the atom formed, I think. Modelling the nuclei as a single particle would effectively spread that loss across all of the individual nuclei for the purpose of modelling frequencies of photons, especially given the uncertainty of the inter-nucleon interactions or oscillations. Does the simplification mean that the nucleus is said to have its own combined wavefunction? I'm sure I can't fully comprehend the complexity but I do appreciate it with vagueness. I am beginning to get the feel for eigenvalue if they are changes in electron energy over the time period during which absorption and emission take place, i.e. they correlate with the photon energies involved? My layman confidence in the correlation between the resulting modelling and reality is probably not as high as yours, but excuse me for even mentioning it because no one has even hinted that we understand reality; and I always consider reality a philosophical topic.
I've wondered about the specifics of that. Given the wave-particle duality of all particles, and the uncertainty, there still are ways to observe either their momentum or their location, but not to know both the momentum and location, if I understand correctly. But what I have wondered about is the science of uncertainty; I understand it to say that particles don't have specific location/momentum in their unobserved "lives". If we can detected the particles individually and confirm either their location or their momentum, is it true that we think that unobserved particles don't have location/momentum, or do I have the wrong impression of uncertainty. Does it really mean that we must just be satisfied with having the probabilities of what the actual locations and momentum are, since they are not knowable, but we know they have those characteristics even though we can't know them? It thought so but didn't know how to phrase it. The time delay seems to me to go hand in hand with the discrete nature of the quantum realm; an impression I got from reading about the process that Planck went through to establish his h ratio. I realize that the way I structured my post did not make that distinction clear. I do question your statement that the blackbodies essentially emit at all frequencies, but I assume you mean that to apply over the full emitted spectrum which does not usually go the the extreme end of the ultraviolet, right? I know that thermalization and blackbodies is different science from the modelling of atoms and photon energies. It is just that my introduction to quantum time delay came from the history of Planck's work and so I tried to use that to tie in the topic of time delay. The "time delay to decay" back to their ground states does make sense, and it leaves me with the question of the particular circumstances of the absorbed photon energy while it is held by the electron. Is it held as kinetic energy that is displayed by the increase in net distance from the nuclei that the electron maintains while it has that energy?
If you can only know either location or momentum, but not both at the same time, why not use two references at the same time, which will overlap. The first will only look at position and the second only at momentum. Then we overlap the two and can know both. The limitation of uncertainty was only set up for one reference at a time, it says nothing about two overlapping references. As an analogy I we have a skilled dancer who does intricate hand and foot movements. If you watch his hand, you can't see his feet well since they look fuzzy to the corner of the eye. If you look at the feet the hands are fuzzy. The solution is to have two judges. If we use a split screen your eyes will need to shift left to right, so you may miss something. Instead will need to overlap the two screens. The uncertainty is an artifact of reference bias using only one relative reference. You need a second judge like the speed of light.
Lol, cute; you must have gotten up early to have had time to come up with that already today. But consider this, if each judge must view the whole dancer in order to detect what either the feet or the hands are doing, and if the dance is so fast that only one judge can look at the dancer before the dance is over, how can two judges help. One has to sit out each dance.
It isn't 'either everywhere or nowhere', the wavefunction has non-zero values in many places but when you actually look at the system you find the electron in a specific location. The fact you don't know where before hand doesn't mean it is nowhere or everywhere. When doing calculations you consider all possible combinations of locations and then sum them up in the appropriate manner but in each term the particles have one and only one location at any moment in time. This is why modelling molecules using quantum mechanics is difficult, in principle you have to consider every possible arrangement of the particles but every calculation has each particle somewhere. The mass of the nuclei is not calculated using binding energies etc, it is done from experiments. Yes, if we started with protons and neutrons we'd have to account for that but we start from nuclei directly. If we could do the necessary calculations we could compute the 'effective model' of the nuclei and construct an approximate wavefunction for the nuclei. Any degrees of freedom internal to the nuclei are ignored. No, the eigenvalues are the energies for a particular configuration. When a photon is absorbed the configuration of the molecule changes and we have a new configuration with a new energy. The energy change will be due to the photon energy. It's the difference between the energy eigenvalues which are the photon energies. These calculations, modelling molecules from first principles, has application in quantum chemistry, plasma physics and nanotechnology.
