
#1
Jan3013, 10:22 AM

P: 246

Everybody says energy is quantized. But for einsteinplank equation
E = h.f If a photon could have any values of f, E would not be quantized I know bohr orbits only accept some frequencies, but hydrogen frequencies are different from lithium or nytrogen frequencies. So what is the MINIMUM value of E? As far as I know, a photon is a quanta of energy, so what would be the quantum? 



#2
Jan3013, 10:27 AM

P: 87

The energy in general can be arbitrary, because you can choose arbitrary frequency. But if you decide to work with one specific frequency f_{chosen}, then h*f_{chosen} is the quantum of that specific frequency.




#3
Jan3013, 10:36 AM

P: 87

Also please note one thing: the fact that only certain photons (with specific energies) can be emitted / absorbed by an atom, is not limiting the possible photon energies. The atomic energy levels are features of these atoms, but electromagnetic field does not care about that. The free em field can have any frequency. It is just that only certain frequencies will be absorbed by atoms, while other photons will not be affected.




#4
Jan3013, 10:50 AM

P: 915

Quantized energy  Photonor is frequency quantized? or does quantization only make sense when in a bounded state at a specific orbital/energy level/shell in an atom? 



#5
Jan3013, 11:22 AM

P: 741

What are the "hydrogen frequencies" of "lithium" and nitrogen? The two definitions for "photon" often give the same final results. There is usually little experimental difference in the photon being a quantum of energy and a photon being a quantum of amplitude. However, there is a shade of difference that occasionally causes confusion especially when one counts photons. One thing that is unclear from introductory courses in quantum mechanics is that the number of particles can be uncertain. The total energy of a wave is often precisely determined even though the frequency is not. Therefore, an uncertainty in photon energy is often manifested as an uncertainty in photon number. "Quantization conditions" are actually constraints on the amplitude of the wave associated with the particle. They don't constrain the frequency of the wave nor do they constrain the energy of each individual photon. So there is no absolute minimum in photon energy. The number density of particles associated with a wave increases with the square of the amplitude of the wave. The total energy is proportional to the number of particles. The number of particles is basically the total energy of the wave divided by the energy of each particle. The total energy of the wave is proportional to the amplitude squared. The EinsteinPlanck equation only determines the energy density for each type of each particle. The EinsteinPlanck equation does not determine the total energy of the wave. I don't fully understand your question, but maybe I partially understand the general confusion. I conjecture that your confusion concerns issues of amplitude and photon number. Does this sound like it could be the problem? 



#6
Jan3013, 01:05 PM

P: 246

But I still have a question. I mentioned the hydrogen, lithium and nitrogen frequencies as the energy levels for these atoms. As there are a finite number of elements in the periodic table, there have to be a finite number of energy levels as well as a finite number of frequencies that can be absorbed or emitted by an atom. So by that I thought frequency was quantized too. But as mpv_plate said, that works only for atoms. And the em field can have any frequency. So here is the question: How can we produce an electromagnetic wave not being by an electron jumping to another electron shell/energy level and emitting a photon? Is there any other method to do that? 



#7
Jan3013, 01:09 PM

P: 87

Frequency is not quantized. You can have any frequency. Bound states tend to be quantized in energy, because they may impose constraints on the possible states. Another example: you can activate a wave in electromagnetic field inside a small metal box. You cannot have any photon (any frequency) in the box, because only specific (discrete) frequencies can fit in the constrained space. 



#8
Jan3013, 01:12 PM

P: 788





#9
Jan3013, 01:26 PM

P: 104





#10
Jan3013, 04:56 PM

P: 741

This is true even in classical mechanics. For instance, the resonant modes of a violin string have discrete frequencies. The boundary conditions of the string cause the wavelengths of the string to change by discrete values. This results in the frequencies changing by discrete values. This discrete division between notes of a stringed instrument have been known since Aristotle. Probably even before Aristotle. Newton understood frequencies of vibrations on strings. However, the separate frequencies on a string were not called quanta. The resonant frequencies of a hydrogen atom are caused by the periodic boundary conditions of the electronwave. In that sense, they are like the waves on a violin string. However, the discrete values of frequency are not the direct result of an ad hoc hypothesis. What is really quantized in a hydrogen atom is radius of the electron's orbit. The radius of the electrons orbit is a type of amplitude. You can think of the radius as the limit of the back and forth motion of the electron. It is this radius, which is a type of amplitude, which is quantized. The discrete values of frequency are an indirect consequence of the fact that the radius is "quantized". The frequencies aren't quantized, but the radii are quantized. You have to be careful about the word quantized. The word is not quite synonymous with discrete. Quantization is a type of discreteness. Maybe the word "digitized would be better. No, I take that back. There are certain qualifications to a digital system. The "quantization" first hypothesized by Planck referred to or The reason that the notes of a violin string are discrete is because the violin string is fixed on both ends. Thus, the violin string has to be "bounded" in order to produce notes. Notes are bounded states! A violin string that isn't tied down does not produce separate notes. A propose that frequencies should never be called quantized. Frequencies are merely discrete. 



#11
Jan3013, 05:38 PM

P: 104

http://www.amacad.org/publications/w...02/wilczek.pdf
see http://www.amacad.org/publications/w...02/wilczek.pdf 



#12
Jan3013, 06:52 PM

P: 741

The BohrSommerfield condition is not a periodic boundary condition for a deformed string. The BohrSommerfeld condition was hypothesized before the de Broglie relationships were hypothesized. Therefore, there was no "wavelength" associated with them. The BohrSommerfeld condition (BSC)as first formulated involved orbitalangular momentum. It was a constraint on the size of the orbits. The word "radius" was perhaps wrong. However, the visual picture was of an electron in a Keplarian orbit around the nucleus. The size of that orbit had nothing to do with wavelength. The frequency of a Keplarian orbit decreases with the size of the orbit. The size of the orbit and Kepler's Laws is what basically determines the frequency. However, the size of the orbit can vary continuously in classical physics. The reason that the frequency does not vary continuously in "old quantum theory" is that the size of the orbit can't vary continuously. BSC was a generalization of the Planck rule for quantization. Planck assumed the atom was a harmonic oscillator. The electron in the atom was just a point charge connected to the nucleus by a type of "spring". The amplitude of this harmonic oscillator was constrained to specific and discrete values which resulted in the energy of the harmonic oscillator being constrained to discrete values. There was no electromagnetic wave and no electron wave. The frequency of the harmonic oscillator was not determined by any boundary condition. The natural frequency of the atom was the square root of the spring constant divided by the mass. De Broglie came up with this "explanation" for the BohrSommerfeld condition where the an integer number of complete cycles had to fit in on the orbit. The de Broglie explanation makes it look a bit like a string. Einstein came up with the idea that the quantization had something to do with particles. In all cases, the quantum constraints act upon the amplitude of a wave not the frequency of the wave. The BohrSomerfeld quantization condition does not determine the frequency of the electromagnetic wave. BSQ applies to the electron, not to the photon. BSQ is not the same as the Einstein condition, E=hf. 



#13
Jan3113, 04:44 AM

P: 104

[itex]\int f_n dt = f_n T = n[/itex], that is [itex]f_n = n / T[/itex] the quantization of the mode with period T, say, in a Black Body radiation is [itex]\int E_n dt = E_n T = h n[/itex], that is [itex]E_n = n h / T[/itex] BSQ can be used to quantize photon, in this case the difference is the bose statistic in the population of the harmonics, and the fact that the photon is a particle with zero mass lambda = c T. The effect of the Coulomb potential of an hydrogen atom is a distortion of the spectrum. In our analogy this correspond to a non homogeneous string 



#14
Jan3113, 06:18 AM

P: 55





#15
Jan3113, 06:39 AM

P: 55





#16
Jan3113, 07:17 AM

Sci Advisor
PF Gold
P: 2,197

All of of these can be directly measured because there are periodic phenomena where the period is set by the the quanta or a fraction thereof. Note that the fact that they are periodic does not stop you from measureing e.g. a charge of 0.2e (which can happen because of screening). In the case of e you have e.g. Coloumb blockade, for resistance the quantized Hall effect and for the magntic flux quanta AharononvBohm rings or (more common) superconducing SQUIDs. 



#17
Jan3113, 08:15 AM

P: 55

Ok, I got it figured out. It's explained here:
http://www.youtube.com/watch?v=B7pACq_xWyw In E=hv that number can only be multiplied by a whole number. So, the equation actually becomes E=nhv. For blue light, for example, the value for hv is about 3. So, only 3, 6, 9, 12 electron volts are allowed for blue light. 



#18
Jan3113, 11:17 AM

Sci Advisor
PF Gold
P: 2,197

Your equation is the equation for e.g. multiphoton excitation of a transition in an atom. 


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